Index of Subjects
Absolute and relative
Leibnizâs understanding of âabsoluteâ and ârelativeâ (or ârespectiveâ) â a certain determined condition providing an absolute effect â a change of determination producing a relative effect
66f., 71, 75, 77, 80, 95, 113, 296, 396, 371, 454, 461, 536f., 649f., 658â662, 673, 680f., 762, 770
Academies
.
see Projects, Scientific, Educational Projects
Acoustics and sound
.
see Physics
Action (âactioâ)
.
see Disputes and Controversies, Natural Philosophy
Administration (government and administration)
142, 188f., 394, 406, 408
Aerzen, Location in the Weser Uplands (âWeserberglandâ)
161, 809f.
Agriculture (Tillage and cultivation of land)
828
Alchemy, Alchemists, Alchemical writings
.
Chemistry
Alchemical chrysopoeia (transmutation of base metals)
208f., 220, 889, 898
Artificial production of gold
215, 341
Alchemical records
224f., 839f.
Alchemical symbols
339, 341, 417, 489, 612, 731
Alchemical information from mythology â legend of âThe Golden Boughâ (Virgil) â Byzantine/ Egyptian writings â terminology of the ancients
223f, 837f.
Arab/ Arabic writers
217
Early-modern alchemy, alchemists, alchemical writings
The denigration of alchemy
xi
The philosopherâs stone â a mythical alchemical substance
185, 220, 318, 342
Basilius Valentinusâ quintessence â his works considered feigned but outstanding (Leibniz) â noteworthy for their concrete character
224, 838
Boyleâs interest in alchemy â his fascination with alchemy and magic â in conflict with his rational thinking
219f.
Bodenhausenâs notes on processes / transmutations â his alchemical records â Blockâs encryption (1699) â secret-key encryption
224f., 839f.
Crafftâs belief (1681â82) in the existence of very remarkable things in nature â his example of a mysterious fluid (a non-wetting water)
215f., 341f.
His skeptical atitude to the presentation of an alleged transmutation at the Court in Hanover (1681) â Leibnizâs enquiries and skepticism
216, 342
Glauberâs alchemistic thought
215, 222f., 340f., 836f., 890
Leibniz and alchemy â his early interest in alchemy â his stay in Nuremberg (1667) and his role as secretary of an alchemical society there
xii, 220, 721, 829, 889
His discussions with Crafft, Scheffer (1681â83) regarding chemical processes for obtaining â gold and silver from tin â silver from lead
215, 341
His intensive study of alchemistic writings
221, 831, 890
His contacts with renowned individuals thereafter â like the Elector of Mainz (von Schönborn)
221, 831f., 890
His knowledge of European alchemists â such as von Chaos, Flamel, Keller, Lull, Seyler
220, 721f., 889
His recollection (1696) of the demise of the practitioner J. J. Becher (1682)
220, 722
His remarks regarding Kleinert (1696)
721, 889
His call for circumspection regarding alchemy â Blockâs corresponding skepticism and admonition regarding alchemy (1698)
220, 722f., 808, 889
His visitations to laboratories
221, 832, 890
His fundamental belief in the concept of a transmutation (1699)
221, 830f., 889
His skepticism about a successful experimental outcome â his comparison with miracles or the work of fantasizing sorcerers â his failure to witness a credible transmutation â his encounters with a series of impostors â his views regarding the near-impossibility of a transmutation, and a corresponding intimate connection with the maintenance of a world order
220f., 830â832, 889f.
His belief in the possibility of a particular or singular transmutation process
221, 831f.
His correspondents and alchemy Moller of Hamburg â his view (1699) regarding adepts and their secret mode of operation
221, 832
Mollerâs acquaintance in Hamburg and his survival as a âcapitalistâ but not as chemist â his example of an adept, who had moved to Hamburg from Brandenburg
221, 833
Leibnizâs approach to Moller regarding Brandâs process for metal ennoblement
221f., 833f.
Mollerâs opinion regarding Brand as a braggart who had come far, but was not really the discoverer of phosphorus â his living in poverty and inability to finance laboratory work â his lacking of universal knowledge
222, 833f.
Mollerâs reference to an acquaintance with a very lucrative particular / singular process
221f., 834
Newtonâs interest in alchemy â his laboratory experiments and study of alchemical texts and the language of alchemy â his understanding of alchemy as a code to be deciphered â a basis for laboratory applications, like the decomposition (transmutation) of metals and the making of gold
219
Pseudonyms and the pseudonymous identities of alchemical authors like Philalethes / Starkey â his alchemical number puzzle
224f., 838
Sendivogius filiusâ/ Johann Harprechtâs âLucerna salis philosophorumâ (1658)
224, 839
Synonymity with Johann Hiskia Cardilucius â as revealed (to Block) by Leibniz (1699/1700)
224, 839f.
The pseudonym of Becher âSolinus Salzthal Regiomontanusâ
224f., 839f.
The scientific pedigree of such authors
224, 838
Alexandria â Astronomers of Alexandria
117, 791
Algebra
.
see Mathematics
Altdorf â University of Altdorf
701f.
America
3, 195, 248â250, 423, 596
American alchemists
224f.
American colonies
190, 408f.
American physicians
224f.
Latin America
319
North America
186, 321
South America
194, 594, 605â607
Brazil â Pisoâs natural history (1648)
605f.
Paraguay
250, 607â610
Peru
248, 250, 422, 605â609
Analysis, analytical
.
see Mathematics Chemistry
Anatomy
.
see Medicine
Anglo-Saxon
.
see England
Apothecary (or Pharmacy)
.
see Medicine
Arachnology
.
see Biology
Archaeology â that of Ramazziniâs âDe fontiumâ (1691) and its influence on Leibniz
164
Architecture
.
see Civil Engineering
Arithmetic
.
see Mathematics
Arms and armor
xi
Arnstein
11, 508
Astrology
118, 207, 220, 793, 826, 830f., 898
Astrology in calendar reform
.
see Calendar
Judicial astrology (âastrologia judiciariaâ) â a form of astrological soothsaying â absolutely contrary to reason â derided by renowned astronomers like Cassini, Huygens, Hevelius â its outright rejection (1699) by Leibniz â his proposal to counteract claims of astrologists by statistical experiment
221, 830f., 898
Meteorological astrology (âastrologia meteorologicaâ)
207, 826
Astronomy
Astronomical truth
114, 117, 783, 790f.
Calendar Reform
Geocentric (Terracentric) world picture
118, 793
Heliocentric astronomy â Copernican-Galilean heliocentrism
xiv
Heliocentric world picture â confirmation
118f. 793, 796
Astronomical observatories
120, 204, 265, 381, 799, 818, 822
Celestial appearances
112, 551
Celestial mechanics
102, 104f., 111, 299, 365f., 369, 539, 550, 875.
Physics, Mechanics
Celestial motions â causes of celestial motions
21, 103, 366, 431, 462, 643
Leibnizâs theory of the causes of celestial motions, in his âTentamenâ (1689)
103â106, 121, 366â368, 376, 431, 462, 464, 466, 643, 875
Comets
102, 106f., 111f., 229, 299f., 365, 370, 381, 464f., 548f., 551f., 725, 876f.
The nature and motion of comets â the tails of comets, being observed to be confined to the plane of motion around the sun, were either of a real or material nature (Newton, Fatio), or an optical phenomenon, and of an affected or emphatic nature (Leibniz)
106f., 111, 370, 465, 548f., 551, 876f.
The comet of 1664
102, 300
The comet of 1680
102, 299
The comet of 1682 (Halleyâs comet)
102, 299
The comet of 1683
102, 365
Newtonâs theory of cometary tails
106, 370
The role of comets in earth history (1696)
.
see Geology
Moon â the moon and lunar astronomy
Lunar motion â lack of a satisfactory mathematical description (1701) â call for verification by observation â theory of Newton (1702)
118, 541, 790, 794f.
Lunar phases
207, 826
Planets â the sun and planets of the solar system
107, 109, 111, 463, 465, 542, 548, 550, 876
Solar eclipses â that of 1684
102, 365, 788
Sun spots
107, 465, 547
Planetary motion â mathematical and dynamical theory based on:
Circular planetary paths of the ancients
81, 763
Ellipses (Keplerian ellipses)
81, 119, 464, 763, 794f.
Ovals (Cassiniâs theory)
119, 794f.
Mechanical causes of the ellipses / ovals
795
Planetaria, planetary machines
102, 299
Planets
Jupiter (and moons) â its postulated elliptical figure (Leibniz, Newton)
105, 339, 369, 466
Saturn (and moons)
105, 339, 369
Planetary astronomy â dynamics of planetary orbits
Planetary motions â cause of planetary motions
102, 111, 462f., 548, 861, 876f., 894
Cartesian vortices
369, 463, 894
Supposition of a course ether vortex â a rotating ether vortex around the sun
58, 87, 102f., 105â107, 111f., 366, 369, 458, 462â464, 545â550, 552, 646, 874â877
Curl / vorticity
167, 482
A transporting fluid (âfluidum deferensâ)
106, 548â550, 875, 894
Circular motion (âcirculatio harmonicaâ)
103, 109, 144, 366, 391, 463, 542f., 548f., 567, 875f., 879
Rotational velocity
103, 366, 875
Radial motion (âmotus paracentricusâ)
103, 366, 463, 875
Centrifugal force (gravity)
81, 91, 103, 106, 109f., 111, 366, 369, 383, 463, 542f., 545, 549f., 762, 875f.
Moons of Jupiter and Saturn â similar explanation of their motions
105, 369, 876
Newtonâs theory of planetary motions â based exclusively on gravitation
109, 540
Newtonâs argument against vortices
87, 111, 549, 874, 877
Huygensâ explanation of gravity
106f., 109â111, 113, 369, 371f., 463, 545f., 875
Huygensâ Discours de la cause de la pesanteur (1690)
57, 109, 111, 113, 371, 451, 462, 541
Planetary paths
Circular paths of the ancients
81, 763
Keplerian ellipses
81, 119, 464, 763, 794f.
Keplerâs three laws of planetary motions
His first, and second law (law of equal areas)
103f., 366, 463, 875
His third law (of 1618)
104, 106, 370
Keplerâs adumbration of the cause of gravity
103, 366
Leibnizâs physical explanation of Keplerâs laws
103f., 366, 463, 875
Other mathematical planetary path constructions â circles, epicycloids, parabolas, polygons
103, 366
Stellar astronomy
Aberration of light â observations (Hooke, Bradley)
119
Parallax of the fixed stars â early search for stellar parallax â Hookeâs observations (1674) â Flamsteedâs observations (1698) â Wallisâ announcement to Leibniz (1699) â Leibnizâs view (1699) of the non-crucial nature of a verification (based on parallax) of the heliocentric world view â Leibnizâs desire for verification (1701) through more accurate observations
119, 796f., 799
Other suns â parhelia or mock suns â Huygensâ work on parhelia
107, 465
Terra (the Earth)
Tides â nature of ebb and flow â Huygensâ and Newtonâs explanations
106, 370
Terrestrial and extraterrestrial or outer space â empty space without gravity or resistance
71, 74, 109, 114, 372, 541, 544, 550, 554, 662â665, 876
Attitudes â partisan mentality (camp thinking)
72, 663f.
Augsburg
.
see Bavaria
Austria
Linz, Linzer Hofgasse (Alleyway)
104
Vienna
6, 8f., 14, 23, 58, 103, 141, 184â187, 189, 200, 218, 220, 257, 275, 316, 320, 352, 354, 357f., 366, 394, 408, 418, 433, 458, 462, 499, 562, 722, 736f., 745, 865, 888f.
The Holy Roman Empire
Battle / Siege of Vienna (1683) â Defeat of the Turks
189, 408
Council of the Empire
14, 745
Imperial Aulic Council
14, 745
(Privy) counsellors at the Imperial Court
6, 276
Imperial Librarian
6, 275f.
Imperial Treasury
220, 722, 889
Ballistae, ballistics, the Science of ballistics
.
see Physics
Barbarian invasions / migrations
10, 430, 828.
Peoples and Languages
Barometer
.
see Instruments
Bavaria
Augsburg
9, 357, 368
Munich
8, 357
Berlin, Berlin-Brandenburg, Brandenburg-Prussia
Berlin
11, 14, 49f., 116, 120, 130, 183, 187, 206â208, 214, 257, 262f., 304, 315, 322, 339, 353f., 507, 605, 702, 745, 756, 782, 785, 799, 807, 818, 825
Brandenburg Court â promotion of science by the Court
11, 183, 204, 315, 354, 507, 820f.
Berlin Society of Sciences (âBerliner Sozietät der Wissenschaftenâ)
14, 44, 47, 115, 120, 203â208, 262, 745f., 752, 784, 799, 807, 818â821, 825, 827f., 858
Astronomical observatory in Berlin (1700)
114, 120
Acquisition of quality astronomical instruments â advocated by Leibniz â a 12/20 foot telescope
120, 799
Proposals for the building and equipment of the observatory â with location the roof of a new pavilion to accommodate instruments â intended for the purpose of utility rather than pomp
120, 799
Rømerâs recommendation for the construction of a meridian circle of his design
120, 799
Leibnizâs (and Wagnerâs) consultations and enquiries â regarding other observatories and buildings, in Jena, Nuremberg, Zeitz
120, 800
Bible â biblical and scriptural references
.
see Religion
Binary mathematics
.
see Mathematics, Numbers
Biography (Leibniz)
Autobiographical self-characterization
xvi, 863, 899
Character traits (Leibniz, Huygens)
24, 449f.
Personal relationships (Leibniz, Boyle, et al.)
288â291
Leibnizâs biographical milestones
Sojourn in Paris (March 1672 to October 1676)
ix, 15, 19, 21, 57, 168, 265, 272, 279, 359, 431, 460, 579f., 646, 739, 896
First London visit (January-February 1673)
168, 179, 209, 329, 490, 579f., 585
Second London visit (October 18â29, 1676)
28f., 517, 519
Visit to Amsterdam and Dutch tour (November 1676) â meeting with Leeuwenhoek in Delft
128f, 131, 241, 301f., 474, 849
First years in Hanover (from late December 1676)
ix, 2, 15, 18, 87, 129, 208, 279, 287, 302, 328, 358, 863
His activities in the Harz mining district (1680s, 1690s)
1, 4f., 11, 133â136, 138f., 142â144, 146, 148, 151, 154, 162, 169, 187, 191, 225â227, 256, 273, 275, 277, 299, 307â313, 321, 342, 344, 356f., 384, 386f., 394, 396, 399, 419f., 428, 508, 565f., 591, 686, 699, 800, 813, 827, 857, 878f., 890â892
His appointment as Court Counselor and Librarian
4, 273
Grand tour of Germany, Austria and Italy (1687â1690) â meetings with mathematicians, scientists in Italy (1689/90) â stay in Rome (April to November 1689)
2, 7f., 21, 54, 58, 102â104, 131, 141f., 163, 200, 220, 263, 356f., 366, 370, 394, 424, 431, 456, 458, 462, 466, 473, 476, 499, 722, 882, 889
Director of the Ducal Library in Wolfenbüttel (1690)
7, 11, 297, 356, 508
Work on sources for international law â publication of the âCodex juris gentium diplomaticusâ (1693)
9, 427
Journey to Holland (November 1694)
11, 194, 196, 508, 592, 716, 719
Effort to move to the Berlin Court (mid 1690s)
11, 507
Privy Counselor of Justice in Hanover (1696)
11, 13
Foreign member of the Académie des Science (1699)
7, 14, 277f., 745
First President of the Berlin Society of Sciences (1700) â extended stays in Berlin (MayâAugust 1700, October 1701âJanuary 1702)
14, 745
Secretive journeys to Vienna (Last months of 1700 and May-June 1701)
14, 745
His admittance to the Court Council of the Empire (âReichskammergerichtâ) and the Aulic Council (âReichshofratâ)
14, 745
His mathematical maturity
ix, xii
His research assistants or associates
9, 13f., 49, 51, 139, 312, 358, 363, 387, 619, 744, 756, 880, 886
His life and death
ix, 28, 241, 251f., 517, 849
His health
.
see Medicine
His literary estate (âNachlaÃâ) and its repository
xvii, 1
Biology, Life Sciences
Theoretical biology â classification of plants â criteria
239, 846
Practical biology and medical practice
239, 846
Living, animate beings
139f., 232, 234, 239, 302, 304, 379f., 728, 846
Inanimate systems
232
Meaning and diversity of life â organicists, physicalists, vitalists
232f.
Vitalism, vitalism beyond mechanism, vital force, vital spirit
233, 240, 422, 893
The characteristics of living organisms â binding and releasing of energy â growth and differentiation â perception and sense organs â self-replication, reproduction â self-regulation and response to stimuli
232f.
Biological thought and concepts
Anatomy
235, 237, 239, 242â247, 253, 265, 345â347, 559, 601, 723, 730f., 734, 739f., 845â847, 850â853, 893f., 896
Anatomy â the science dealing with the structure of plants, animals, the human body (Gakenholz, 1701)
247, 851
Classification â science of classification of species â pre-Linnaean classification
232, 237â239, 844â847
Diseases â animal and plant diseases
259, 502
Evolution (evolutionary biology) â diversity and inheritance â origins without evolution â medieval thought on evolution â pre-Darwinian evolution
232f., 239, 846, 862, 894
Fossils, fossilized creatures, fish, plants
141f., 226â228, 231, 343f., 384, 419, 421, 730, 891
Mineral ore containing fossilized plants â received from Heyn in Leipzig (June 1690)
141f., 394, 421, 891
Precious minerals (gold, silver) and coral â received from Trondheim, Norway (1697)
236, 731
Organisms
130, 232f., 380
Animals. see Zoology
Genetics
230
Plants. see Botany
Physiology
4, 239, 242, 246, 266, 742
Reproduction â sexual reproduction
232f., 239f., 243, 347, 846â848, 893â895
Harveyâs âExercitationesâ (1651)
234, 727
Theory of preformation (preformationism)
130, 234, 240f., 379, 727, 849
Swammerdamâs theory (1672)
131, 347, 380f.
Leeuwenhoekâs theory (1677/78) â the animalculist (spermist) theory â human / mammalian sperm, its nature and production â the entire organism is pre-formed in animalcula, or little animals â the process of fertilization or nurturing of the animalcula
129f., 234, 240f., 302â305, 379, 726â728, 848f., 894f.
Leeuwenhoekâs discovery (1677) of animalcula, in mammalian sperm
129f., 234, 379
Leeuwenhoekâs âObservationesâ (1677â78) â philosophical interpretation â the Leibniz-Arnauld correspondence (1686/87). see Philosophy
Listerâs objection (1697) in the âPhilosophical Transactionsâ (1698)
234, 727
Parallels drawn by Joh. Bernoulli (1698) to the infinite and infinitely small in mathematics â the coexistence of lines and surfaces, surfaces and bodies â differentials and integrals
234, 727
Bernoulliâs conception of a world (micro-cosmos) of little animals â Leeuwenhoekâs world of animalcula with a further micro-cosmos within it â a micro-cosmos with a sun and fixed stars, having planets with satellites or moons â an earth with mountains, cliffs, fields, woods, rivers, lakes, seas, living animals
234, 728
The ovist (ovulist) theory of preformation â the entire organism pre-formed in eggs
234, 240, 727, 848, 894
The process of fertilization â the fecundation of the eggs by the seeds â unfolding or de-convolving of the offspring â role of a spirit or vital force in the fertilization process
130, 240, 379, 848, 893f.
Evidence of a connection between the vegetable and animal realms â direction of the male seed to the female egg in both plants and animals â transformation and development of the seed or egg through nourishment on fertile ground â generation and production of a plant or foetus â upgrading of the male sex and downgrading of the female sex
232f., 240f., 848f., 893f.
Dispute between animalculists and ovists / ovulists
234, 240, 727, 848, 894
Leibnizâs vision (1701) of a possible reconciliation of the positions â his own position being close to that of the animalculist Leeuwenhoek and removed from that of the ovist Kerckring â his views on preformation (after 1701) as expressed in his philosophical works â his penchant for Leeuwenhoekâs theory, with the enhancement of the male sex, and the corresponding degradation of the female sex
240f., 848f.
Leibnizâs correspondence with Leeuwenhoek (1715â16)
241, 848
Respiration
239, 489, 585, 846f., 894
Skeletons
235, 729
Taxonomy. see Classification
Biological (Botanical, zoological) experiments. Experiments
Waldschmidtâs experiments (1687) with a vacuum flask-vacuum pump apparatus â with plant leaves placed inside the apparatus, and with the roots remaining in open air â water and sap were drawn from the roots, through the meatus to the leaves â reverse experiment (roots inside the apparatus) with a null result
233, 422
Waldschmidtâs explanation â based on the operation of valves in the vessels of the plants
422
Leibniz alternative explanation â based on the operation of inflected fibers in the vessels
422
Waldschmidtâs canine experiment â on the blood circulation of a dog â pumping air through a small fine tube into a vein of the animal, resulting in its sudden death
233, 422
Waldschmidtâs bell mouth tube â a âspeaking trumpetâ or acoustic horn â voice transmission over a quarter to half a mile
233, 422
Biological instruments. Instruments
Semen observed under the microscope â animalcula in water permeated with pepper (Leeuwenhoek)
129f., 234, 302â305, 379f., 728
Botany, Botanists
Descartes (Cartesian botany)
238
Stisserâs botanical interests
His botanical-medical garden in Helmstedt (1692)
235, 729
His opus âBotanica Curiosaâ (1697)
235, 729
Rumpf, Moluccan botanist â Consul / merchant of the island Ambon
His âDe Caryophyllis Regis Ambonicisâ (1697â1698)
236, 732f.
His planned multi-volume botanical opus â the first part lost in a shipwreck (1692)
236f., 733
His opus âHerbarium Amboinenseâ (1741â50)
237, 733
Botanical reproduction â sexual reproduction of plants â Camerariusâ âEpistolaâ (1694)
240, 847, 893f.
Burckhardâs meeting with Leibniz (February 1701) â his reference to Camerariusâ âEpistolaâ
893f.
Burckhardâs outline of the sexual organs of plants â the phenomena of monoecy and dioecy â monoecious and dioecious plants
240, 847f.
Leibnizâs letter to Gakenholz (April, 1701) â consideration of reproduction processes in animals and plants â a connecting element between the animal and vegetable kingdoms
240, 848
Correspondence of mammalian sperm to the pollen of seed-producing / flowering plants
848, 894
Correspondence of the style of a flower to the vagina in a placental mammal
240, 848, 893f.
Correspondence of the ovary at the bottom of a style to a mammalian ovary
240, 848, 893f.
Process of fertilization involving plant ovaries or eggs, pollen grains or seeds
848, 893f.
A vital force in the living organism coming from the pollen, penetrating the ovary, and resulting in the fecundation of either the eggs or the seeds
240, 848, 893f.
Flowers, fruit, fruit-trees, fruit-walls
45, 163, 195, 237f, 251, 596, 712f., 747, 844f.
Botanical (plant) species
Algae, coral, coral algae
236, 731
Arrowwood (viburnum)
204, 818
Litophyton marine soft coral, received from Trondheim, Norway (1697)
731
Cypress
204, 818
Musk plant
236, 732
Rootstocks (rhizomes)
733
Wormseed â Levant wormseed (âsemen sanctumâ)
236, 732
Wormwood (Southernwood or southern wormwood) â Persian flowering plants âartemisia abrotanumââ Cleyerâs and De Jagerâs investigation (1684)
236, 732f.
Botanical (plant) taxonomy â development of a taxonomy, or classification system â classification of plants according to certain criteria â Gakenholzâs discussion with Leibniz (March 1701)
237, 844
Leibniz proposal for a consideration of roots as the basis for plant classification
237, 844
Gakenholzâs open letter to Leibniz (April 1701) â proposal for development of a classification system based on parts of plants such as flowers, fruit, seeds or roots
237, 844
Gakenholzâs complaints about a prevailing orientation towards antiquity â a lack of comparison with the real world â a lack of suitability here for a general use of methods striving for mathematical exactness
237, 844f.
Gakenholzâs thoughts on a variety of established classification systems â based on fruit, seeds, flowers â requiring long-term observation
237, 844f.
Leibnizâs adherence to a classification based on roots â advantage of constant availability / accessibility â disadvantage of lacking sufficient variations, and unsuitability as a sole classification characteristic
237, 844f.
Leibnizâs thoughts on plant classification (April 1701) â insufficiency of classification by a single criterion â appropriateness of combinatorics. see Combinatorics
Relevance for development of botanical systematics â analogy with 16th /17th century Ramist geometry. see Mathematics, Geometry
Organic bodies as machines (machine-like entities). see Machines
Descartes views on the mechanical life of plants
238
Blockâs comparison (1698) of the human body to a closed machine â like a clock, which one could not correct without opening it up, and risking its destruction
264, 738
Plants, animals, humans viewed as machines adapted for certain tasks
239, 846
Plants as machines of nature â their internal structures (inner workings)
238f., 845
Humans were adapted for contemplation, plants and animals adapted for helping humans in fulfilling such tasks â the challenge to explain such tasks, and the mechanisms involved in their realization
239, 846
Leibnizâs understanding of organic bodies as machines for the fulfillment of certain tasks, duties and functions â like nutrition and reproduction, and preservation and perpetuation of knowledge
238f., 846
Leibnizâs long-standing interest in prehistoric creatures, or the animate beings of earlier epochs. see Geology
The science of these prehistoric creatures â Leibnizâs letter to Gakenholz (April 1701), with concepts of comparative anatomy â comparison of animals (âcollatio animaliumâ) â concepts of reproductive biology â developmental and evolutionary biology â a connection of plants and animals based on respiration â respiratory organs (lungs) â a continuity of plant and animal realms with transition from plants to animals through intermediaries like insects â Swammerdamâs âInsectaâ (1669)
239, 846f., 894f.
Zoology
Animal behavior (Ethology) â example of tigers, the âtiger animalâ (âpanthera tigrisâ) â its aggressive-assault behavior â energy efficiency practices
xvi, 4, 236, 731, 862f., 899
Animal reproduction
240, 243, 347, 846, 848, 894f.
Animalcula, Larva or ghost (necromancy)
303, 420
Arachnology, arachnologist, arachnids
249
Mole (talpa) â anatomy of the mole â sexual organs of the mole
243, 346f.
Mussels (bivalve shellfish) â mussels from Jakarta
248, 351f.
Protozoology â Leeuwenhoek seen as father of protozoology and bacteriology
234
Rare fish species â dissection (Mariotte, 1680)
198, 324
Zoology and Leibniz â his interest in the anatomy of large mammals
235, 723
Study of the skeletons of dead or extinct animals
235, 729
Elephant-like creature found in Thuringia (1696) â its cranium or skull â excavation of bones at Gräfentonna (Tonna) â report of the âCollegium Medicumâ in Gotha
235, 729f., 846
Skeleton of an elephant in Florence
235, 729f.
Mullenâs dissection of an elephant (Dublin, 1681) â his âAnatomical accountâ (1681) â the cranium or skull of the elephant
235, 729â731
Mullenâs anatomical observations concerning the eyes and ears of animals (1682), the eyes of fowl and fish, the ears of fowl
235, 729â731
Mullenâs comparison of the organs of animals and humans
235, 731
Rayâs âSynopsis methodicaâ (1693), regarding quadrupeds and serpents
235, 730
Hunting of whales â a whalebone or baleen whale â parts received from Trondheim (1697) â its mandible or lower jaw (Fischbein) â its remarkable penis
236, 731
Import of exotic animals, of which specimens included
Civets â a large spotted civet cat
236, 731
Monkeys â a long-tailed monkey
236, 731
Squirrels â a brown squirrel (from East India)
236, 731
Bohemia
Graupen (Krupka)
8, 188f., 216f., 357, 413f.
Prague
257, 352
Brandenburg. see Berlin, Berlin-Brandenburg, Brandenburg-Prussia
Brandy distillation Project. see Economics
Bremen
447
Breslau
498
Bruchsal
414
Brunswick-Wolfenbüttel (principality) â courts in Wolfenbüttel and Celle
8, 11, 14, 196, 212, 247, 315, 318, 337, 350, 354, 356, 508, 718, 745
Brunswick (town and duchy)
6, 10â12, 186, 275, 321, 356, 428, 508
Calculating machines. see Machines
Calculus, infinitesimal calculus. see Mathematics
Calendar â Calendar reform. Churches, Synods
Old and new styles
2, 114, 116, 331, 515, 591, 729, 782, 786f.
Unification of calendars
115, 785
Leibnizâs vision for the Protestant calendar reform â as political lobbyist for acceptance of the reform â his efforts abroad for the Protestant calendar reform â his letter to Rømer (1700)
14, 114â118, 202, 206, 745, 782f., 786f., 790f., 823
Civil calendar â astronomically-exact fixing of the civil year â possible uncoupling from the ecclesiastical year
114â117, 783â789
Ecclesiastical calendar â moveable and immoveable feasts
114â117, 783, 788f.
Anglican rules and tables, in the âBook of Common Prayerâ (1662) â mistake in the rule for Easter (Wallis) â corrected in astronomical tables
114f., 117f., 782â784, 788â793
Leibnizâs advocacy of achieving agreement between civil and ecclesiastical calendars
114, 783
Gregorian (new-style) calendar â Gregorian reform â Gregorian Easter calculation â Gregorian lunisolar calendar â Papal Calendar Congregation
2f., 114â118, 782â790
Leibnizâs aim to achieve agreement of the Gregorian Easter calculation with astronomical truth
114, 117, 783, 790f.
His appeal to the Académie des Sciences (1700)
117f., 783, 787, 791, 793f.
His contact with the Vatican (through Cassini) â the Papal Calendar Congregation
114â116, 783â786
The Protestant adoption / rejection of the Gregorian calendar
Dutch provinces
Friesland, Groningen (1700â1701)
116, 787
German Protestant states (September 23 / October 3, 1699)
114, 782f.
English rejection of Protestant calendar reform
Confessional and theological antagonism â anti-Catholic sentiment (John Wallis)
116
The Julian (old-style) calendar â the Julian Easter calculation
2, 114, 117, 782f., 787â789
Wallisâ purported rectification with ease of â the equinox calculations â other inequalities of motion
788f.
Technicalities of the Easter calculation
Moveable and immoveable feasts â date of moveable feast of Easter â Easter calculation
114, 117, 783, 788f.
Date-determinations of equinoxes â autumnal and vernal (or Spring) equinox
114f., 117, 783f., 788f., 791f.
Anticipation of the equinoxes â use of date and of date-after the equinox â discrepancy of c. three days in four hundred years
788f.
Full moon â date-determinations of full moons â use of date (Sunday), and of date after (Sunday after full moon)
114f., 783f.
Solar and lunar cycles â solar year â midpoint equation of the sun â unpublished results (Flamsteed, Newton)
114â118, 783, 785f., 793f.
Years, and leap years â rearrangement of leap years â inter-calendrical modus (Reyher /Tiede, 1701)
116, 785
Issues of controversy
The use of â true or average movementâ right ascension and declination â longitude and latitude
118, 793
Heliocentric or geocentric positions
118f., 793, 796
Astronomical tables for calendar calculation
Keplerâs tables â âRudolphine tablesâ (1627) â founded on erroneous observations â deviations of equinox calculations from later more exact calculations â vernal equinox three hours premature â autumnal equinox delayed by three hours
114, 117f., 783, 788, 792f.
Streeteâs tables (1661 and 1674)
117, 788
Flamsteedâs tables (1680)
117, 788
Juniusâ tables (1699) â his project for more exact tables based on ephemerides â his exchanges with Cassini and Rømer â differences regarding the inadequacy of Keplerâs tables
115f., 117f., 785, 792f.
Astrology in the calendar reform â possible inclusion / exclusion of aspects appropriate for astrology â abuse of / by astrology
118, 207, 793, 826
Wallisâ preference for the use of English-language tables
118, 793
Later (then unpublished) observations
The observations of Newton and Flamsteed on solar and lunar motions â considered (by Wallis) to be more accurate than previously printed tables in English
118, 793
Summary by Newton / Flamsteed â sent to Leibniz and forwarded by him to others in Germany and France
793
Lobbying by Leibniz (1700) in political circles for acceptance of the calendar reform â based on astronomical truth and on reason and rationality
117, 790
Benefits of public (Royal) authority support â in England, like in China
117, 790f.
Leibnizâs call for a transnational and inter-confessional exchange
117, 792
Canada â demographics and possible relocation of peoples â possible settlement of black Africans in Canada
186, 321
: Slavery, Slave Trade
Cartesianism. see Controversies and Disputes, Natural Philosophy
Celle (principality of Brunswick-Wolfenbüttel) â the court
6, 10f., 152, 183, 185, 196, 212, 247, 275, 315, 318, 337, 350, 354, 401, 428, 508, 718
Celtic, Celticization (Celticisation). see Peoples and Languages
Chemistry. Alchemy
Acids â strong acids
Aqua fortis, spirit of niter, saltpeter acid (nitric acid)
122, 163, 217, 378, 413, 711
Oil of vitriol (sulfuric acid)
163, 613, 711
Spirit of salt (hydrochloric acid)
163, 711f., 836
Acids â weak acids
Lemon juice
251, 611
Sprit of ammonia
612
Vitriol driblets (drops of vitriol)
251, 612f.
Urine / Uric acid
611
Advancement of chemistry â through a combination of method and experiment â Leibnizâs suggestion to Stisser (1699) â longing (Stisser) for a consolidation of chemistry through meticulous experimental examination
222, 835
Analytical chemistry
216, 862, 888
Antimony. Mercury, Cinnabar of antimony
âRegulus of antimonyââ metallic antimony reduced from its ore
218, 417
Art of chemistry (Chemistry as an art) â characterization as the oldest of the arts (Stisser, 1700)
223, 837
Leibnizâs understanding of the tradition of alchemy / chemistry from ancient times. see : Alchemy / Alchemists in history
Chemical knowledge in antiquity
223, 837
Advancement / Consolidation of chemistry
222, 835
Experimental chemistry (chemical experiments)
6, 213, 217f., 275, 412, 415, 417
Foundations of chemistry
222, 722, 738, 835, 889
Postulated chemical principles â often more melodious than veritable
222, 835
Arsenic
160, 252, 740f., 808
Regarding use as an antipyretic. see Medicine, Bloodletting
Atoms, chemical atoms
223
Atomism. Corpuscles, Corpuscular philosophy
Borax
160, 808
Chemical interactions
Starting substances, or elements â their imbuement with subtle particles â veiling / unveiling of chemical substances
223, 836, 890
Chemical maturation (âmaturatioâ)
219, 418, 888
Chemical revivification, resuscitation â animation, transanimation
223, 836, 890
Chemical transmutation (âtransmutatioâ) â an element transformed into another element
209, 216, 218â224, 328, 342, 412, 418, 721, 830â839, 888â890, 898
Quest for such transformations. Metals
Chemical transplantation (âtransplantatioâ) â substances exchanged in a chemical interaction, reaction or process â a single âelementâ might be common to two other starting substances â veiling / unveiling of substances in reactions â products of interactions, reactions or processes might be contained as subtle particles in the starting substances
217, 222f., 241, 415, 836, 888, 890
Process environments â elements might possibly alter their form depending on the environments
223, 836, 890
Chemical laboratories
Boyleâs chemical laboratory (Pall Mall, London / City of Westminster)
213, 411
Establishment of a chemical laboratory in Hanover â under the directorship of Pratisius (1690)
218, 416
Stisserâs chemical laboratory in Helmstedt â his âActorum laboratorii chemiciâ (1698)
219, 721
Other laboratories. see Laboratories
Chemical / alchemical literature
215, 219, 340
Chemical processes
Trial of a process in Copenhagen (Elers, 1684) â involving the reduction of gold powder in aqua fortis (nitric acid) â initial success and ultimate failure
216f., 413f.
Chemical visions â including chimeras, daydreams, fantasies, illusions
99, 110, 133, 545, 720, 722, 776, 830f., 878, 889
Chemical / process engineering â processes carried out in open air â of particular practical importance with the supply of air providing improvement in the effectivity of fire
162, 706, 709f.
Distillation
Distillation in antiquity
223, 837
Distillation of sulfur â Papinâs new process (1697) â with six (or more) alembics or retorts in series and the final outlet into the open air â production of liquefied gases â liquefied spirit of sulfur, or oil of sulfur â greatest quantity in final retort â complete liquefaction without fumes escaping into the air
162f., 710f.
Combustible materials â insights into chemical processes
163, 711
Condensation of flue gases â greater in cold rather than heat
710
Phase Transition (Sublimation) â flowers of niter purified by sublimation â sublimation of mercury
163, 218, 416, 711
Production of strong acids â extraction or production of sulfuric acid
163, 711
Medicinal Chemistry
Effervescence and fermentation
100, 615f.
Importance of spirits of sulfur for chemistry and medicine â as a remedy for scurvy
162f.
Conservation of foodstuffs
Conservation in kitchens and at sea â providing fresh meat and water free of contamination
162, 709, 712
Techniques for the conservation of foodstuffs (1697/98) â conservation fluids using spirit of sulfur diluted with water
162f., 613, 709, 712
Papinâs conservation of fruit and vegetables â apples, pears, plums, raspberries â his conservation of meat and fish â associated medical benefits
163, 712f.
Chemical research
215, 341
Chemical substances and economic utilization. see Projects
Chemists. Alchemy, Alchemists
Chemists
149, 214, 221, 267, 337, 339, 400, 804, 831f., 859f., 889f.
Iatrochemists (chemical physicians)
259, 500
Misochemists (âmisochemiciâ) â those hostile to chemistry
256, 852
Cinnabar. see Mercury
Corpuscles, corpuscular philosophy, corpuscular light rays. see Physics
Corpuscular matter theories â Boyleâs theory â Newtonâs theory
123, 208f., 223, 554
Gold. Metals
Ennoblement of base metals â transmutation of base metals into gold (Chrysopoeia). Alchemy,
Alchemical chrysopoeia
191, 208, 221, 328, 497, 883
Gold extraction (or reduction) processes. Economics
Gold panning â technique of panning in rivers (Leibniz, Crafft, 1688)
217, 414
Gunpowder
Production of gunpowder and saltpeter â its chemical properties â a process for its manufacture with leaching and concentrating in ditches or trenches
216, 413
Hypothetical process to establish a perpetual saltpeter works (Elers, 1684)
216, 413
Suggestion for improvement of saltpeter production â using a vault or dome (Leibniz, Crafft, 1688) â with the product appearing on rocks following blasting
216, 413
Iatrochemistry (chemical medicine). Medicine, Chemical medicine, Iatrochemists (chemical physicians), and Medicine (Chemical Medicine / Chemistry in Medicine), the Chemiatric school in Medicine, its diagnostic and therapeutic teachings.
Lead
Douceurâs secret process for giving lead the color of molten bronze (1683)
217, 415
Lead oxide (red lead)
217, 415
Leibnizâs chemical studies
His perception of Boyle and his accumulation of experimental data â his experimental industriousness and judgement â his failure to formulate theories â his reticence in drawing conclusions
88, 288
His information about J. J. Becher (+1682) â his chemical writings
140, 390, 722
His interest in chemical experiments (Dresden, early 1680s)
6, 275
His interest in a fuming liquid process (Celle, early 1680s)
5, 212, 274, 281, 337
Mercury
Alleged transmutation of mercury into gold by von Chaos (1658)
220, 721, 889
Cinnabar (mercury sulfide mineral)
214, 217, 253, 339, 415, 854, 888.
Chemical Projects
A cinnabar process â investigated by Italian alchemists (1685) â Bodenhausenâs interest in the process (1690) â Leibnizâs designation as a chemical âtransplantatioââ an adulteration of the process (1690) â falsification of the cinnabar â use of cinnabar of antimony
217, 415, 888
Medieval understanding of mercury â as a basic principle of metals â in the alchemical text âTurba philosophorumâ
219, 721
Quicksilver (liquid metal mercury)
416
Study of mercury (Bodenhausen, 1690)
415f.
Sublimation of mercury (Geber or Gebir, ed. 1668) â Bodenhausenâs study and Leibnizâs skepticism (1690)
218, 416f.
Production of mercury from the âRegulus of antimonyâ (Florence, 1690)
218, 417
Metals. Metallurgy, Metallurgical Processes
Alloys, alloying of metals
139, 387, 485
Chemical âmaturationâ of metals (Leibniz, 1687) â for improving the processing of ores â for increasing knowledge â for greater economic benefit
218f., 418, 888
Chemical transmutation of metals â for the possible production and extraction of gold and silver
190, 209, 214â216, 218f., 338f, 341, 410, 418, 888
Counterfeit or fake gold â from the workshops of von Chaos and Wenzel Seyler â made by the charring (carbonization) of coal â inspected by Leibniz at the Imperial Treasury in Vienna (1688)
220, 721f., 889
The efforts of Rothmaler in Vienna (1689)
218, 418, 888
The âLobkowitzâ process â for the transmutation of silver into gold and silver (Crafft, 1689â90)
218, 418, 888
The Holeysen separation process (Vienna, 1690) â gold yielded from auriferous silver â submissions to the emperor â Holeysenâs discussions with Leibniz
218, 418, 888
Brandâs (purported) process for metal ennoblement (1698)
221, 833
Mollerâs (reported) very lucrative process (1699)
222, 834
Minerals, crystals, rocks. see Geology; Iceland spar.see Physics, Light and Optics
Phosphorus (white phosphorus)
Discovery of phosphorus â history of the discovery
208â211, 328â331, 412f.
Hombergâs history (1692)
208, 213f., 412
Leibnizâs âHistoria inventionis phosphoriâ (1710)
209, 214, 328, 413
Brandâs discovery (in Hamburg, c. 1669)
159, 197, 208â211, 213, 221f., 271, 328, 330â333, 410f., 707, 833f.
Crafftâs Intelligence regarding the discovery (1676) â its presentation at the Court in Hanover (May 1677)
210, 330
Crafftâs disclosure to Boyle (London, Sept/Oct 1677)
210f. 331f.
Boyleâs other German informant â his laboratory assistant (Hanckwitz)
213, 411
Leibnizâs contract with Brand (July 1678) â Brand in Hanover (1678â79) â production of phosphorus
210, 331
Kunckelâs âPhosphorus mirabilisâ (1678)
209, 328f.
Boyleâs âThe aerial noctilucaâ (1680) â his method / process
209f., 213, 329, 331â334, 411
Leibnizâs process for the production of phosphorus â his report to Tschirnhaus (June 1682)
The Leibniz / Brandâs process â repeated and protracted distillation procedures â starting or raw material (human urine)
211, 333â335
The process and intermediate stages â oil of urine â a âcaput mortuum oleosumâ â a core fire-containing substance / a black loose or soft material â a hard salt byproduct / an amber-like hard stone
211, 334f.
Special properties of the final product â brightness and luminescence
211, 334f.
Leibnizâs claim to superiority of his process â attributed to an additional step for the refinement of the âcaput mortuum oleosumâ
211, 335
Other processes / presentations of phosphorus (1682)
Secret formula on offer in Paris
211, 336
Experiments by members of the Académie
211, 336
Leibnizâs revelation of his production process to the Académie via Tschirnhaus (June 1682)
211, 277, 333, 335f.
Leibnizâs receipt of two scientific secrets in exchange for his â a process in which ostensibly herbal salt grew like a plant in water â a process in which gold was made volatile without fulmination
212, 337, 414
Boyleâs publication of his âIcy noctilucaâ (1682)
336
Brandshagenâs presentation of phosphorus for the king of Denmark (1682) â his cosmetic or blemished complexion after a facial phosphorus application with adverse after-effects
211f., 336
Public performances with phosphorus â enhancement of phosphorescence in the dark
212
Theoretical importance of phosphorus Tschirnhaus on phosphorus and alchemy (1682) â the accordance of phosphorus with the second of the three universal principles of alchemy, namely salt (a solid state or fixed salt), sulfur (an oily or sulfuric liquid), and mercury (a volatile or mercurial spirit)
212, 336f.
Brandshagenâs chemical experiments (Hanover, 1687) â his phosphorus production following Reimersâ urine collection (AprilâMay 1687)
213, 412
Leibnizâs communication to Bodenhausen (1690) â with details of the production process and verses about phosphorus â presentation at the Florentine court â interest of princes Ferdinando and Gian Gastone
213, 412
Other phosphorus-like (luminescent) substances
Boyle-Leibniz discussion (1673)
209, 329
Balduinâs âphosphorus hermeticusâ (1675) â a phosphorescent form of calcium nitrate
209, 329
Breatridgeâs spontaneously-igniting powder (1680)
209, 329
Demonstration of a smoking / fuming liquid (1680â81) â Schelhammerâs attribution to an inner fire â Leibnizâs rejection of any similarity with phosphorus
5, 212, 274f., 281, 337
Properties / uses of phosphorus / phosphorus-like substances â afterglow (or phosphorescence) â a means of distillation without fire â combustion and ignitability â encapsulation of fire â conservation of fire / heat (on a journey) â carbonization (of wood)
212, 413, 722, 888
Salts
Glauberâs salt
222f., 836, 890
Salt revivification, transanimation, resuscitation
223, 836, 890
Transmutations of salt(s) â Stisserâs understanding of transmutation (1699) â his examples from the mineral, vegetable and animal realms
222f., 834â836, 890
Salt works (Brine works)
Desalination, desalinization â process for the desalination of sea water
139, 150, 190, 201, 219, 387, 410, 499, 573, 803.
Projects
Salt production processes. Economics
Salt (or brine) wells â origin of the salt in wells
147, 687
Lacyâs desalination plant near Modena (1690)
190, 201, 410, 499
Desalination / salt extraction from seawater in Holland
219, 573
Crafftâs project based on a precipitation process â Leibnizâs interest and skepticism (1695â1696)
219, 573f.
Papinâs machine for seawater desalination (1699)
150, 803
Salt works at Halle (early 17th Century) â Leibnizâs recollection (1696)
574
Salt works at Heyersum (near Hildesheim, 1697)
156, 700
Silver mines. see Mining
Soda or sodium carbonate (natron)
836f.
Sulfur â the phenomenon of electric sparking. Physics,
Magnetism and Electricity
Vitriol
Alum, vitriol of Argile (vitriol of clay)
712
Leibnizâs view of vitriol as a basic principle of metals
219, 721
The âtinctura vitrioliâ (Stisser, 1698)
219, 721
China
Calendar office in China
117, 791
China missions
48, 754, 822
Religious conversion of the Chinese â Leibnizâs missionary zeal
208, 827f.
Jesuit mission
8, 50, 248, 357, 423, 756
Protestant missions
13, 618
Anglican missionary efforts in China â journeys to China by English merchants (1697)
208, 827
Support for the mission from the Berlin Society â along the overland route to the orient
208, 827
Leibnizâs suggestion (new year 1697) of the use of the dyadic or binary number system in the missions â intended to counteract a pagan or heathenistic philosophy
27, 645f., 753f., 828
His view of the prodigious origin of all numbers out of 1 and 0 â an archetype of the secret of creation â the coming into being of all from God and Nothing (1 and 0)
754
His communication (January / February 1697) to the China Missionary Grimaldi
48, 754
His view of the main use of binary arithmetic in the investigation of the properties of numbers
48, 754
Christian missionary ambitions combined with the advancement of science â propagation of the faith by means of science â an objective of the Berlin Society (1700)
208, 827f.
Desired spread of the Christian religion among the (partly)
heathenish and still (partly) barbarous â even among barbarian peoples
828
Chinese mathematics. Mathematics
Acquisition of mathematical instruments in China (1699)
208, 827
Binary Fohy (or FuXi) sequence
50, 756
Chinese figures of Fohy (âFuXi hexagramsâ)
50, 756
Peking (Beijing) â The âTribunale Mathematicumâ
8, 357
Chiromancy. see Medicine, Limbs, Palm Reading
Christianity / Christendom
788
Christian Charity
683f.
Chrysopoeia. see Chemistry, Alchemy
Churches, Christian churches
Anglican (Anglo-Catholic) church
116, 208, 827
Anglican anti-Catholicism sentiment
116
The âSociety for the Propagation of the Gospelâ
208, 827
Catholic (Roman Catholic) church
xiii
Catholic theology/ theologians â ecclesiastical policy â the Roman Inquisition
xiii, 13, 105, 114, 117, 367f., 618, 788
German Catholic dioceses â Cologne â Münster
11
Synods â Synod of Nicæa (Nicene Synod, 325 A.D.)
789
: Calendar Reform
Foreign missions. see China missions
Reconciliation of the Protestant churches
13, 618
Reunification of the Christian churches
14, 745
Clausthal (Clausthal-Zellerfeld / Zellerfeldt)
136, 144f., 226, 344, 384, 566f., 569, 891.
Mining
Combinatorics â Renaissance and modern combinatorics
238, 845
Leibnizâs dissertation on the combinatorial art (1666)
238, 751f., 845
Leibnizâs combinatorial characteristic
18, 284f.
Category combinations (combinatorics)
Juridical, mathematical, philosophical, scientific categories
238, 845
Systematic categories in botany. see Biology
Commonweal, common good (âbonum communeâ)
19, 195, 197, 201, 316, 360, 505, 595, 597, 606, 718, 720, 787, 888
Controversies and disputes
Leibnizâs meeting with Boyle (1673) â his disparaging remarks about Boyle and his work â his misgivings about Boyleâs development of the vacuum pump â his insistence on Guerickeâs priority over Boyle â his resentment towards Boyle
89â92, 210, 290â293, 331
Boyleâs continuing interest in Leibniz â his expression of affection towards Leibniz
89, 289
Leibnizâs misgivings about the Boyleâs studies of the properties of air â his insistence on the superiority of Guerickeâs work
89â91, 210, 290, 293, 331
Leibnizâs mistrust of Boyleâs role in communicating intelligence about Drebbelâs submarine crossing of the Thames (c. 1620)
179, 488f., 585
Misgivings about the discovery and study of phosphorus â Leibnizâs insistence on Brandâs priority over Boyle â his insistence on the superiority of his own process
211, 333, 335
Leibnizâs recollection of other instances of non-recognized discovery claims â Snell van Royenâs law of refraction, wrongly attributed to Descartes and Kepler â Keplerâs priority in explaining gravity on the basis of centrifugal force
91, 301, 383f.
Leibnizâs perception of German reticence in claiming success â of preferential treatment being given to foreigners â of prejudice against Germany and Germans
38, 90, 292, 632
Satirization of Leibniz â J. J. Becherâs satirical work (1682) â ridicule of discoveries and projects of contemporaries like Leibnizâs imagined rapid transit system
7, 140, 146, 188, 278, 390, 398, 880.
Transport, Transportation
Leibnizâs discord with Tschirnhaus (1682â84) â following unapproved publication of his quadrature method
19f., 359f.
Priority issues in the context of the formulation of the minimal principle of optics (1682â83), following the publication of Leibnizâs principle of optics â his principle of the easiest light path (1682)
120f., 125, 300f.
Leibnizâs dispute with Vanni (1684â85) â concerning the static moment of a heavy body on an inclined plane
96f., 375
Controversy about the true measure of force (from 1686)
Leibnizâs demonstration of Descartesâ âremarkable errorââ his âBrevis demonstratioâ (1686) â reaction of the Cartesians and Papinâs rejoinder (1689)
56â58, 63, 362f., 458, 534, 646
Leibnizâs dispute with the Cartesian Abbé Catelan
18f., 21f., 53, 358, 432, 453
Papinâs opposition (January 1691) to Leibnizâs assault on Cartesianism
57f., 457f., 646
Leibnizâs reassertion of his anti-Cartesian stand (September 1691)
59f., 460f., 647
Leibnizâs support for Corradi in a dispute with Stabe de Cassina â issue of dangerous emissions in chemical processing using vitriol (1689â90)
190, 410
Leibnizâs conciliatory approach (1690â1695) regarding an explanation of gravity / gravitation â his own vortex theory â theories of Newton and Huygens
106f., 111f., 463f., 547f., 550, 876
Leibnizâs priority claims (1693) regarding winding (or ore-hoisting) machinery in mining â use of an endless rope / cable for weight compensation
134, 138f., 143â145, 386f., 407, 565â567, 569f., 879f.
Conflict (1694â95) with the Mining Office over the design of a power supply system for pumping and winding machinery
145f., 567, 571
Public philosophical dispute with Foucher (1692â93)
54f.
Dispute with Papin about âvis vivaâ. Natural Philosophy
The âvis viva controversyâ â dispute conducted in articles (published up to 1691), and in private correspondence (from 1692)
First phase from January to December 1692 â Papinâs âSynopsis controversiaeâ (Oct./Nov. 1692)
60, 462
Rekindled correspondence with Papin in 1695
61â63, 526â535
Leibnizâs time-out (two months early in 1697)
68, 656
Papinâs time-out (spring to fall, 1697)
69, 656f.
Final phase of the debate (January 1699 to springtime 1700)
78, 873f.
Dispute with Papin about action (âactioâ; 1696â1700). Natural Philosophy
50, 287, 362, 450, 525, 646, 757
Action
66, 74â81, 85â87, 648, 669â682, 757â762, 772â775
Dispute regarding Papinâs attempts (1696/97) to demonstrate a loss or gain of force in the substitution of bodies
67â70, 459f., 654â659
Leibnizâs final letter to Papin dealing with the measure of force and action (April 1700)
774f.
Guglielminiâs dispute with Papin (1691â1697) about the fundamentals of fluid flow and fluvial mechanics â mathematical abstraction versus engineering practice
167, 481f.
Huygensâ critique of infinitesimal analysis â dissension between Leibniz and Huygens (1691â1692) about the âLeibniz seriesâ and a similar series of Huygens
24, 437f.
Publication of the catenary problem solutions
22, 24f., 432f., 439f., 442, 628, 864f.
Exchange of inverse-tangent methods
24, 437
Huygensâ dispute with Renau dâEliçagaray (1689â1694) â about the method of steering and maneuvering a sailing ship
182f., 588â590
Leibnizâs thoughts regarding the dispute (1694â1695)
183, 590
Discussions about the foundations of the calculus
Clüverâs criticism of the differential calculus (1694â1695) â its failure to achieve ultimate geometrical precision â example of the relationship of unity to infinity
41â43, 523f., 639, 642
Nieuwentijtâs criticism of the calculus (1694â96) â his âConsiderationes secundaeâ (1696) â Knorreâs review (March 1697) â Leibnizâs âExcerptaâ (June 1697) â Johann Bernoulliâs criticism of Nieuwentijt (1697)
31â33, 41â43, 523f., 621, 639â642
Menckeâs role in the dispute with Nieuwentijt
32, 41f., 524, 640f.
La Hireâs criticisms and Leibnizâs answers (1697)
34, 43, 623f., 644, 868
Leibnizâs approach to such criticisms â revealed to Clüver (June 1697) â deferment and referment â reliance on the judgement of adepts / experts
43, 642
De Volderâs difficulties with the calculus (1698) â dispelled following Joh. Bernoulliâs explanations
43, 639f., 643
The conflict between Jacob and Johann Bernoulli
Drawn-out conflict / the isoperimetric problem (1697)
37f., 630â632
Leibnizâs criticism of Jacobâs behavior â disruption of the correspondence with Jacob (until 1702)
38, 632
The Dispute about the calculus. Mathematics, Calculus
Questions of independence, priority and plagiarism â the priority dispute
11, 19, 28â30, 34, 38f., 359, 508, 517f., 521f., 624, 632â639, 868
Eminence of continental mathematicians
30, 522, 638
Eminence of English mathematicians
11, 28â30, 500, 508, 517, 519, 522, 753
Leibnizâs publication and conflict management policy â his defense of his discovery claims
19, 48, 359, 450
Correspondence between Leibniz, Oldenburg, Newton (1676)
29f, 40, 519, 638f.
Wallisâ focus on Newtonâs calculus of fluxions (1693)
30, 39f., 521, 634â639
Wallisâ insinuations / resentment against Leibniz (1695)
41, 47, 626, 639, 752f.
Leibnizâs view of Wallis as an English nationalist â his complaint to Burnett of Kemney (1695) â his review of Wallisâ Opera (June 1696) â his criticism of Wallisâ biased, one-sided treatment
30f., 522f.
Wallisâ subsequent complaint to Leibniz
523
Beginning of Leibnizâs correspondence with Wallis (1696) â and discussion of priority issues (from December 1696)
634â639
Limited circulation of scholarly results â a factor in priority issues
39f., 636
Joh. Bernoulliâs complaint (August 1696) about Wallisâ failure to acknowledge the differential calculus â his suggestion that the fluxional calculus was built on information received from Leibniz
39, 635
Fatioâs allegation of plagiarism against Leibniz (1697)
34, 624, 868
Critique of Menckeâs editorial policy at the Acta Eruditorum Menckeâs abhorrence of polemical disputes
47, 752
Menckeâs alleged preferential treatment of foreigners â in contrast to the treatment of Germans by foreigners
38, 632
Skirmish with Mencke concerning David Gregory (1697) â Gregoryâs belated solution of the catenary problem â in the Philosophical Transactions (August 1697), and in the Acta Eruditorum (July 1698)
36, 38, 46, 629f., 632â634, 749
Leibnizâs (anonymous) criticism (February 1699) and Gregoryâs reply in the Philosophical Transactions (December 1699), and Acta Eruditorum (July 1700)
38, 46, 633, 749
Accusations of censorship against Gregory â Leibnizâs call (January 1701) for Gregory to obtain Newtonâs approval â repercussions for the priority dispute
38, 632â634
Fatioâs and Wallisâ accusatory publications of 1699
Fatioâs belated solution of the brachistochrone problem â his apparent desire for recognition and feeling of having been excluded in the announcement of the problem â his rejection of mathematical challenge problems â his allegation of plagiarism against Leibniz and his insistence on Newtonâs priority
44â46, 746â749
Derivations of the problem of the solid of revolution of least resistance (Fatio and Joh. Bernoulli)
45â47, 746f., 751f.
Wallisâ publication of the Leibniz-Newton correspondence (1676) â Continental-European support for Leibniz in the competition of methods â supporters like Joh. Bernoulli, LâHospital, Varignon
25, 29f., 40, 48, 519, 638f.
Bernoulliâs view of Wallis as an overeager defender of English glory â his fear of the anger and wrath of Fatio and Wallis
47, 751
Leibnizâs two-track reaction to Fatioâs publication
Complaint sent to the Royal Society (August 1699) â rejoinders in the Acta Eruditorum (November 1699) â defense of his standpoint (May 1700) â greeted by Joh. Bernoulli (June 1700)
46, 749â752
Wallisâ and Sloaneâs condemnation of Fatio (September 1699) â Royal Societyâs expression of veneration for Leibniz â Newtonâs disapproval of Fatioâs attacks against Leibniz
46, 750, 753
Fatioâs reply to Bernoulli and Leibniz, sent to Mencke (1700)
47, 752
Leibnizâs replacement of the notation of the method of fluxions with that of the differential calculus in Fatioâs reply sent to Mencke
752
Rift in Joh. Bernoulliâs relationship with brother Jacob â Leibnizâs role as a mediator in this dispute â his criticism of Jacobâs behavior towards Johann
37f., 48, 631f.
Swiss alliance of Jacob and Fatio directed against Leibniz â Jacobâs correspondence with Fatio (1700â01) â complaints about a perceived hegemony of Leibniz â Fatioâs reports of English resentment against Leibniz
41, 44, 47, 639, 746, 752
Leibnizâs admission to the Académie des Sciences (1699)
48, 753
French criticism of the foundation of the Leibnizian calculus â powerful opponents alongside supporters at the Académie â Varignonâs role (together with LâHospital) as defender of the differential calculus
14, 34, 43, 45, 48, 623f., 745, 747f., 753, 868
Rolleâs critique of the foundation of the calculus (1700) â expansion of the dispute (from 1701)
34, 48, 623, 753, 868
The Académie Commission set up to settle the conflict (1701)
48, 753
The Burnet diluvian controversy in Leibnizâs correspondence with Büssing (1696â1697)
228f., 583, 723â726, 897f.
Ramazziniâs dispute with Schelhammer (1699â1700), about changes of mercury column levels with the weather
100, 776â778
Leibnizâs explanation of the phenomenon â quest for a solution of the problem based on demonstrations / proofs and on mechanical experiments
100, 777f.
Experiments, Thought Experiments
Papinâs high-pressure steam engine (1707â1708). Engines, Enginery â design approved by Leibniz, but rejected by Newton and Savery â Saveryâs accusation of plagiarism against Papin
149f., 698, 801f.
Dispute between animalculists and ovists (ovulists) in the theory of preformation â Leibnizâs meeting with Leeuwenhoek (November 1676) â his Correspondence with Leeuvenhoek (1715â1716)
128, 130, 234, 240f., 301, 379, 726f., 848f., 894
Cosmology. Astronomy, cosmological, cosmogenic theories Creation. see Religion
Cryptography
Cryptographic script or cipher code
173â177, 184, 315, 483â486, 713â715, 862
Concealment of information â encryption / decryption â encoding / codebreaking
174f., 177, 184, 225, 315, 483â486, 715, 840
Contemporary military conflicts â Siege of Montmélian (1691)
175, 486
Copology
174, 484f.
Cryptanalysis
175f.
Historical development of cryptography
174, 484
Early modern English cryptography
176
17th Century â proximity to algebra â Viète and Wallis
176, 713f.
Theory and theoreticians â Practice and practitioners
Bodenhausenâs secret-key encryption
225, 840
Wallisâ cryptographic knowledge â his opus on the âArt of decipheringâ (1653) â instruction of his grandson (Blencow)
176, 714f.
Leibnizâs interest â his unsuccessful attempt to persuade Wallis to share his knowledge â Wallisâ refusal for political reasons â the need for secrecy in conducting state business â the need for royal approval
175, 713â715
Cryptography seen as a clouded pursuit â a method needing continual adaption
177, 715
Leibnizâs cipher machine
175
Steganography
Haesâ tract âSteganographie nouvelleâ (1693) â his cipher code â its use in diplomatic communications â his system of encryption
173â175, 483â486
Steganology
Haesâ technique for hiding / detecting information â use of alphabetical, numerical, and combinatorial tables
174, 484f.
Watermarking
174
Curves. see Mathematics, Curves and Surfaces
Deluge, diluvian. see Geology
Demography, demographics â the science of populations â political arithmetic. see Economics, Political Economy
Denmark, Danish
xv, 2, 115, 152, 183, 200, 209, 227, 236, 262, 315, 327, 401, 731, 784
Copenhagen
97, 143, 152, 177, 183, 211, 213, 216, 245, 262, 298, 312, 315, 323, 336, 377, 400f., 410, 413, 734
The Danish court / king
115, 152, 183, 236, 262, 315, 400, 731, 784
Ven, the Island of Ven
97, 298
Discoverers and innovators
132, 683
Disputes. see Controversies
Dresden. see Saxony
Dutch, Dutch republic. see Netherlands, Holland
Dynamica. see Natural Philosophy
Leibnizâs planned publication âDynamicaââ Bodenhausenâs role in the edition and publication â retrieval and return of Bodenhausenâs manuscripts (1698) â the role of M. G. Block
50â58, 81, 92, 103, 363â365, 375, 451, 453â456, 459, 525, 537, 736f.
Dynamics
450, 525
Force in Leibnizâs dynamics. see Force
Galilean law of falling bodies
36, 627, 869
Laws of dynamics â metaphysical foundation. Natural Philosophy
Derivations of the (true) measure of force â a priori and a posteriori derivations
60, 526, 536f.
Leibnizâs Descartes critique
54, 455
Reasoning in dynamics. see Reason, Reasoning
Science of dynamics
50, 456
Dynasties
House of Austria
6, 276
House of Brunswick-Lüneburg
174, 484.
Hanover
House of Este
12, 509
House of Welf (Guelf or Guelph)
7, 9f., 13, 226f., 307, 356, 419, 427f., 430, 499, 508, 566, 610, 618, 892
Dynastic history â Leibnizâs historiographical assignment â his projected âopus historicumâ â archival sources
7â13, 52, 356f., 430, 452f., 508f., 566, 618, 892
Earth history (pre-history). Geology
Earth Sciences. see Geology
Economics, Economic systems and theory
406, 591
Feudalism, serfdom and slavery
186, 320.
Slave Trade
Mercantilism, mercantile economics, economic policy
184, 191, 315, 406, 496
Mercantile economic projects (1690s). see Projects
Mercantile trade / trading / trade wars. see Wars
Cameralism, cameral sciences â a German variant of mercantilism â a âscienceâ of government, involving societal reform and economic development
188f., 407, 828
Leibnizâs mercantilist-cameralist conviction â seeking the advancement of German-style cameralism and public administration â having a good police regime with orderliness and supervision
188f., 407f., 828
Economic liberalism â in the guise of a âcapitalistâ chemist in Hamburg (1699)
221, 833
Economic projects. Projects, Economic, Techno-Economic Projects
Economic prosperity
184, 316, 328
Leibnizâs interest in economic or trade advancement â entrepreneurial involvement with or without princely or baronial participation
191, 497
Entrepreneurs, entrepreneurial activity
191, 194, 497, 508, 594, 801, 809, 888
Finance and commerce
187, 406
Leibnizâs calculations of interest and discount, of bonds and debentures
16, 187, 281, 406
Evaluation of life annuities and insurance
17, 187, 284, 406
His âMeditatio ⦠de interusurio simpliceâ (1683) â values of loans and repayment schedules â the method of compound interest (âanatocismusâ)
16, 187, 281, 407
His exchanges with Ferguson (1683â84)
187, 406f.
Government economic planning and administration â at state level in Hanover â at Imperial level in Vienna
189, 408
Leibnizâs advocacy (1688) of the establishment of an Imperial mining college or council â the establishment and coordination of the occurrence of mineral and ore deposits â with an associated laboratory and a chamber of arts, for the presentation of mechanical inventions and innovations
189, 408
Purpose of the Imperial mining institution â counteraction of imports of ores and minerals â colonization of regions of Hungary following the re-conquest (1683)
189, 408f.
Economic utilization of chemical processes or substances â use as paints
190, 214, 337, 409, 888
Monetary systems â proposals for improvement â Leibnizâs collaboration with Crafft â joint memorandum for the emperor (1688) â discussions with Holeysen in Vienna (1690)
187, 189, 406f.
Business ventures, undertakings, processes â cost effectiveness, economic feasibility â economic efficiency of the Hungarian mines â excerpts from Holeysenâs papers
9, 187f., 218, 358, 407, 418
Claims concerning gold extraction processes â discussions with Crafft (1688) â questions of cost-effectivity â costs of related ingredients
188, 208, 328, 407
Salt production processes (salt works) â cost-effective assessments of such ventures â brine, sole, and salina (concentrating house) â exchanges with Mohr (1686) and Heyn (1686â87)
141, 147, 156, 188, 191, 394, 407, 497, 574, 590, 687, 700
Street illumination with oil lamps â exchanges with Crafft (1689â90)
407
Improvement of the system of coinage
191, 406, 579
Economic development of kiln technology â ore and glass smelting â glass working for optical equipment
158, 160, 191, 497, 591, 704, 808
Metal refinement or ennoblement â gold, silver and lead production
191, 497
Retort manufacture
158, 191, 497, 706
Pearl cleansing procedures
191, 497
Porcelain manufacture
191, 591
Oil production processes
191, 497
Increase of agricultural production â use of manures
191, 497
Development of silk production â growing of mulberry trees â rearing of silkworms
191, 408, 497
Drapery â clothes (fashion) â linen drapery production
185, 318, 408f., 590
Wallpaper manufacture
187, 191, 322, 590
Improvement of the wine and brandy trade
191, 496
Argument for measures against brandy / cognac imports â projected alternative to French brandy produced from wine
12, 191f., 194â196, 496, 508, 563, 591, 596, 716â718
A projected brandy manufactory at Münden (1693)
192, 591
Development of a new ferment at Hamburg (1693)
192, 591
Production of brandy from native sugar
192, 591
German domestic production of distillates
192, 591, 716
Processes used for distillates in Holland
192, 591
Projected use of sugar solutions â syrup or treacle
192, 195, 591, 596
Negotiations in Hamburg about the process
192, 591
The Leibniz / Crafft brandy project (1693â95) â conceived as economic retaliation against France and a French trade monopoly in foodstuffs and merchandising â intended to damage French foreign trade â inflicting long-term damage by means of trade wars â the legitimacy of such trade wars â also in times of peace
12, 192â196, 508, 591â596, 716â718
Contract for the formation of a company â signatories Leibniz and Crafft (1694) â proceeds intended partly for pious, and charitable purposes â for promotion of practical arts
12, 192, 194f., 508, 591, 594f., 716
Projected production of a brandy substitute â further idea of producing vinegar from the residue of the distillation process
192, 591
Intended location of production in England and / or Holland â preparations in Holland â Leibnizâs and Crafftâs journey to, and stay in Amsterdam (November 1694)
11, 192, 194, 196, 508, 591f., 716, 719
Final proposal sent to William III â call for the formation of a company enjoying royal privilege â with monopolist privileges and exclusion of French influence
12, 192, 194, 508, 591f., 594
Project intended to â increase the alliesâ power, wealth â promote navigation, plantations â enable expansion in south America
194, 593f.
Fate of the project â delays and final demise (1695) â attributed to adverse economic factors â including high sugar / syrup prices in Europe
195, 595f.
Crafftâs new proposal (1696) â removal of the fusel oils from fruit and corn liquor by means of distillation with quicklime
195, 596
Crafftâs contact with Baron von Stauff â for Leibniz a dubious and unsavory character â his projected finance plan and continuation of the brandy project â located in Amsterdam or Vianen â his idea for the presentation of the plan to the âStates Generalâ
195â197, 716â718, 720
Leibnizâs accusation of breach of contract â his refusal of any further financial support
196, 718f.
Crafftâs fear of a âcivil deathâ (âciviliter mortuusâ) â of insult and humiliation â of his transfer to a charitable institution, a hospital, infirmary, or workhouse
717f.
His demise, death and aftermath
195â197, 718f.
Leibnizâs judgement on Crafft â his talents as a chemist and technician â his inability to manage money â his quest for personal fortune and glory â his abhorrence of the pursuit of an ordinary profession â his indifference to the common good
197, 330, 720
Political economy
190, 497
Political arithmetic â the application of mathematics to economic-political matters â to economic welfare issues, and sustentation
191, 497f.
English bills of mortality â Pettyâs âEssaysâ (1686â87), regarding the two cities (London, Paris) â their people, housing, hospitals, etc.
191, 498
Neumannâs empirical observations â his theological-political observations â baptismal and mortality registers (in Breslau)
498
Education. Projects, Higher Education
Ehrenfriedersdorf. see Power, Water Power, Saxony
Einbeck, and Sulbeck near Einbeck
141, 146, 394, 398
Elasticity. see Materials, Natural Philosophy, Physics
Energy â Energy conversion, storage, transmission. see Power
Engineering, engineers â the art of engineering
162, 488, 812
Chemical or process engineering. see Chemistry
Civil engineering (âCivilbaukunstâ)
Sturmâs civil engineering (âDer bürgerlichen=Bau=Kunstâ) â design and construction of roads and bridges â water-supply and sanitation systems
156f., 702
Historical connection between civil and military engineering â connection between engineer and soldier â 17th-century attenuation of this link
156f., 701
Architecture and civil engineering â architects, civil engineers, master builders
120, 153, 156f., 161, 698, 701f., 808, 861
Mathematicians and engineers, including Goldmann (+1665), Lauterbach (+1694), and Sturm (+1719)
156f., 574, 701f.
Sturmâs ambitions â as architect, draughtsman, master builder â as mathematics professor â as poet, preceptor and polymath â as designer of a castle of grief (âcastrum dolorisâ)
156, 702
Sturm as advocate of the art of civil engineering (âCivil Bau-Kunstâ) in letters to Leibniz (in 1697â98)
156, 701
Gengenbach as architect â his drawings (1700) of a fortification model â of a pull-out or fold-out table â of an Italian andiron â of carriages and lanterns
161, 808
Engineering enterprises
Papinâs contemplated (1696) new machines and inventions â difficulties in their realization
147, 157f., 688, 703f., 829
Leibnizâs own engineering discoveries â similar difficulties in their realization
147, 161, 688, 808
Papinâs petition (1696) for his release from the service of the landgrave of Hesse-Kassel â his desire to return to England â rejection of the application â granting of concessions (1697)
157f., 704f.
Waterworks (in England, France, Saxony)
95, 140, 143, 297, 388, 390â394, 397f.
Waterworks in garden design and architecture
Garden design (1696) at the electoral gardens at Herrenhausen (Hanover)
153â156, 698â701, 813
Design of waterworks at Herrenhausen â including cascades, waterfalls, ornamental fountains
153f., 156, 698, 700
First contemplated scheme â erection of a vertical water wheel for raising water into a tank reservoir in a tower â intended for the supply of the fountains through pipes â Court decision (August 1696) for this scheme â intended construction on the river of a Persian or scoop wheel of 50-foot diameter â additional construction of a mill, to help offset costs
154f., 698, 700
Second contemplated scheme â erection of a water wheel on a river branch near Hanoverâs ânew townâ district â provision of a fountain water-supply â an additional urban water-supply, using a lengthy system of wooden pipes
154f., 698f.
Third contemplated scheme (Leibnizâs preference) â construction of a canal passing through the electoral gardens â connecting two locations on the river â raising water into a tank in a tower â fountain water-supply from the tower â use of a hydraulic flume (on stands)
154f., 698â700
Additional canal benefits â navigation along the canal â creation of a waterway for gondolas between Hanover and Herrenhausen â supply of water mills along the course â hydraulics works kept off the main river â no impairment of shipping traffic â reduced exposure to seasonal dangers like river currents and ice formation
154f., 699f.
Urban water supply
Leibnizâs urban water-supply scheme â establishment of a âwater-supply networkâ
154, 698
Medieval / early modern supply systems â in London and in central and eastern European cities (networking)
154
Thoughts of Leibniz and Du Mont regarding protective measures against flooding â excavation works to build a dike, making use of the excavated earth
154f., 699
Canal construction and navigation â costs / cost factors â cladding of the canal sides â prevention of erosion â protection of the canal and gardens
155, 699
Maintenance of the canal water level â regulation of water flow â building of canal locks â building of cascades
154â156, 699f.
Draining of the canal for repair and maintenance works
154, 699
Regulation of the water quantity â for the operation of a water wheel â the water supply for the fountains
154f, 698f.
Concrete measures for the waterworks (May 1697) â Linsenâs services offered â his tests of a piston for a water pump
156, 700f.
Urban power sources and supply
Wind, water, horse power â windmills, water mills / fluvial water mills â horse mills
153f., 572f., 699
Flour mills â envisaged use of watermills by bakers / bakeries â in Amsterdam and other Dutch towns
153, 572f.
Water power â pumped storage in elevated reservoirs â reserve supply for watermills
153, 572, 862
Pump forms â circular cross-section (standard) â four-sided (rectangular) section â pump with pyramidal form
153, 571â573
Leibnizâs experiment (1696) â with a quadrangular cross- section pump â its length, width, stroke length
153, 573
Military engineering and engines
3, 151, 157, 399, 574f., 701f.
Military architecture â battles, sieges / besiegement
175, 189, 408, 486, 575f.
Military academies. see Projects, Scientific and Educational
Sturmâs military engineering (âDer Kriegs=Bau=Kunstâ)
157, 702
Ballistae â military engines
151â153, 399â402, 574â578
Cannons, guns, muskets â improvement in the production of canons
5, 152, 273, 323, 399, 577, 809
: Metallurgy, Metallurgical Processes
Military engineers
150, 153, 156, 496, 698, 802
Military innovations
Military bridge tested by the duke of Celle (1683/84)
152, 401
Danish artillery (1683â1687) â military technologies in Copenhagen â howitzers â grenade or artillery shell launchers â Brandshagenâs mortar bombs
152f., 177f., 213, 324, 401, 411
Iron and steel production for military purposes
Mass production of steel in Saxony (1686/87) â smelting furnace
153, 402
Damascene steel â production of quality steel since medieval times â of interest at the Danish court (1683/84) â production of damascene blades in Saxony (1687)
401f., 152f.
Other military innovations in Saxon production â copper coatings for canon muzzles â grenade throwers â halberds â light armor
153, 402
Danish artillery (1683â1687) â military technologies in Copenhagen â howitzers â grenade or artillery shell launchers
152f., 401
Dutch military technologies â arsenal in Delft â planned demonstration of a repeating firearm at Rijswijk (1694) â subsequent demonstration in Amsterdam
576f.
French ballistic mortars â trial of such mortars
152, 401
Fortification â fortification systems, principles, techniques â Teylerâs tract concerning fortification (1679) â fire power / fusillades â fortification arrays
150, 161, 574â576, 802, 808, 882, 894
Fortifications of the town of Breda (1683) â employment of a wind-powered water elevator
142, 395â397, 894
The âslang-molenâ â a water screw (Archimedean screw) â a rotating wooden spiral, like a helical staircase
142, 395f.
The âketting-molenâ â a chain elevator system (or chain mill) â a system of troughs attached to the chain
142, 395f.
Fortification works at Neuf-Brisach (Neu-Breisack) â Vaubanâs process for transporting earth (1699â1703) â power sources: manpower and horsepower â drawing / sketch sent by Leibniz to Papin
150f., 802
Comparable works (âGazette dâAmsterdamâ, 1700) â a machine for transporting a large quantity of sand
151, 802
Mining engineering. Mining, Mining engineers
Science of engineering â Engineering science
3, 163, 402, 407
Hydromechanics
163, 402, 474, 476f., 882
Hydrodynamics â Torricelliâs efflux law
165, 167, 405, 477, 481, 883
Hydrostatics â hydrostatic pressure â Archimedes principle
164â167, 180, 299, 403, 475â481, 491, 883
Hydraulics (applications of hydromechanics)
Engineering hydraulics before Leibniz â Castelliâs continuity law (1628)
164, 403
Vertical velocity distribution in a stream â Castelliâs postulated linear distribution (1660) â increase from the river bed to the surface
164, 403â405, 477, 882
Engineering hydraulics in Leibnizâs time â hydraulic engineer Cornelis Meyer â structure built in the river Tiber (before 1678) â earth wall, levee or dam â Meyerâs tract on fluvial navigation (1683)
164f., 404
Mechanics of fluids (Fluid mechanics)
Fundamental laws of fluid mechanics â quest for an exact rule to supersede Castelliâs â Leibnizâs skepticism (1690)
163â165, 403, 405, 882f.
Studies of fluid motion in open channels
164â166, 403, 476f., 882f.
Consideration of the flow of water around an obstacle in a stream â question of the velocity change downstream from the obstacle â Leibnizâs expectation of a negligible change
164f., 403f.
Ramazziniâs experimental investigation (1689â90) â his âTractatus physico-hydrostaticusâ on the springs / wells of Modena (1691)
163â165, 402f., 474â476
Ground (Geological) structure â ground pressures / temperatures â barometric / thermometric levels
99, 475f., 775
Ground water â water containment â water flows
475
Ascent of waters â artesian aquifers / wells â spring sources / origins
99, 163â165, 403, 474f., 775f.
Medical considerations â sources of pure water â water contamination / pollution
475, 501f.
Boccabadatiâs investigation of fluvial mechanics â based on practical experience in the floodplain near Modena â his observations and measurements (1690) along the Po tributaries Panaro (Scultenna) and Secchia (Gabellus)
164f., 403â405
Guglielminiâs investigation (1689â90) putting the laws of fluid flow on a new foundation â fundamental questions in open-channel flow
164, 167, 403, 476f., 481, 882f.
Considerations of canals / channels / flumes â of channel slope â of inclination of the water surface â of water pressure â of upper and lower layers
165â167, 476, 479, 481, 532, 872, 883
Guglielminiâs mathematical considerations â involving only proportions of homogeneous magnitudes â physical entities like gravitation and resistance (friction) not considered
476f.
Guglielminiâs work on the measure of flowing waters (1690â91)
480
Leibnizâs reception of the work â his review of the basic tenets â of the postulated parabolic velocity increase from the water surface to the channel bed
165â167, 405f., 477, 481, 883
Laws of fluid flow based on the fall (hydraulic head) of the channel â the slope or inclination of the water surface â the pressure of the water
167, 476f., 481, 883
Essentially an abstract mathematical approach â with gravitation and resistance forces not considered
167, 481, 883
The âscala fallacyââ based on a false assumption of the applicability of Torricelliâs efflux law in open-channel flow
165, 405, 883
Leibnizâs conclusion of the invalidity of the postulated velocity distribution in real rivers and canals
165f., 403, 406, 477, 883f.
Papinâs investigation (1690) of the âWurtemberg Siphonâ â his comparison of the efflux / effluent from an inclined water pipe at the side with that through an orifice in the bottom of a cylindrical container â under the same conditions, with equal cross-sectional areas of the pipe and orifice â the same hydraulic head
178, 478, 487, 886
Papinâs critique (1691) of Guglielminiâs work on fluid flow in open channels â of his fundamental theorem â of his postulated parabolic velocity increase
165â167, 405, 477, 481, 883
Guglielminiâs réplique (1692) in his âEpistolae duae hydrostaticaeâ and the âMiscellanea Italica physico-mathematicaâ
166, 478â480, 883
His treatment of Galileoâs laws of falling bodies â of their validity / invalidity in fluid flow â of fluvial flows in layers and the mutual influence of lower and upper layers â of fluid efflux velocities out of orifices, or openings in a cylindrical container â out of a pipe in the side wall or an orifice in the bottom
166f., 476â479, 481f., 883
Papinâs more detailed criticism (1695) â his consideration of analogies and differences between solid bodies and fluids
166, 479f.
Guglielminiâs reply to Papinâs criticism (1697) â his postulated parabolic velocity increase, from the water surface to the canal bed â based on Torricelliâs efflux law
165, 167, 405, 477, 481, 883
His consideration of the general applicability of the law to open-channel water flow over both horizontal and inclined canal beds â the general validity of Galileoâs laws of falling bodies in fluvial mechanics
167, 481, 883
His physical-mathematical tract on fluvial flows (1697) reflecting â both conditions in real rivers and canals and engineering practice â not mathematical abstraction
167, 481â483, 884
Issues / parameters of hydraulics / fluvial mechanics (1689â97)
Laws of fluid flow â fall or hydraulic head of a channel â slope or inclination of the water surface, channel bed â pressure of the water â gravitation forces â resistance forces
164f., 167, 403, 405, 476f., 481, 882f.
Curl or vorticity flows
167, 482
Streamlines â theory of streamlines â hydraulic grade lines â hydraulic / piezometric head variation
163, 402, 476
Engines, enginery. Machines, machinery, mechanization
Combustion / explosion engines
Combustion
160, 182, 212, 246, 413, 585, 710, 805, 850, 862, 878, 880
Explosion
94, 109f., 374, 543â546, 690, 862, 876, 878, 880
Explosion theory of gravity. see Physics
Gunpowder (explosion) engine â promptitude of the explosion â receptacle or cylinder â its lack of elastic play â danger of bursting / rupture â comparison of explosion and steam engines
146f., 690, 695, 862, 878, 880f.
Papinâs experimental results â revealing that the effect of gunpowder increases with the resistance to be overcome
148, 695, 881
Further research required regarding â the exploding gunpowder conglomerate â the means to control its expansion
148, 695, 881
Papinâs view that with further development the effect produced by a pound of water might exceed that of a pound of gunpowder
148, 693
Engines to power a vehicle and facilitate transport. see Transport
Military engines. see Engineering, Military Engineering
Mining engines. Mining
Pneumatic Engine (Vacuum Pump). see Instruments
Leibnizâs idea of a vacuum or pneumatic extractor
92, 421
Pneumatic engines or machines
Leibnizâs idea of a pneumatic engine to power a vehicle and facilitate transport
148, 881
His idea of a means of the â improvement of the contact between a piston and pump cylinder â making airtight or sealing the contact
148, 691f.
His idea of using mercury â similar to the use of water with wooden pumps in the corrosive environment of the Harz mines
148, 692
The air pressure inside the cylinder â arising from the expansion / dilation of water vapor â to be balanced by the mercury
148, 692
Components / parameters involved â the height / length of the Cylinder â the stroke of the piston
149, 692, 697
Mercury lubrication / sealing â reduction of friction losses
148, 691f.
Papinâs doubts about the functionality of Leibnizâs pump-lubrication /sealing idea with mercury â with considerable resistance losses anticipated from the alternating movement of the three interlaced tubes
148, 694f.
Leibnizâs understanding of the resistance effects in relation to pump performance â dependent on the length of the pump cylinder (or the stroke of the piston), the cylinder (or piston) diameter, and the square of the diameter
149, 697
Papinâs steam digester (1679â82) â his âengine for softening bonesâ (1681) â culinary applications / uses
243f., 348f.
Other applications considered. see Medicine, Diseases
Steam engines and pumps â superiority over a pneumatic engine: Papinâs experimental test â providing knowledge of the variation of the internal force of the air with heat and time
147f., 690f.
His steam pump â for raising water from a depth by the power of steam â capability to pump water only to a height of 70 feet
148, 693
His principle of the atmospheric steam engine (1690) â atmospheric pressure from the condensation of steam
147, 688
His experiments (1698) using the principle of the dilation / expansion of steam â principle of rarefaction more effective than atmospheric pressure accompanying condensation â use of both suction and compressive effects
147, 688f.
Agreement with Leibniz regarding Papinâs result that a small increase in the degree of heat leads to a greater effect
148, 693
Leibnizâs explanation of the connection between the strength of the expansion force and the height attained in lifting a body â an adiabatic expansion process, with loss of force through cooling during the expansion of steam
149, 696
Spirit-of-wine powered engines and pumps â a power source for a two-stroke piston engine â a combustion or rarefaction stroke â a compression or condensation stroke
182, 585f., 878, 880
Possible use of spirit of wine as a fuel (1695) â Leibnizâs conjectures â Papinâs experiments
182, 585
Prohibitive costs of the fuel â use of water as a seal over the piston â imperfect impermeability of the engine to water and to the spirit of wine
182, 587
Saveryâs steam pump â patent granted by the English Parliament â his tract âThe miners friendâ (1702)
149f., 698, 801f.
Leibnizâs indirect correspondence with Savery (1704) â Saveryâs invitation to Hanover
149f., 801
Papinâs high-pressure steam engine â his treatise on the design of the engine (1707)
150, 698
Papinâs design approved by Leibniz â rejected by Newton and Savery â Saveryâs plagiarism claims
150
Other applications besides the raising of water â propulsion using steam power. see Transport
Expansion of steam like the power of gunpowder â Leibnizâs penchant for gunpowder explosivity. see Power, Gunpowder
Expansion of other liquors or vapors â advantages of water vapor or steam â it being less explosive than gunpowder â water being readily available everywhere
147f., 686, 690
England
Anglo-Saxon Settlement
231, 841
Cambridge
2f., 119, 795
Cornwall. Mining
Truro
387
English crown â Kingâs council / court â Hanoverian accession, succession, court, etc.
4f., 9, 11, 13, 108, 169, 174â176, 199, 232, 271, 274, 313, 428, 484, 486, 508, 540, 715, 737, 790
English advances in science and technology
201, 499
English mathematics and mathematicians
11, 28f., 175, 500, 508, 517, 519, 522, 753, 793
English mining, mining engineers â including Kir(c)kby in Saxony
139, 201, 387, 499
English parliament
149, 790, 801
English physicians
90, 201, 247, 258, 265, 292, 350, 499, 738
Great plague of London (1665â66)
225
London
Pall Mall
288
Royal mint â Newtonâs appointment as warden (1696)
522
Royal Society of London. see Projects, Academies
St. Jamesâs palace
89, 289
Whitehall â Garden of Whitehall
580
Overseas Territories â Saint Helena island
782, 794
Oxford
40, 103, 117, 430, 633, 639, 788
Revolution of 1688â1689
192f.
Enlightenment
xivf., 142, 159f., 774, 885, 888.
Knowledge
Epidemiology. see Medicine
Erfurth
224, 838
Ethics
xi, xiii, 205, 744, 820
Ethiopia, Ethiopian
285
Ethnography, Etymology. see Peoples and Languages
Ethology and animal behavior. see Biology, Zoology
Europe, European
Continental European rivers â Danube â Leine â Rhine â Rhine-Meuse-Scheldt delta â Po and tributaries Panaro and Secchia
154, 164f., 403, 414, 5016, 663, 698
Evolution. see Biology, and also People and Languages
Experiments, experimentation, experimental approach
Enlightening experiments (âexperimenta luciferaâ) â enriching experiments (âexperimenta lucriferaâ)
208, 222, 835, 887f.
Experimental approach to complement reason â practical experience or experiment
50, 61, 74, 668, 523, 527, 863, 870
Experimentalist von Guericke â Schottâs âMechanica hydraulico-pneumaticaâ (1657) â von Guerickeâs âNew Magdeburg experimentsâ (1672)
90, 290f., 293
Experimentalist Boyle â pioneer of the modern experimental method â his experiments measuring the weight and elasticity and (spring) of air â his âNew experiments physico-mechanicallâ (1660)
90, 101, 219f., 291, 780
Real experiments â accumulation of experimental data
88, 288
Engineering experiments â Leibnizâs experiment (1696) with a pump assembly having a quadrangular cross section
153, 573
Newtonâs optical experiments. Physics, Optics
Spectacular experiments â luminescence and refulgence
205, 821f.
Light-emitting devices â based on different illuminant or luminescence phenomena
205, 821f.
âMechanoluminescenceâ â resulting from mechanical action on a solid â sparkle produced using hard sugar
205, 822
Luminescent objects or curiosa â based on Joh. Bernoulliâs demonstration (1700) of glowing mercury vessels (following shaking)
205, 821f.
Luminescent insignia â scepters, crowns, and a luminous showcase (âmuseolumâ)
205, 821
A luminous vial sent by Joh. Bernoulli â his âperpetual phosphorus vialââ presented by Leibniz at the Berlin court (1701)
205, 821
Hoffmannâs recipe (1701) for a fiery spirit (âspiritus igneusâ) â presented by Leibniz to the royal family
205f., 822
Thought experiments â pure-thought assumptions
59, 460, 871
Engineering thought experiments Leibnizâs engineering thought experiment â with force as the product of mass and velocity squared
531f.
Weights at the circumference of a horizontal wheel over a stream â powered by an undershot vertical water wheel in the stream â with cog-heel, lantern-pinion gear mechanism
62f., 529â534, 871f.
Consideration of â breadth and cross section of the stream â stream depth and inclination or surface area of the radial vanes â specific gravity of the water or other fluid
62f., 532, 872
Model of water consisting of balls or globules
63, 533
Physical / Mechanical thought experiments
Papinâs thought experiment â with force as the product of mass and velocity
62f., 532
Weights at the circumference of a horizontal wheel â rotation of the weights powered by falling weights â with rope, pulley (cylindrical drum) transmission
62, 529f. 534, 871f.
Variation of the horizontal wheel drive â of the horizontal wheel diameter â of the velocity of the weights carried
63, 534f., 871f.
Thought experiments on percussion and elastic spring â on the very nature of percussion and elastic spring â on resilience of elastic spring
59f., 66, 68, 70f., 461, 647, 649, 654, 660f., 872
Physical effects considered where absorbed force is ceded again
647
Substitution and surrogacy. Natural Philosophy
Papinâs thought experiment (1696) involving the collision of a larger with a smaller body, with an intervening spring â the smaller body is replaced at zero velocity by a much larger surrogate body â the surrogate body absorbs the impact of the larger body, and the elastic resilience, or recoil of the spring â alleged loss of force following the collision â no total transferability of force â violation of the law of conservation of âvis vivaâ
67, 651, 872
Leibnizâs interpretation of Papinâs thought experiment â replacement only admissible if the force lodged in the inner spring of the bodyâs particles be transferred to the surrogate body â complete transfer theoretically possible from a larger to a smaller body
67, 651, 872
Capability of a smaller body of arresting / reversing a larger body
67, 651f., 872
Capability of a smaller body of carrying off a larger body â where the latter is moving more slowly and precedes the former â without loss of velocity
81, 84, 763, 768
Discussion of the mechanism of substitution â practical execution of a substitution â assumption of an (almost) perfect hardness with a total transfer (almost) of force to the spring
67â70, 459f., 651â659
Impact of recoil possibly not central / off-center â resulting in a possible rotation of the body â diminution of resistive potential
68, 652f.
Papinâs thought experiments (1697) to demonstrate gain / loss of force in substitutions â equivalence / non-equivalence of a substitution and separate collisions of the bodies involved
68â70, 79, 652â659
Upholding / violation of the conservation of force requirement
69, 657
Leibnizâs explanation of the substitution process based on a âvis vivaâ
67f., 70, 651, 653, 658
Papinâs explanation of the process based on a âvis mortuaâ
67, 70, 651, 658f.
The dead force concept to establish which bodies bring each other to a standstill
71, 658, 661, 664, 761
The living force concept to establish which bodies produce the same absolute effect
67, 650, 658f., 661
Central points of Leibnizâs interpretation (Dec. 1697) â bodies of different magnitude might have the same quantity of force â a substitution is possible so that the quantity of force of the bodies is conserved
70, 659
Leibnizâs thought experiment (Dec. 1697) about the collision of a body against two other bodies â the first body is then replaced by a wall â each of the other two bodies impacts a side of a spring, whose other side is attached to the wall
70, 660
Each of the other bodies is stopped by the wall even though they have unequal forces â according to Leibnizâs definition of absolute / living force
70, 660
Two-body / three-body collision thought experiments â colliding spheres or balls â instantaneous or momentary collisions â total transfer of the quantity of motion â conservation of the quantity of motion â sum of the quantities of motion
66f., 71â73, 77, 80â85, 648â658, 663â666, 761â770, 872, 874
Head-on collision of two bodies â the larger body (at rest) and the smaller body (in motion) â an apparent contrariety where the smaller body could carry off the larger one
84, 768
Two-body collisions of âstrongerâ and âweakerââ possible linguistic paradoxes
70, 661
Leibnizâs definition of âstrongerâ and âweakerââ the âweakerâ yields to the âstrongerâ â the stronger might be forced into reverse while the weaker continues along its path
70, 659, 661
Collision of two bodies with velocities inversely proportional to their masses â resulting reversal of the motions
66, 649
Oblique / diagonal / slanting impact of three bodies â simultaneous or separate impacts of the three bodies â skew angle of inclination of path â change in the direction of oblique impact â oblique impact of a body against two others at rest
64, 66, 73f., 81, 536, 648, 664, 666f., 669, 764, 873
Velocities of the colliding bodies are represented by the sides or diagonal of a square â following the diagonal collision, the first and second bodies move off along the extended sides of the square â the third body comes to rest at the corner â impact with partial or total force transfer
72â74, 78â81, 84f., 655f., 664f., 668f., 757, 759, 761f., 763, 768, 770, 873
Experiment in reverse â the first and second bodies come to rest at the corner â the third moves back along the diagonal
72â74, 664, 667f., 873
Leibnizâs and Papinâs different interpretations of the diagonal collision
65f., 68, 70â73, 79, 81, 652, 658f., 661f., 664, 759, 873f.
Papinâs consideration of the resistance encountered in collisions (November 1698)
74, 668
Leibnizâs idea of geometrically-compounded resistances â resolution into components possible (November 1698)
74, 668f.
Papinâs consideration of obliquity/ skewness in collisions (December 1698)
74, 669
Leibnizâs idea of a replacement of spheres by long thin cylinders (July 1699) â rejected by Papin
84f., 768, 770, 874
Papinâs explanation of the three-sphere oblique-collision experiment â separate versus simultaneous collisions with the latter impacts being shorter and less forceful â example of a non-simultaneous impact of two elastic spheres against an identical third sphere â one encounters a chord rather than a diameter of the third sphere
69, 73, 79, 657f., 667, 759f., 873
Papinâs understanding that there is no total force transfer in the collisions â the striking bodies do not come to rest, but continue in their paths following impact
73, 667
His position opposed to that of Leibnizâs assumption (March 1699) of a perfect hardness â and of an instantaneous collision of the three balls
79f., 759â761
His insistence the total transfer (and conservation) of the quantity of motion, would of necessity result in a âperpetuum mobileâ
80, 761f.
His view (April 1699) that even assuming a perfect hardness, the sum total of the quantities of motion would, following the collision, be less than before
81, 762
Location and Time â alterations of location and time
77, 681f.
Papinâs thought experiment (January 1698) about a two-body collision â as seen by two observers at two different locations in space â firstly, at an air-free and gravity-free location, where equal quantities of motion are observed, and where equal forces are likewise observed â secondly, at a location where a hailstorm is raging â the hail particles are unimaginably small and their velocity is extraordinarily large â the bodies are of equal magnitude, and move against the hail stream before losing their movements and falling back â the traversed distances are found not to be proportional to their quantities of motion â doubling the quantity of motion results in a quadrupling of the traversed distance â for the first observer (Papin) the hailstorm accounts for the result â the second observer (Leibniz) has to introduce a new force to explain the outcome
71f., 662f.
Leibnizâs reply (January 1698) â his interjection on âcamp thinkingâ â his view of Papinâs interpretation as resulting of necessity in a âperpetuum mobileâ â with an infringement of the principle of the equality of cause and effect
72, 663f.
Leibnizâs own thought experiment â based on the law of âvis mortuaâ and rules for the composition of movements â his interpretation applicable both in terrestrial gravity, and in a space devoid of gravitational force â his assessment of Papinâs âhailstormâ, as being relevant in relation to the quantity of motion â and involving a loss of movement during the ascent, and gain during the descent
72f., 664â666
Ideas of an ultimate decisive physical experiment to settle the controversy between Papin and Leibniz â Papinâs idea of such a physical experiment (August 1698) â Leibnizâs call for an experimental decision (September 1698) â thus an experimental proof to compliment reason â reference to previous agreement of reason and experiment â Papinâs retraction of the experimental option (October 1698) â decision to revert to reason
61f., 73f., 527f., 666â668, 871, 873
Leibnizâs physical thought experiment (March 1700) to explain mercury column changes with the weather. see Instruments, Barometer
Leibnizâs and Joh. Bernoulliâs thought experiments â thought and physical models for water and air (1699â1700)
101f., 781f.
Florence. see Italy
Force. see Natural Philosophy, Physics
France
Avignon
324f.
Cayenne (French Guiana)
197, 324
Dijon
324f.
La Rochelle
236, 732
Neuf Brisach en Alsace (Neu-Breisack)
150, 802
Paris â Académie des Sciences. see Projects, Scientific, Educational Projects
Observatoire de Paris
381
River Seine
397f.
Saint Germain
397
Versailles
165, 266, 397f.
Frankfurt am Main â Location of the German diplomatic conference on reunifications
97, 184, 198, 298, 316, 325, 381
Frankfurt an der Oder
156, 204, 702, 818
Furnaces, forges and kilns
Experiments / investigations with melting furnaces
Leibnizâs first experiments with melting furnaces â his cooperation with Brand (Summer 1679) in the investigation of phosphorus
159, 707
Investigations with ovens built by Johann Daniel Crafft
159, 707
Papinâs glass-kiln development (1697â98)
158, 704
His improvement of a newly-developed oven â glass melting process using the âHesse pumpâ â scaled-down process and envisaged large-scale version â construction of a laboratory and of a new oven
158f., 704f., 706f.
Papinâs series of experiments â his new melting furnace intended solely for the production of iron retorts or alembics â use of an improved centrifugal (Hesse) pump
157f., 706
Leibnizâs view of the importance of glass melting for optics â and the production of polished sheet or mirror glass
158f., 704, 706â708
Tschirnhausâ laboratory for precious stones (1700) â his grindery or grinding shop for precious stones and jewels â his private laboratory on his estate in Kieslingswalde
160f., 806, 808
Blast, cementation and reverberatory / reverberation furnaces
Late 17th / 18th century innovations â used for tempering and annealing bar or rod iron
160, 805f.
China or porcelain ovens â also for glass ovens in manufactories
160, 806
Leibnizâs views on engineering innovations in general â the difficulties in realization and implementation â the necessity of large-scale trials to counter a widespread skepticism towards innovations
161, 808
Blast furnaces
Papinâs new blast furnace â description and drawing (October 1698) â showing air passage above and below burning fuel (wood), using a centrifugal (Hesse) pump
158f., 706â708
Blast and suck operation by means of a ventilator pump â blast and suction air regulation â blowing flames to the melting crucible â use of a smokestack with suction effect â height-limit of the smokestack (2 feet)
158, 706f.
Blast and suction air regulation â simultaneous drawing of flames to the crucible
158, 706f.
Heat impact of the fire â use of a heating plate for extraction of glass melt through an opening in the upper oven wall
158f., 707
Glass melt from the furnace â suitable for the production of mirrors, window glass, hollow cylinders, iron products
158, 707
Leibnizâs thoughts regarding the process of glass melting â his assessment of Papinâs innovation
159, 707
Control / regulation of fire intensity attained â possible alternatives or improvements â the use of ordinary bellows â abandonment of a special extraction plate â melting operations possible on such a plate â desideratum of rendering superfluous the polishing of plates, over which the molten glass was spread
159, 707â709
Leibnizâs doubts about the novelty of Papinâs plates â Papinâs belief in the superiority of his furnace method â based on his observations (in 1681) on the island of Murano (near Venice) â involving the moving of a large stone into an oven â the spreading out of molten glass over the stone using iron spatulas (or palette-knives) â the removal using a draw-plate or drawing die
159, 708f.
Papinâs own corresponding method (of 1698) for the production of plate or mirror glass â with molten glass being drawn onto oven plates
159, 707f.
His key innovation regarding the heating flame â its passage both above and below the molten material
159, 707f.
Reverberation furnaces â contact specifications for processing ores â contact with the fuel prohibited â contact with combustion gases allowed
160, 805
Example of copper smelting at the Falun mine, Sweden â involvement of foreign smelters and chemists
159f., 804f.
Levanto and his smelting process â essentially a process for roasting or calcination in a roasting oven or calcination furnace â fueled with wood (twigs or branches) â the production of roasted blende by calcination, and subsequent melting in an air furnace
159â161, 804â806
Failed trials of the process, by both Levanto and Kunckel von Löwenstern
160f., 804â806, 808
Leibnizâs proposal for operation of the two furnaces (1699) â with a gradual powering-up of the air furnace, but dependent on the consistency of the material
160, 806
Galenism, Galenist
252, 741.
Medicine
Gardens. see Engineering, Garden Design and Architecture
Geography, geographers
231
Cartography, cartographers
10, 430
Geographical explorations of the coasts of the North Sea and the Baltic Sea â reported to Wallis (1699)
229f., 840f.
Orient, orientalism, orientalists
10, 208, 231, 430, 811f., 827
Geology, geologists
xv, 227
Geological and earth science â geological research and studies â geological, geomorphological, cosmological, and cosmogenic theorizing
xiv, 226f., 229f., 277, 344f., 419f., 475, 840, 862, 891f.
Geological, geomorphological theories
Earth history/ historiography â history and form of the earth
235, 723f.
Leibnizâs ideas on earth history â origin and history of the earth â his posthumously-published âProtogaeaâ
164, 227, 229, 419f., 475, 723, 725, 892
Burnetâs âTelluris theoria sacraâ (1681/89) â his âDoctrina antiqua de rerum originibusâ (1692)
228, 724f., 897
Büssingâs critique of Burnetâs earth history â a kind of literary history (Büssingâs view)
725, 897
Büssingâs âDissertatio Anti-Burnetianaâ(1695)
228, 724, 897
Whistonâs âNew theory of the earthâ (1696) â his postulated role of comets in earth history â his opposition to Burnetâs new theory of the earth
228f., 725, 897
Deluge â the deluge in earth history â Biblical narrative and interpretations â questions of its historical veracity
xiv, 229, 726, 898
The Burnet controversy â explanatory models of the deluge â Burnetâs account â Büssingâs scenario
229, 725f., 898
Leibnizâs skeptical view
229, 726
Antediluvian form of the earth â upsurge of subterranean waters
229, 726
Postdiluvian form of the earth â subsidence / settlement of the surface â possible fissures in the crust â possible return of flood waters into subterranean cavities
229, 726, 898
Temporal changes of the earthâs surface
229f., 840f.
Geological formation history of coastlines
230, 840f.
Leibnizâs interest in the geological formation history of the English channel â intended as a means of establishing temporal changes of the earthâs surface
230, 840f.
Geographical / geological interpretations of mythology â Odysseusâ supposed journey in northern Europe â Rudbeckâs hypotheses and rejoinders (1699)
230, 841, 898
Explorations of European coasts â of the North sea and Baltic sea (1699)
229f., 840f.
Questions of the geological configuration of the European Atlantic coastline â the coasts near Calais and Dover (1701)
230, 840f.
Pre-history/ pre-historical finds â Leibnizâs discovery of fish fossils in shale (1683)
227, 419, 891
His studies / views concerning earth history (1684) â on the formation of rocks and minerals (mineralogenesis) â on subterranean formation of minerals by fire â attributed to spirits trapped in the mines
227f., 420f., 892f.
His deviant views to Agricola, Descartes, Steno
227, 420, 892
His critique of Descartes â of the his lack of practical experience in mines â his obsession with written sources
228, 421, 892
Mineral ores from the Ilmenau mines (Heyn, 1690) â shale and limestone with fossilized plants
228, 421, 891
Leibnizâs history of the house of Welf â the geological history of the Welf territories â the natural history of the Harz district
226f., 419, 892
His interest in the cave âBaumannshöhleâ (1687)
227, 419, 892
Tentzelâs report on mammoth fossils (1696) â found at Gräfentonna (or Tonna) â having been changed into mineral stone in the wet sand
235, 239, 729f., 846.
Biology, Zoology
Mineralogy, minerals. Chemistry
Magnetic minerals â Lodestone
549
Mineral crystals / Crystalline materials
Amber
211, 226, 334f., 344, 582f., 891
Asbestos mineral
127, 561
Iceland crystal / Iceland spar
121f., 124f., 376f., 468, 554, 556f.
Jasper (variety of quartz)
806f.
Porcelain (ceramic material)
127, 160, 191, 561, 591, 806
Talc / Talcum (mineral)
127, 416, 561
Mineralogical research / studies
226, 344, 891
Mineral ores â formation of rocks
226f., 343, 420, 891f.
Origin and formation of minerals (mineralogenesis) â formation of ore deposits (in mines)
226â228, 343, 420, 891f.
Processing procedures for ores
226, 344f., 891
Ores from regions of geological interest â in East India, the Harz mountains, Muscau (near Görlitz, Saxony), regions in Poland
226, 892
Paleontology
225, 342, 419, 723, 840
Fossils â fossils found in mines â animal / body fossils â fish fossils
226f., 231, 419, 730, 891
Catalog of British fossils (Lhuyd, 1699)
231, 841
Queries about the origin of an amber deposit (1680)
226, 344, 891
About fossilization specimens in Mansfeld slate (1681)
226, 344, 891
About a goldmine on Sumatra (1681â82)
226, 344, 891
Geometry. see Mathematics
Germany, German nation â prejudice aginst the Germans
90f., 292
German empire. see Holy Roman empire
Integration / Unification
184, 316
Prosperity of Germany
184, 222f., 315f., 836
God, Divine Creator
xivf., 48, 229, 726, 753f., 798, 898
Görlitz. see Saxony
Gravity, gravitation. see Natural philosophy and physics
Greece, Greek â classical mythology â the argonaut Zetes
224, 230, 621, 837, 841, 897
Habsburg dynasty
189, 408
Halberstadt
254, 855
Halle
198, 204f., 262, 325, 574, 605, 820
Leopoldina. see Projects, Scientific, Educational Projects
Hamburg
10, 152, 185, 192, 200f., 209f., 221f., 228, 253, 271, 318, 328, 331f., 377, 401, 410, 428, 499, 591, 597, 645, 724f., 831, 833â835, 854, 890, 897
Hameln â the French émigré community
253, 698, 854
Hanau (Town in territory Hesse)
236, 732
Hanover
ixf., xiii, xv, xvii, 2, 4â9, 11â13, 15, 17â19, 21, 25, 35, 52â54, 57, 87, 89, 102, 104f., 121, 128f., 134, 142f., 145f., 148â150, 153â156, 162, 165, 168f., 171, 173â175, 185, 187, 189, 192, 195, 197, 200, 202, 208â211, 213, 218f., 226f., 229, 242f., 250f., 253, 275, 278f., 287, 297, 301f., 312f., 322, 327â329, 331, 333, 344f., 347, 356, 358, 365, 367, 376, 395, 398f., 404, 408, 412, 416, 418, 428, 431, 437, 451, 454f., 477, 485f., 508f., 562f., 581f., 583, 591, 695, 608, 626, 690, 700f., 786, 801, 853, 863, 880, 885f., 893
Hanoverian court / ducal / dynastic / electoral (1692â1806)
4, 5, 9, 108, 169, 174f., 199, 214, 216, 224, 232, 244, 261, 271â274, 290, 307, 313, 318, 330f., 339, 342, 359, 394, 428, 484, 486, 505, 508, 540, 563, 565, 567, 601, 610, 617, 698, 700f., 725, 737, 744, 775, 801, 839, 853, 897
Electoral gardens at Herrenhausen
153â156, 698â701, 813
Town of Hanover â its ânew townâ district
154f., 698f.
Location Linden, near Hanover
162, 812f.
Location Wunstorf, near Hanover
226, 344, 891
Harburg (south of Hamburg)
185, 318
Harz mountains. see Mining
Helmstedt â University of Helmstedt (âAcademia Juliaâ)
14, 92, 171, 201, 212, 216, 219, 235, 242f., 254, 275, 294, 337, 345f., 597, 619, 701f., 721, 729, 744f., 814, 834, 855, 886
Hesse-Kassel, Landgraviate of
58, 147, 161, 157f., 170, 174, 178, 180f., 201f., 207, 484, 487, 492f., 578f., 597, 687, 704f., 802, 829
Kassel
10f., 59, 173f., 178â180, 201, 236, 253, 430, 483f., 487, 490, 492, 508, 597, 713, 732, 853, 886,
Library, archivists / librarians in Kassel
10, 173, 430, 483
Marburg
58, 178f., 233, 422, 458, 487f., 490, 646, 886
Hildesheim
10, 156, 428, 700
Heyersum (near Hildesheim)
156, 700
Holstein-Sonderburg-Plön
193, 592
Holy Roman empire
12, 225, 508, 791, 839.
Vienna
Hungary
139, 189f., 388, 408f.
Economics and Mining
Habsburgsâ re-conquest (1683) â colonization of certain regions
189f., 408f.
Hypotheses (in the sciences)
81f., 85, 96, 103, 108f., 119, 123, 228, 230, 234, 264, 266, 366, 375, 383, 421, 466, 469f., 473, 507, 539f., 542f., 547f., 552, 554, 556f., 622, 649, 653, 727, 737f., 743, 763f., 771, 774, 791, 836f., 841, 875â877, 892, 896, 898
Illumination â urban illumination â street illumination with oil lamps
188, 407.
Economics
India, Indian â Indian seed
89, 290
Infinite
28, 42â44, 58, 73, 82, 109f., 224, 234, 438, 478, 516, 542, 546, 554, 623, 638, 640, 643, 646, 666, 727, 738, 746, 764, 838
Infinitely small
31, 36, 44, 66f., 234, 523, 623, 627, 649f., 653, 727f., 746, 869
Infinity
42, 55, 162, 234, 286, 457, 515, 554, 642, 685, 727f., 812, 830, 870
effective infinity and infinite divisibility
55, 457
Infinitesimals. see Mathematics, Calculus
Inquisition. see Churches
Instruments
Astronomical instruments â astrolabes, globes, quadrants, sundials
199
Balances â beam balances â precision balances
96, 100, 293, 374, 778
Barometer
Mercury barometer
474, 495
History of the barometer â the Torricellian experiment
100f.
Discussions (1697â1700, with Ramazzini, Schelhammer) about the motion of mercury in the Torricellian tube
474, 495, 775â778, 824
Leibnizâs explanation of barometric phenomena â his balance instrument
777f.
Experiments, thought experiments
Constituent parts and operation â horizontal beam balance â water pipe with floating ball â equilibrium state maintenance: Water pipe with sinking ball and equilibrium state infringement
100, 778
Air-pressure measured by the height of fluid column â the pressure-height problem â influence of weather changes on the rise and fall of the mercury column
100f., 776f.
Discussion with Hoffmann (1700â1701) â Leibnizâs explanation of the phenomena and of the operating principle of the barometer in the Torricellian tube
100f., 778f.
Hoffmannâs barometric-meteorological observations
206, 823f.
Emulation / simulation of rain drops in air
100, 778
Solution of the anomaly / paradox as to why serene air is lighter than pluvial air
294, 778
Other barometer forms
Aneroid barometer precursor
100
Portable barometer â construction of a portable barometer
(1697/98)
99, 776
Static barometer
91, 293
Hygrometer
99, 258, 299, 500
Optical instruments â Lenses and mirrors
Lenses, lens optics â glass lenses
37, 126â130, 158, 160, 187, 302â305, 322, 379, 561f., 704, 807f.
Mirrors, mirror optics
126â128, 158f., 306, 331, 378, 471, 561â564, 704, 706â709, 753
Construction and improvement of Copper mirrors
126
Concave mirrors
126â128, 158, 306, 378, 471, 561â564, 704
Convex mirrors â production (Nuremberg, 1695)
128, 564
Tschirnhausâ lenses and mirrors â his commitment to their improvement / perfection â his concave copper mirrors
126f., 378, 471, 561
Display of a mirror of his at Amsterdam (July 1695)
564
Convex glass lenses (burning glasses) â manufacture of convex lenses
127f., 158, 160, 561â563, 704, 807
Tschirnhausâ new machine (1694)
127, 561
His processes for making glass spheres (beads) from paper ashes and vegetable matter â also from molten porcelain, asbestos, talc (talcum)
127, 561
His burning glasses with the capability of burning a mark in wood under water â and of rendering molten materials like pitch, sulfur, colophony (rosin resin) â even of reducing of metals to a glass form â like gold to ruby glass
127, 562
Advantages of his convex lenses over concave mirrors, namely high effectivity â reduced weight and size â easy transportability â more enduring polish or glaze â dirigible / directable refracted rays â their being aimable / directable at fluids and powders
127, 562
Sale of his optical products â proceeds from sales intended for the establishment of a fund for the advancement of the sciences
127f., 562
Demonstrations of his burning glasses (and a concave mirror) â at the court in Hanover (Fall 1694) â in Amsterdam (December 1694)
127f., 563
His meeting with Huygens (1694)
128, 563
Huygensâ preference for glass concave mirrors with a diameter of up to 4 feet â having a coating on the back side and a small plane mirror near the focal point â with rays being directable to combustible material
128, 564
Microscopes and telescopes / Microscopy and telescopy Huygensâ âDes telescopes et des microscopesâ
125, 471
Tschirnhausâ practice-related optical investigations â his improvement of the illumination of instruments â his envisioned breakthrough in optical instruments â possibly akin to Galileoâs âStarry messengerâ (1610)
126f., 472
Limits of resolution capacities of optical instruments â objective of approaching these resolution limits
127, 472
Microscopes, microscopists
Desired features of microscopes â enlarged field of view â light weight â magnification
472
Leeuwenhoekâs microscopic observations / investigations â presentation to Leibniz (1676) â his commitment to microscopic research â his reports sent to the Royal Society â his methods and instruments â his (secret) observations â his observational methods and their preservation for posterity â the planned written bequest and their value for medicine and the medical arts
128â132, 301â306, 682â685
Spherical or globular (single lens) microscope â developed by Jan Hudde â improved and employed by Leeuwenhoek â subject of Leibnizâs interest (1678)
130, 304f.
Microscope without a lens (Tschirnhaus, 1685) â held in proximity to the observing eye
126, 378f.
Observation through a slit (Scheiner, 1619)
126, 379
Compound microscope (with two lenses)
130, 305
Thermometer
Construction of the thermometer â thermometer (in Leibnizâs Dynamica) â use in medicine
52, 99, 207, 258, 299, 365, 451, 500, 775f., 824, 826
Vacuum pump â development of the vacuum pump (pneumatic engine). see Engines
Invention â the art of invention or discovery (âars inveniendiâ)
176, 631, 714
Discoveries and innovations
135, 309, 402
Mechanical inventions and innovations
189, 408
Scientific and technical inventions
127, 140, 149f., 158, 177f., 180, 182, 185, 199, 205, 209, 214, 244, 291f., 304, 317f., 323, 327f., 332, 348f., 383, 391, 408, 413, 460, 488, 491â493, 572, 577, 587, 689, 697f., 703, 707, 709, 717, 800â802, 805, 809, 820f.
Ireland
x, xiii, 193, 231, 288, 291, 332, 841
Cork
288, 291, 780
Donegal (Inishowen peninsula)
xiii, 232
Dublin â Dublin Philosophical Society
125, 235, 281, 470, 729â731
Dungarven (County Waterford)
291, 780
Irish Protestant ascendancy
xiii
Williamite campaign (1690). see Wars, Jacobite / Williamite War
Italy
2, 7â10, 21f., 33, 37, 54, 58, 103â105, 141, 163, 166, 200, 220, 244f., 249, 251f., 258f., 263, 327, 356f., 366, 368, 370, 394, 402, 424, 428, 430f., 433, 456, 458, 462, 466, 473, 476f., 480, 499â502, 601, 605, 612, 620f., 630f.,722, 735, 741, 839, 867, 882, 888f.
Bologna
8, 131, 164, 260, 357, 403, 425, 473, 477, 504, 882
Ferrara
8, 357
Florence, Tuscany, Florentine court â Grand Ducal Library
8, 10, 12, 23, 33, 52, 54f., 131, 169, 176, 213, 220, 224, 235, 245, 248, 357, 365, 412, 423, 430, 433f., 443, 456f., 473, 483, 509, 525, 560, 582, 620f., 713, 723, 729f.,735, 839
Florentine problem. see Mathematics, Curves and Surfaces
Genua
265
Italian Renaissance â art, artists and painters
132, 477, 683
Leibnizâ Italian journey (âiter Italicumâ)
2, 7f., 21, 263, 356f., 366, 370, 424, 466
Lombardy
504
Milan
809
Modena
8, 99, 163â165, 190, 201, 206, 255, 258â263, 357, 403f., 410, 425, 474â476, 500f., 503f., 506, 604, 775f., 858
Measurements in the subterranean springs and wells â barometric and thermometric investigations â barometric and medical ephemerides (1691)
99, 163f., 255, 261f., 403f., 474f., 502â506, 604, 775f.
: Medicine, Physics, Geophysics
Military camp at Spilamberto, near Sassuolo, South of Modena
260, 503
Naples
809
Padua
131, 243f., 246, 425, 601f.
Pisa
33, 620
River Po and tributaries (Panaro and Secchia)
164f., 259, 403â405, 501f.
Rome
8, 104, 114, 131, 164, 357f., 366f., 424f., 452f., 473, 783, 785
Accademia Fisico-Matematica Romana
104, 367
Pope, papacy, pontifex, pontifical â Papal Calendar Congregation
105, 115f., 368, 783f., 786, 789
Vatican, cardinals, curia
114â116, 783â786
Tiber (River)
164f., 404
Venice (republic of Venice) â Murano (island near Venice)
8, 51, 54, 105, 159, 190, 200, 213, 217, 263, 327, 357, 364, 367, 412, 415, 424f., 455, 709, 737, 807
Sicily
740
Jakarta / New Batavia (Indonesia)
248, 351, 733
Jena
49, 120, 202, 212, 337, 597f., 729, 800
Astronomical observatory
120
Jesuit order of priests
8, 50, 66, 96, 178, 236, 248, 276, 291, 357, 375, 423, 648, 732, 756
Journals
Acta Eruditorum (Leipzig)
7, 16, 19â24, 26f., 30â32, 35, 38f., 41f., 44â47, 55â60, 91f., 95â97, 102f., 105, 107, 109, 112f., 120f., 126, 131, 147, 166f., 170, 176, 178, 187, 204, 226, 228, 243, 257, 280â282, 286, 292, 295, 297, 300, 342, 348, 353, 359â370, 372, 374â376, 378, 406f., 419, 431â436, 438â443, 445, 458â462, 466f., 477â481, 487f., 510â513, 515f., 521â525, 542, 559f., 620, 625, 630, 632â638, 640â643, 645â648, 723f., 747, 749f., 751f., 820, 864, 866, 869, 875, 883, 886, 891, 897
Giornale deâ Letterati (Modena)
33, 621,
Histoire des Ouvrages des Savans (Rotterdam)
33, 621, 867
Journal des Sçavans (Paris)
25, 34f., 44, 52, 54f., 123, 153, 178, 198, 235, 243, 281, 325, 453, 457, 510, 572, 622, 730
Miscellanea Curiosa Medico-Physica (Halle)
198, 236, 243, 248f., 260f., 325, 346, 351f., 423, 502, 504, 732f.
Nouvelles de la République des Lettres (Amsterdam)
20, 56f., 361, 363, 646, 864
Philosophical Transactions (London)
35f., 38, 46, 88, 91, 129f., 324, 289f., 293, 379f., 624, 629f., 632f., 727f., 750, 868
Jews, Jewish, Judaism â Dutch Jews
186, 320
Jurisprudence, jurist, juror
xif., 11f., 145, 275, 508, 567, 571
Kassel. see Hesse-Kassel
Kiel
116, 785
Knowledge
Theory and practice â Leibnizian perception (principle) â unity of theory and practice (âtheoria cum praxiâ)
15, 175, 199, 201, 597, 828
Early-modern consequences for science and technology â a âcraftsman-scholar cleavageâ â relation of the scholar / scientist to the artisan / craftsman / practitioner â apprentices and students
132, 167f., 198â200, 238, 683, 885
Professional group identities â âtheoreticusâ (savant, Gelehrter) â âpracticusâ (artiste, Künstler) â âempricusâ (artisan, Handwerker)
167f., 198f., 255f., 885
Mathematical practitioners â practical mathematics and artisanal activity
199, 862
Artisanal enlightenment â artisansâ workshops â instrument makers â minters of coins (moneyers)
9, 143, 199, 358, 565, 885
Physicians and surgeons â practical and artisanal activity â prosthetic technology â making artificial limbs
199f.
Universal (pansophist) knowledge
222, 834
Laboratories
57, 158, 160f., 189f., 213, 218f., 221f., 253, 395, 408, 410f., 416, 457, 705, 721f., 735, 806â808, 832â834, 853, 889f.
Languages. see Peoples and Languages, Grammar, dialectic, rhetoric
Learning â organization of learning
230
Republic of letters â world of learning
47, 272, 684
Academies, academic institutions, universities. Projects, Scientific, Educational Projects
Outside the academy â non-academic science and engineering â professional scientists and engineers
89, 157, 885, 896
Learned and scientific societies
12, 197, 508
Leipzig. see Saxony
Life Sciences. see Biology
Light. see Physics
Linden. see Hanover
Logic
xi, xiii, 205, 286, 744, 820
London. see England
Lüneburg
99, 139f., 325, 387, 391
Dynasties, House of Brunswick-Lüneburg
Machines, machinery, mechanization. Engines, Enginery
Calculating machines â development as part of a larger project for the mechanization of thought â interdependency of philosophical principles and mathematical and scientific results
169, 314
Conception of a general script to enable (for every topic) calculation and proof â like in algebra and arithmetic â found in Leibnizâs correspondence with English contacts â like Clüver, Haak, Hooke (1673â1680)
169, 314
17th-century calculating devices â calculator of Pascal (âPascalineâ) â improvements by Grillet
170, 578, 582
Calculating cylinders of Schott and Petit
170, 579
Morlandâs machine type and variants â use of slide rules and Napierian logarithms
170, 578
Exemplar in possession of Karl of Hesse-Kassel
170, 578
Machine constructed by Haes himself (1680s) â the Haes adding machine (1695) â adapted for German coinage / accounting
170, 579
Machine made by Cotterell
170, 578f.,
Tschirnhausâ machine â gearless machine conceived by him (1694)
170, 579
Leibnizâs calculating machines â his four-function calculating machine â with decimal entry and result positions â with addition / subtraction and multiplication / division functions
168â173, 312f., 483, 578â583, 885
Versions of Leibnizâs machine
His three-place wooden demonstration model â presented to the Royal Society (February 1673) â his contact with Moreland (February 1673)
168, 579f.
His improved metallic version of the machine â with six entry and twelve result positions â constructed by Ollivier and presented to the Académie des Sciences (January 1675) â completed in Hanover (mid-1680s)
168, 312f., 580f., 885
His âolderâ machine â with eight entry and twelve result positions â completed by Kölbing in Hanover (1694) â presentation to visitors Tschirnhaus (Fall of 1694) and Burnett of Kemney (April 1695)
578f., 581â583, 814, 885f.
Intelligence concerning the machine sent to:
France (LâHospital, Toinard) â LâHospitalâs commission (1694) for a duplicate of the machine
170f., 581f., 885
Holland (Crafft, Huygens)
170, 582, 885
Italy (Bodenhausen)
171, 581f.
Difficulties in completing the construction â lack of skilled craftsmen in Hanover â interest (or involvement) of Dutch and French clockmakers
168f., 171f., 312f., 581, 816â818, 886f.
Leibnizâs second or âyoungerâ machine â with eight entry and sixteen result positions â report sent to Bodenhausen (1695) â commencement of construction work by Scherp in Hanover (1694/95)
171f., 583, 814â816
Transfer to Helmstedt (March 1700) â construction / repair by Warnecke under the direction of Wagner â with the âolder machineâ as a model â problems of the interaction of the parts of the âyoungerâ machine
171â173, 583f., 814â817, 886
Wagnerâs admiration for Warneckeâs efforts, and disdain for his predecessor Scherp â issues of expenditure, waste, and possible deceit in the overhaul and reworking of components â Scherpâs imprecisions, and his machine construction defects
171â174, 814â817, 886
Leibnizâs praise (1701) for his former clockmaker Kölbing
172, 816, 886
Components of the âyoungerâ machine â the carriage, decimal carrying mechanism, pentagonal disks, drawing spindle, rotary disk, upper part of the machine â completion of parts reported (spring time 1701)
172f. 814â817
Warneckeâs efforts for improvement of the âolder machineâ in Helmstedt (from July 1701)
172, 816
Wagnerâs calculation examples â addition and multiplication â removal of errors and incomplete calculations
172f., 816f.
Operation of the value transfer mechanism between the setting mechanism (input) and the result mechanism (output)
173, 817
Correction procedure by means of a horizontal positioning of the pentagonal disks â manual through-connection of incomplete positions and a manual rotation of the crank
173, 817
Removal of errors in both machines â by means of precision-engineering alterations
173, 817
Suspension of work on the calculating machines â due to grave illness of the clockmaker â recovery and resumption of the work (end of 1701)
173, 817
Interest of correspondents in Leibnizâs calculating machine â commissioning of duplicates
170f., 581f.
Machines as machine-equivalent figures for calculation
151, 283, 882, 884
Mathematical drawing machines â apparatus or machine for drawing mathematical curves
169f., 483
Pneumatic machines
148, 691f.
Engines
Threshing machines â machine at the location Aerzen (in the Weser Uplands) â Voigtâs drawing of the threshing machine (1699)
161f., 812, 809f.
Explanation of its battering or threshing mechanism â its manner of advancing
161f., 809â812
An operator turns a camshaft to move the thresher-cylinders â threshers were attached to a carriage, which was moved or pedaled along the threshing-floor â use of a rack and pinion gear mechanism
161f., 810â812
Leibnizâs suggestion for optimizing the mechanism â replacing the cogged wheel-lantern pinion system with a pulley system
161f., 810f.
Leibnizâs idea of making use of water and wind â an alternative power sources to manpower â as a prime mover for the threshing-machine
162, 813
Corresponding requisites â a water raceway â a pumped-storage system with reservoir â availability of a wind mill
162, 813
Another threshing machine reported at the location Linden, near Hanover
162, 812f.
Mechanization
xiii, 162, 169, 186, 314, 321, 811f.
Mechanization of the world picture â mechanization and social change. Projects, Economic and Techno-Economic
Projects, Manufactories
Leibnizâs views regarding social change accompanying technological progress
133, 161f., 862
Leibnizâs reply to Voigt (January 1700), regarding the implications of his threshing-machine â loss of employment due to mechanization â example of the machine at Aerzen â a single operator could do the work of fifteen laborers
162, 811
Example of the proscription of the ribbon-loom (1685)
161f., 811
Leibnizâs view of the problem of employment loss though mechanization â rejection of the assistance of machines not acceptable with alternative occupations arising through mechanization â only preliminary readjustment difficulties expected for workers
162, 811f.
His comparison with the use (in France / Spain) of animals in harvesting â resulting in the saving of human labor
811f.
His proposal for remuneration based on performance â recording of completed machine tours or working shifts required
162, 812f.
Magdeburg
90f., 262, 291â293, 383, 605
Magnetism. see Physics
Mainz â Electorate of Mainz
168, 190, 220, 257, 354, 408, 579, 721, 832, 889
Malacca (Malaysia)
248, 351f.
Mansfeld (Harz Mountains)
226, 344, 891
Manufactories, manufacturing. see Projects
Marburg. see Hesse-Kassel
Materials
Strength of materials and its history â history of elasticity â development of the theory of elasticity in the 17th century â elasticity as a structural principle of nature â elastic springs
3, 60, 65f., 92f., 94â96, 296f., 299, 345, 372â374, 461, 538, 647, 649
Hardness, perfect hardness
59, 68f., 80f., 114, 372, 461, 652, 654, 656, 761f., 874
Theory of structures â theories of Galileo, Mariotte, Hooke â their different theoretical assumptions
95f., 296f.
Galileoâs assumptions â rigid bodies and sudden breaks â his theory of fracture strength
95, 296f.
Mariotteâs work for the royal waterworks â his investigations of aqueducts / conduits â assumption of elastic fibers or filaments â communication of experimental results
95, 296f.
Critique of Galileoâs theory of fracture strength â different proportionality factors found by Galileo, Mariotte, Leibniz
95, 297
Development of the âMariotte-Leibniz theoryâ â Leibnizâs âDemonstrationes novae de resistentia solidorumâ (1684) â Mariotteâs âTraité du mouvement des eauxâ (1686)
95f., 297, 374
Leibnizâs theory of strength of materials â elasticity as an explanatory principle â breaking or fracture / rupture strength with elastic tension preceding break or fracture
92, 95f., 296f., 299, 372, 374f.
Leibnizâs starting hypothesis (1684) â strain or extension of carrier beam fibers being proportional to tensioning or straining force
96, 374f.
Uniform break-proof beams â their form and configuration
96, 374
Profile of a uniform fracture-resistant carrier beam â subjected to its own weight (1684) and an additional attached load (1690)
96, 375
Leibnizâs conviction that the carrier beam problem was only solvable with his infinitesimal calculus
96, 375
Mathematics
Algebra
17f., 27, 29f., 39, 169, 176, 200, 279, 283f., 286, 307, 314, 327, 361, 514, 516f., 520, 534, 645, 714
Binomials, binomial development
17, 284
Combinatorial and universal characteristics
18, 284
Combinatorics
Determinants, determinant theory
17, 284
Non-homogeneous equations
17, 284
Wallisâ âAlgebraâ (Opera, vols. 1 and 2) â Newtonâs gift sent to Mencke (1696)
29f., 176, 520, 714
Analysis, mathematical analysis
20, 24, 27f., 31, 36, 40, 96, 283, 286, 360, 375, 439, 445, 448, 514, 516f., 524, 621, 628, 637f., 754
Analysis of the infinitely small. see Infinitesimal Calculus
Analytical methods
439
Fundamentals of analysis
448
Infinitesimal analysis. see Infinitesimal Calculus
Imaginary and real expressions
17, 284
Ordinary analysis
96, 375
âAnalysis situsâ
13, 17, 27, 48, 283, 514, 619, 754
Applied mathematics
745, 884
Arithmetic
7, 24, 27, 48f., 169, 191, 203, 279, 281, 283, 285, 314, 437f., 442, 444, 498, 514, 578â584, 599, 637, 645, 754â756, 816, 818, 887
The four arithmetic operations â addition, subtraction, multiplication, division
169
: Calculating Machines
Exponentiation â exponents and roots â composite roots
16f., 21, 31, 42, 279â282, 284, 362, 444â447, 523, 641, 864
Exponential equations â transcendental exponential equations
21, 31, 42, 279, 362, 445, 523, 641, 864
Exponential expressions or logarithms (inverse function to exponentiation)
441â446
Logarithms (Napierian)
170, 578
Arithmetical tetragonism â the tetragonist method
483, 637
Binary or dyadic arithmetic. see Number Systems
Diophantine arithmetic
27, 279, 514
Political arithmetic. see Economics, Political Economy
Infinitesimals â arithmetic of infinitesimals
30f., 448
Calculus, infinitesimal calculus
ix, 11, 15f., 18, 20f., 27â31, 34f., 43, 64, 95f., 113, 281f., 358, 360f., 372, 375, 431f., 448â450, 508f., 516, 519, 521, 523, 535, 623â625, 643, 645, 863f., 868f.
Calculus an expression of reasoning or rational thought
241.
Reason, Reasoning
Foundation and forms of the calculus
xii, 11, 31, 40, 48, 444, 508, 517, 523, 636, 639, 753
Epistemological foundations of the calculus
31, 523
Priority issues. see Disputes and Controversies
Leibnizian calculus and notation
xii. 15, 18, 21, 29, 47, 358, 362, 510, 519f., 523â525, 752, 864
Leibnizâs new method (âNova methodusâ)
15, 20, 51, 147, 280, 360, 364, 431, 688
Finding maxima and minima, curvature, points of inflexion
16, 280, 282, 514f.
Differential calculus
14f., 20, 22â25, 31, 33â36, 39â45, 47f., 51, 113, 121, 280, 283, 301, 359f., 364, 371, 432f., 435â437, 448, 509, 518, 524, 621â623, 625, 628, 635â640, 642â645, 745, 748, 752f., 865â869
Differentials â of first-order, second- and higher-order
15, 31f., 41f., 234, 523f., 640f., 727
Differential equations â of first-, second-, higher order
27, 30, 514f., 520f., 645
Theory of differential equations â attribution to pure quadratures (integrals)
27, 514f.
Solution of differential equations â power series method
29f., 514, 521
Exponential equations
21, 31, 42, 279, 362, 445, 523, 641, 864
Differential geometry
27, 514f.
Geometry
Infinite â conception / nature of the infinite / infinitely small
43f., 643, 746
Infinitesimals, infinitely small magnitudes
30f., 448
Conception / nature of infinitesimals
44, 448, 746
Infinitesimal differences â infinitely small changes
32, 67, 653
Discussion between Leibniz and Joh. Bernoulli â their respective conceptions of the infinite / the infinitely small
44, 234, 727f., 746
Questions of rigor of the differential calculus â objections raised against the calculus â proofs less rigorous than those of the ancients
43, 643
The calculus essentially an analytical method for achieving results
43, 439, 643
The integral calculus (Leibnizâs recondite geometry)
18, 20f., 43, 95, 133, 265, 358, 360, 431, 644, 861, 863
Integration theory
27, 514f.
Integrals â basic integrals â integrals of known geometrical interpretation
515
More complicated integrals â reduction / transformation using substitutions
514f.
Notation / terminology of the Leibnizian calculus â differential / integral symbols â their improvement and unification
29, 47, 519f., 524f., 752
Alleged superiority of the Leibnizian calculus
15, 21, 23, 45, 280, 362, 432f., 439, 444, 747, 864f.
The Newtonian calculus
11, 29, 47, 507, 519, 752
Newtonâs Calculus of fluxions
28â30, 39f., 47, 518, 520f., 634â639, 748, 752
His âDe analysi per aequationes ⦠infinitasâ (1669) â seen by Leibniz in London (1676)
28f., 517f.
His letters of 1676 (intended for Leibniz) â the âepistola priorâ â the âepistola posteriorâ â Leibnizâs replies
29f., 40, 519, 638
Gregoryâs role in obtaining the letters of 1676 â subsequently published by Wallis (1699)
639
Newtonâs calculus / method of fluxions â intended publication (1693) â presentation of the calculus of fluxions in Wallisâ âDe algebra tractatusâ (1693)
39, 520, 634f.
Newtonâs calculus â Newtonian notation
29, 47, 519f., 524f., 752
Other forms or methods of the calculus
Huygensâ geometrical methods
20, 24, 360f., 376, 435f., 439, 510, 866
Wallisâ tangent method â compared with Leibnizâs differential calculus â equivalence / non-equivalence of the methods
40, 636f.
Others methods like those of Archimedes and Fermat â similarities, interdependences, and differences
40, 449, 637f.
Questions of nomenclature and notation
28f., 39, 47, 284, 519f., 524f., 636, 752
: Controversies and Disputes
Transcendental calculus
281f., 445f., 448f.
General Mathematics
Higher form of general mathematics
515
Clüverâs âscientia infinitiâ (1686)
42, 642
Leibnizâs âscientia infinitiââ a planned work with participation of other mathematicians â invitations sent (1694) to other mathematicians (Jacob and Johann Bernoulli, Huygens and LâHospital) â Menckeâs proposed publication of an outline of the conception of the work (1694)
13, 27, 29, 44, 514â516, 520, 619, 644
Contents of the work â quantities, theory of quantities â finite quantities (algebra) â infinite quantities (infinitesimal calculus)
27f., 516f.
Geometry
Elementary geometry / mathematics
27, 514
Geometry without tables
283
Euclidean geometry
238, 845
Geometry of Apollonius
449
Geometry of Descartes (Cartesian geometry)
449, 645
Extension to transcendental curves
645
Geometry of Viete
449
Geometrization / mathematization
24
Geometrical methods â those of Huygens â those of Italian mathematicians
20, 23f., 360, 433, 435, 439, 510, 865f.
Geometrical precision
42, 642
Graduation â Renaldine circle graduation rule
745
Higher geometry
27, 515
Geometric characteristic (âcharacteristica geometricaâ)
17, 279, 283
Geometry of location (âgeometria situsâ)
17, 283
Practical geometry
Ramist geometry (16th / 17th century) â cruder than / inferior to Euclidean geometry â a form of practical geometry which disparaged proofs â figures judged on the basis of their form â focus on benefit or usefulness
238, 845
Quadrature(s)
7f., 17, 19, 24, 42f., 279, 281, 283f., 359, 436â438, 441â445, 448â450, 515, 642f.
Quadrature methods
19, 24, 359, 436, 645
Quadratures of circle and hyperbola â reduction of quadratures to those of circle and hyperbola
445, 448
Quadrature / squaring of the circle
7f., 17, 24, 281, 283f., 437f., 449
Leibnizâs correspondence with Ferguson (early 1680s) â quadrature of the circle using the âwitch of Agnesiâ curve
17, 284
Leibnizâs âTrue proportion of the circle to the squareâ (1682)
39, 281, 635
Leibnizâs arithmetic quadrature of the circle (1682) â the âLeibniz seriesâ â his âtrigonometric series or geometry without tablesâ â first use of the term âtranscendentââ his use of term with unknown in the exponent
7, 16, 24, 280f., 283, 437f.
Use of the he technical term âtranscendent (al)â
16, 23, 279f., 282f., 307, 434, 445f., 448f., 511, 514, 645
Series â theory of series
27, 514f.
Leibniz infinite series (1682)
16, 24, 280, 437f.
Huygensâ infinite series (1690)
438
[Joh.] Bernoulli series (1694)
515
Power series development
514
Numerical series
645
Curves and surfaces
Alhazenâs problem
284
Arc length of a curve (rectification)
24, 436, 441, 443, 513, 645
Area under a curve (quadrature)
24, 436
Quadratures / rectifications expressed algebraically
645
â[Joh.] Bernoulli problemâ
23, 434f., 866
Brachistochrone (curve of fastest descent) problem
26, 32â37, 42, 45f., 48, 512f., 619â631, 641, 645, 747â749, 753, 867â870
Announcement / task formulation (1696â97)
Bernoulli (Joh.)âs flysheet about the problem for Dutch, English, French and Italian Mathematicians â his note (February 1697) in âHistoire des Ouvrages des Savansâ
26, 32â35, 513, 620f., 624f., 867f.
Bodenhausenâs flysheet about the problem for Italian mathematicians
33, 629
Leibnizâs announcement in âGiornale deâ Letteratiâ (September 1696) and âJournal des Sçavansâ (November 1696)
33f., 620â622, 867
Solutions found or published (1696â99)
Newtonâs solution â achieved in a single day, following receipt of Bernoulliâs flysheet â his anonymous âEpistolaâ, in the Philosophical Transactions (January 1697) â seen by Leibniz as a proof of the effectiveness of the infinitesimal calculus â in form of both the differential calculus and an analogous method
35, 513, 624f.
Leibnizâs complaint (April 1697) about Newtonâs preemptive publication
625
Leibnizâs own solution â the cycloid or âtachystoptataâ â achieved in a single day, while on a coach trip to Wolfenbüttel
625f.
LâHospitalâs solution (April 1697)
34, 48, 624, 868
Joh. Bernoulliâs two procedures (direct and indirect) â one based on the law of refraction
26, 36, 512f., 627
Publications (Philosophical Transactions) â Newton (January 1697) â David Gregory (February 1697)
36, 513, 624f., 629f.
Publications (Acta Eruditorum, May 1697)
Solutions by Jac. Bernoulli, Joh. Bernoulli, LâHospital and Newton
513, 627, 641
Contributions by Leibniz (Introduction) and Tschirnhaus (commentary)
35, 37, 45, 625, 629, 747, 869
Aftermath of the publication
Joh. Bernoulliâs eulogy (June 1697) of Newtonâs achievement â his complaints about Tschirnhausâ behavior in the contest
37, 626â629
Leibnizâs insistence (1699) on not having had knowledge of Bernoulliâs flysheet being sent to Newton
35, 626
Catacaustic curve
16, 282, 870
Catenary (hanging chain) curve problem
22, 24f., 36, 38, 46, 432, 436f., 439â445, 447, 510, 628, 632, 634, 749, 864â866, 869
Encoded solution of problem (Huygens)
439â441, 443
Construction, features and properties of the catenary curve
439â445
Its surface of revolution â space generated by its rotation â its center of gravity â area between the curve and its axis â rectification of the curve
440f.
Evolute / Involute. Tractoria / Tractrix
Involute of catenary (tractoria / tractrix) â evolute of the tractoria / tractrix (catenary)
24, 436, 441, 443, 866
Relation of the catenary to the loxodrome
442
: Loxodrome / Rhombic Lines
Curvature(s)
Curvature center, radius
36, 627
Curvature behavior of curves
515
Curve arrays â properties of arrays
515
Families of curves â investigation using the infinitesimal calculus
515, 645
Different curvatures of a curve â curvature or flexure changes â infinitely small sections â infinitesimal changes
36, 67, 80, 514f., 627, 761
Movement along a flexuous line or curve
80f., 83, 761â763, 766
Constraining force â example of centrifugal / centripetal force â bodies possess this force in order to conserve their state
80f., 761f.
Conservation of direction (rectilinear movement) â non-conservation of curvature (curvilinear movement)
80, 83f., 761, 766, 769
Transition from curvilinear to rectilinear movement â essentially a change of state â Papinâs opposite view (1699)
81, 763
Cycloid
26, 32, 36f., 436, 445, 450, 512, 619f., 627, 629, 866f., 869
Properties of the cycloid â obtained analytically
448
Tangent to the cycloid
448
Cycloidal pendulum
17, 24, 284, 866
Pendulum clock. see Physics, Applied Physics
Cycloidal segment. see Brachistochrone, Solutions
Diacaustic curve
16, 282, 870
Drawbridge problem (1692â95) â Sauveurâs problem to find the locus of a moving weight maintained in equilibrium â solution: Limaçon (Snail of Pascal)
26, 512, 866
Elastic curves â studied by Jacob and Johann Bernoulli
95
Families of curves â envelope of a family â orthogonal trajectories â determination methods developed by Leibniz and Joh. Bernoulli (1694) â influence from physics in relation to the Brachistochrone problem, and âHuygensâ constructionâ (wave theory of light)
37, 437, 515, 630, 870
Geometrical curves
Hyperbola â quadrature of the hyperbola
43, 438, 441â445, 448f., 643
: Sum of secants of arcs, Huygensâ series
Isochrone curve problem
19, 359, 863
Isoperimetric curve problem (1697) â classical isoperimetric problem â variational and extremal task assignments
37f., 513, 619, 630â632
Limiting curves of â the simple tautochrone or isochrone pendulum â the tautochrone or isocrone double pendulum
24, 436, 866
Linear curves â Johan de Wittâs âElementa curvarum linearumâ in Leibnizâs correspondence (1697â99)
193
Loxodrome (Rhumb-line) curve
25, 437, 441â445, 865
Parabola â semicubical parabola (the isochrone) â quadrature and rectification of the parabola
19, 21, 34, 42, 103, 112, 282, 359, 370f., 431f., 441, 443, 511, 624, 642, 863, 868.
Isochrone Problem
Paracentric isochrone problem (Leibnizâs problem)
21, 432, 865
Real-world applications (or origins) of curves â physical influences
25, 37, 437, 630, 865, 870
Secants of arcs â sum of secants â longitudes as a sum of secants â method of finding the sum of secants (Huygens)
444f.
Snail of Pascal curve (âLimaçonâ)
26, 512, 866
Solid of revolution of least resistance problem
45â47, 747, 751f.
Spiral curves â Archimedean spiral
25, 437, 865
Surface area of a hemisphere â âFlorentine problemâ (âaenigma geometricumâ)
23, 433, 865
Tangent method, method of tangents / inverse-tangents
17, 21, 24f., 29, 40, 46, 279, 284, 361f., 437, 447f., 514, 520, 636, 749, 864
Leibnizâs method
17, 24f., 40, 279f., 284, 448, 514, 636
Huygensâ âequivalent methodâ
21, 361f., 440, 864
Inverse-tangent method (Fatio)
28, 46, 437, 447, 518, 749
Inverse-tangent problems (Huygens) â exchange of inverse-tangent methods
24f., 46, 437, 749, 864
Tschirnhausâ method
16, 279, 282
Wallisâ (Newtonâs) method
29, 40, 520, 636f.
Tractoria, tractrix (Involute of the catenary)
24, 436, 866
Transcendental curves â representation by finite equations â transcendental quantities
282, 445f., 448f.
Mathematical change (evolution, revolution)
xii
Mathematical creativity
21, 431
Mathematical discourse
54
Mathematical history and pedagogy
x, 32, 193, 645
Mathematical instruments
208, 578â584, 827
Analog equation-solving instrument (âConstructor, instrumentum algebraicumâ)
314
Compass
172, 180, 491, 495, 815
Mathematical instruments in China. see China
Protractor
172, 815
Mathematical magnitudes
31, 523
Incommensurables â composite incommensurables
450
Mathematical pedagogy. see Pedagogy
Mathematical problems and methods
Calculation of annuities, discount, simple interest
16f., 187, 281, 284, 406
Extreme value problems â extremal problems â extremal principles
17, 36, 56, 284, 513, 526
Mathematical contests â challenge questions
19, 21f., 26, 33, 37, 45f., 432, 439f., 510â514, 630, 747, 749, 863â867
Mathematical classification â typological classification
514
Mathematical methods â separation of variables
21, 431, 514
Mathematical principles
xiii
Mathematical problems rooted in the physical world
37, 630, 870
: Brachistochrone Problem, Catenary, Loxodrome
Mathematical substitution
514f.
Mathematical terminology
284, 448
Mathematical textbooks â for the dissemination of mathematical knowledge
44, 645
LâHospitalâs âAnalyse des infiniment petitsâ (1696) â for dissemination of the differential calculus
25, 34, 43f., 509, 623, 644f., 868
Joh. Bernoulliâs reaction to the publication â in view of LâHospitalâs private lessons from Bernoulli (1691â92)
43, 644
Other textbooks â textbook discussed with Vagetius
44, 645
Mathematical sciences
702
Mathematical theorems â application in medical physiology (Guglielmini)
742
The Pythagorean theorem
72, 664, 788
Mathematization of medicine
263, 425, 895.
Medicine
Mathematization of mechanics, engineering and technology
861
Mathematicians
Female mathematicians
54, 862
Mathematical practitioners
167, 198f., 327, 862, 884â887
Numbers â investigation of the properties of numbers
48, 754
Number theory
17, 27, 283, 514
Number theoretical applications
49
Reciprocal triangular numbers
17, 284
Science of numbers (Numerology)
Characters of numbers
285
Mystery of numbers
754
Properties of numbers
48, 754
Use of numbers
18, 284
Number systems
3, 18, 27, 48f., 285, 514, 645, 753, 755
Binary or dyadic (base 2)
18, 27, 44, 48â50, 204, 285f., 514, 645, 746, 753â756, 818
Binary or dyadic arithmetic
27, 48f., 645, 754f.
Binary or dyadic calculus
44, 746
Binary or dyadic logic â progression
286
Binary or dyadic progression of numbers â the âprogressio dyadicaâ
49, 285f., 756
Philosophical / Theological interpretations. âChinaâ, and âReligion, Creationâ
Binary Fohy (or FuXi) sequence
50, 756
Chinese figures of Fohy (âFuXi hexagramsâ)
50, 756
Decimal or decadic (base 10)
18, 49, 173, 285, 755, 817
Hexadecimal (base 16)
50, 756
Octal (base 8)
50, 756
Other number systems (e.g. base 11 and base 12)
18, 285
Leibnizâs references to binary arithmetic (early 1680s) â letters to Clüver, Ferguson, Tschirnhaus
48, 285f.
His later references (around 1700)
746, 753â756
His fear expressed to LâHospital (1699, 1701) that his ideas might be lost for posterity
48â50, 754â756
His plea (1701) to the Académie des Sciences to undertake investigations on binary mathematics â his efforts (1701) to gain the cooperation of Parent
49f., 755f.
His discussion of binary arithmetic with Joh. Bernoulli (1701) â the latterâs reference to Weigelâs work âTetractysâ (1673) â Leibnizâs insistence on the existence before Weigel of number systems other than the decimal â and on The value of his own number theoretical applications
49, 755
Leibnizâs introduction of Dangicourt to dyadics (1700) â continuing co-operation under Leibnizâs direction â Dangicourtâs publication, in the âMiscellanea Berolinensiaâ (1710)
49, 756
Leibnizâs communications with Bouvet (1701), with his theological interpretation and his latest results â Bouvetâs adoption of binary mathematics
50, 756
: China, Chinese Mathematics
Pure mathematics
151, 279, 283, 288, 645, 745, 865f., 882, 884
The mathematical sciences (âscientiae mathematicaeâ)
745
The âBernoulli problemâ â Joh. Bernoulliâs problem (1693) and solutions
23, 434f., 866
The âproblema alterum pure geometricumâ (1697)
645
Matter
.
Natural Philosophy, Dynamica
Fluids
94, 127, 163, 166, 228, 246f., 256, 373, 421, 474, 476, 478, 480â482, 562, 747, 850, 852f., 882, 892f., 896
Rarified fluids
45
Theory of matter
92, 223, 372
Sensible / Insensible matter
63, 535, 540, 617, 687, 877
Mechanics. see Physics
Mechanization. see Machines
Medicine
Art of medicine, âres medicaâ, matters medical, medicinalia, medicinal or pertaining to medicine
132, 241, 248â250, 252â255, 422, 425f., 560, 601, 605â611, 613, 615f., 844, 853, 855â857, 895
Concrete and abstract / potential
241, 425f., 895f.
Medical science
243, 250, 346, 610
Theoretical medicine
255, 506, 742
Anatomy
235, 237, 239, 242â247, 253, 265, 345â347, 559, 601, 723, 730f., 734, 739f., 845â847, 850â853, 893f., 896
Anatomists
xv, 131, 227, 240, 347, 380f., 601f., 848
Anatomical discoveries, insights, observations, reports, studies
235, 242â245, 253, 345f., 601f., 729f., 734, 850, 853
Anatomy of the ear. Physics, Acoustics,
Aurality / aural experience of sound
93
Problem of identifying a missing entity in the hearing organ (1681/82) â homotonic with every sonorous body
242, 346
Ossicles (âossiculaâ), ossicular chain (middle ear) â stimulation by vibrations / oscillations of the air â production of a corresponding sound in the ear
93f., 372f.
Cochlea (inner ear)
93f., 295
Ear drum (tympanic membrane)
94
Otology. see Diseases
Anatomy of fluids
246f., 850, 852, 893, 896
Gakenholzâs âEpistolaâ (open letter, 1701) on the emendation and correct practice of medicine â concerned with human body fluids â blood, serum and vital (or animal) spirits
237, 844f., 850, 852, 893, 896
Special roles of experimental science and chemistry â revealed in the works of nature â the chemical reactions of life â with the seat of most illnesses being found in body fluids
247, 852
Gakenholzâs argument that the human body should be considered as a machine or automaton â the heart being the prime mover of the machine
247, 851
Circulation of the blood â anatomical studies of the vessels emanating from the heart
246f., 850â852
His allegation of the backwardness of medicine â attributed to a superstitious veneration for the ancients and to wrong priorities in medical studies and training
246, 850
His advocacy of an anatomy of fluids in medicine, and of a reform of anatomical or postmortem examination
246f., 850â852
His understanding of the body in the context of organs and vessels
246, 850, 896
His focus on the circulation of the blood â arteries, veins, the heart chamber â aorta (the largest artery) â their connectivity and interrelation
246f., 850f.
His views regarding incisions and their avoidance
246, 850
His experience with injections and re-injuries of vessels in corpses
246, 850
His thoughts on infusions, blood transfusions, and the value of corresponding experiments with animals â his emphasis of the role of chemistry in medicine, the need for physicians to study chemistry, and to understand the processes in nature â his criticism of the excrescence of chemical pharmacy â his advocacy of the study of plants, with regard to their healing powers, their color, odor, taste, and their combustion or incineration properties â his reference to investigations of the reaction of plant sap with human blood, differences found in the reactions with arterial and venous blood, and the resulting lack of clarity about the effectiveness of such medicaments
246, 850
Published review of Gakenholzâs âEpistiolaâ (1701), highlighting its particular focus on the â study of blood and other body fluids â anatomy of fluids â study of vessels emanating from the heart â field of anatomy, involving study of the passage of blood from the heart through the aorta, and then through the body to the kidneys â role of experimental science (chemistry in particular) â consideration of the structure of plants, animals, and the human body as machines or automatons, with the heart as the prime mover
247, 851f.
Blood
Blood circulation â blood supply â the passage of blood from the heart through the aorta / the body to the kidneys â arterial and venous blood
233, 246f., 422, 850f.
Blood vessels â their form and shape
242, 345
Leibnizâs theoretical considerations â triangular vascular formations
241, 345f.
Meibomâs observations (1681â82)
242
Leibnizâs call for microscopic investigation
242, 345
His hydraulic machine model with â elastic blood vessels having a polygonal cross section â irregular entry of blood (machine input) and regular rate of flow (machine output)
242, 345f.
His application of trigonal prismatic geometry â blood vessels represented by a circumscribed polygon, with a possible range of multi-faceted polygons â from best case (triangular) to worst case (circular)
242, 345
His corresponding physical model â the most simple hydraulic machine to emulate blood flow â consisting of a hollow triangular prism or tube, filled and constantly supplied with water through an orifice
242, 345f.
The mechanical problem of reconciling the intermittent or pulsed fluid intrusion (input) with continuous fluid extrusion (output)
242, 345
His more general consideration of elasticity as an explanatory principle in anatomy â with greater flexibility of the multi-faceted polygonal structure being obtained by increasing the side length while reducing the number of sides â optimal structure form being triangular
242, 345f.
Bloodletting â Therapeutic Phlebotomy / Venesection
Alleged abuse of phlebotomy abroad â in Italy
(Bodenhausen) â in France, Spain and Italy (Block)
245f., 252, 735, 741
La Scalaâs âPhlebotomia damnataâ (1696)
252, 740f.
Leibnizâs advocacy (1698) of the moderate application of bloodletting
252, 740
Positive effects of the method found in the treatment of animals
252, 741
Bloodletting might act in the same way as arsenic as an antipyretic â with nature reacting to an artificially-produced health threat
252, 740f.
Blockâs view (1698) of bloodletting as the last resort of the Galenists
252, 741
Possible medical applications of bloodletting with â fever and blood heat â unconsciousness / disturbance of consciousness â blood congestion in the lungs or heart
252, 741
Leibnizâs request for Ramazziniâs opinion (1699)
252, 741
Cannibalism, Medical cannibalism
253f., 853â855
Corpse medicine
253
Anatomical knowledge from post-mortem examination of corpses used for â the development of examination and treatment methods â obtaining medicaments and medicinal or pharmaceutical products
253, 853
Goddardâs dropsâ / Kingâs drops â Charles IIâs distillation in his private laboratory â based on a recipe for the liquefaction of material from inside human skulls â wonderful or miracle-like reports about the drops
253f., 853â855
Leibnizâs interest and Papinâs skepticism (1699)
253, 853f.
Mumia â a substance obtained from pulverized Egyptian mummies â used as a medicament
253, 854
Use of corpses for therapeutic purposes â a proposed treatment method â by rubbing a sore, swelling or wart with the finger of a corpse â Bouquetâs account (1701) of an unsuccessful trial in Hamburg, and a successful trial and lasting cure there
253f., 854f.
Rationale of corpse medicine â medical benefit derived from extended suffering, death struggle, mortal agony â the agonal state of long-suffering patients, tortured and executed prisoners â soldiers in their death throes on a battlefield
254, 855
The corresponding production of substances having curative or immunization effects â serving as ingredients for medication â analogous to bloodletting and the resulting improved defense mechanisms of the body
254, 855
Post-mortem rituals â necromancy (ânecromantiaâ) and necrophilia
220, 830, 836, 898
Cardiology â Cardioplegia or heartbeat
236, 732
Chemical medicine / Iatrochemistry. Chemistry
Ramazziniâs acquaintance with iatrochemistry â the diagnostic and therapeutic teachings of the chemiatric school
259, 500
Aetiological theories â therapeutic strategies proposed by Ramazzini
259
Chinese medicine â method of diagnosing diseases by pulse observation
247f., 351
Cleyerâs method (1680â82) â his âSpecimen medicinae sinicaeâ (1682)
236, 248, 351, 732
Boymâs âClavis medicaâ (1686 ed.) on Chinese Cardioplegia
236, 248, 351, 732
Schröckâs questionnaire for Cleyer (1698)
236, 732
Diseases
Asthma â mountainous, mining asthma
857f.
Breast diseases â cancer and ulcers
249, 424
Consumption â pulmonary phthisis (âHüttenkatzeâ)
256, 348, 857f.
Dysentery â medication against dysentery
248, 250f., 261, 422f., 505f., 606f., 612
Gangrene
606
Gout / Podagra â the âPatrician maladyâ
195f., 248, 252, 263, 354, 423, 596, 613f., 717
Oncology, Cancers
249, 256, 424, 857
Malignant breast cancer
249, 424
Occupational and environmental lung diseases â pulmonary disease âBergsuchtâ (later âSchneebergâ) â occupational lung cancer
256, 506, 857
Otology / Diseases of the ear. see Anatomy, Aurality
Rachitis or rickets â analogy to Papinâs steam digester or âengine for softening bonesâ (1681)
244, 349
Schraderâs thoughts (1681) on petrification and induration of visceral organs â his knowledge about the embalming of corpses
244, 350
Rheumatic diseases
252
Scurvy â remedy for scurvy
163, 713
Spirit of sulfur as a remedy. see Chemistry
Epidemiology â epidemics and pestilence
4, 101, 206f., 225, 248, 251, 257â262, 352â354, 423, 500â503, 505, 604, 612, 779, 824, 826, 858f.
Bubonic plague â affliction and spread from Vienna to Prague and Leipzig (early 1680s)
225, 257, 352â354
Pronounced spread among the common people (Crafft)
257, 352
Cause of Leibnizâs lingering in Saxony (July 1680)
257, 353
Restriction of the movements of other travelers â Crafftâs inability to travel from Dresden to Berlin (April 1681) â Menckeâs / Pfautzâs stay in Oldenburg and inability to return to Saxony (Spring 1681)
257, 353
Leibnizâs ideas on health care policy â his proposals to combat the spread of the plague / âVorschläge gegen die Pestâ (1681?), including the closure of borders
257, 353
His medical deliberations on the plague â his conviction that the malady resided especially in the bodyâs humors, above all in the blood
257, 353, 893
His reference (September 1680) to infusional medicine (âmedicina infusoriaâ) as an effective remedy
257, 353
His suggestion to investigate the cause of the pestilence, by investigating changes in the blood of infected persons
257, 353
Medical ephemerides
202, 261, 502, 505, 604, 822f.
Preparation of medical ephemerides. Modena
Ramazzini as Leibnizâs most important correspondent in Medicine (from 1690) â his role in the dissemination of Ramazziniâs writings
258, 262, 500, 604
Publication of Ramazziniâs first epidemiological work (1690)
258, 500
Use of physical instruments in medicine â the barometer, hygrometer, thermometer
258, 500
Establishment of a relationship between diseases / illnesses and the prevailing weather conditions
258, 500
Introduction of statistical investigations in medicine
258, 500f.
Demography, the statistical study of population â the quantitative recording of mortality, morbidity, population development
257f., 500f.
Establishment of the causes and prevention of diseases â causes found in the weather, in occupational conditions, and the living environment
258f., 501
Epidemiology â investigation of causes and circumstances of the occurrence of epidemics
258, 501
History of epidemiology in the 17th century
258, 501
The role of Sydenham as an epidemiologist in the Hippocratic tradition â his concept of the âconstitutioâ
258, 501
The epidemic constitution for a year or season â efforts for the annual publication of such âconstitutiones epidemicaeâ
258â262, 501â506
Ramazziniâs publication of epidemic âconstitutionesââ his five annual âconstitutionesâ (1690â94)
258f., 501f.
Content, considerations, scope â descriptions of all epidemic diseases occurring in the Modena region â provision of information and data about symptoms, courses of diseases, therapeutics â weather and climatic influences on the occurrence of diseases
259f., 501f.
Health, welfare of farm animals and livestock â welfare of useful or crop plants like wheat, vine
259, 501f.
Social, urban, rural sections of the population â the extent affected by a particular epidemic
259f., 501f.
Epidemics in the Emilia-Romagna region (1690â94)
259, 501
Malaria epidemics (1690â91) â extreme precipitation and flooding along the Po tributaries (early 1690) â with the accompanying epidemic affecting the rural population
164, 403, 258â260, 501f.
Ramazziniâs description of the course in relation to the individual seasons â accompanying ills like cereal / wheat rust and animal diseases
259, 502
Contrasting dry and warm conditions (1691) â with the epidemic primarily affecting the poorer urban population
259, 502
The typhoid epidemics (1692â94) â with different prevailing weather and climatic circumstances
259, 501f.
Ramazziniâs attention dominated by typhoid afflictions â the transmission of infectious diseases â his view of the spreading through the air â transmission of the pestilence from Africa by a wind from the south
259f., 502f.
Ramazziniâs epidemiological considerations â the plight of the Modenese region (1691â92) considered to have arisen from a series of afflictions â specifically a difficult climatic and epidemic situation, economic decline, threat of war and French intervention, shortages, including difficult provision supply for the Italian and allied Bavarian troops
260, 502f.
Deployment of troops in the Modena region during war time regarded as epidemiologically innocuous
260, 502
Suspected connection between the epidemics and shortages, and infant malformation and mortality
260, 503f.
Pathology
Leibnizâs influence on the reprinting of Ramazziniâs âconstitutionesâ by the Academia Leopoldina (1691, 1692) â his revived correspondence with the Academiaâs president Volckamer â his further influence on Ramazziniâs appointment as (the 201st) member of the Leopoldina (1693)
260f., 502â505
Leibnizâs insistence on the necessity of collecting medical statistics in Germany, and of the Leopoldina using its influence to promote such undertakings
261, 505
Leibnizâs call for physicians to carry out and publish medical compilations for other regions and time intervals â sent to Pellisson-Fontanier (December, 1692) and to Franck von Franckenau in Wittenberg (January, 1694) â subsequently forwarded to colleagues at other locations, including Berlin, Dresden, Halle, Leipzig, Magdeburg, and Torgau, Zerbst
260, 262, 503, 604f.
Bodenhausenâs reference (1695) to an infectious dysentery epidemic in Italy
251, 612
Vagetiusâ reference (1695) to the spread of the plague / epidemic disease throughout Germany
261, 604
Interruption (after 1694) of the series of ephemerides published by Ramazzini â Leibnizâs enquiry (1699) about the continuation of the series
262, 856
Ramazziniâs justification (1700) of the publication interruption â due to data collection having proved cumbersome for physicians, a lack of remuneration, and an absence of any new notable epidemic occurrences
262, 858f.
Leibnizâs advocacy (1700) of data collection even in the absence of special occurrences
262, 859
Hoffmannâs âDissertatioâ (1700) â his schediasm on the influence of winds on the human body
778
Leibnizâs and Hoffmannâs project for the annual publication of medical-meteorological observations â under the aegis of the Berlin Society of Sciences (1700)
206, 262, 825, 858
Leibnizâs health â characterized by an overall state of good health for most of his life
251f
Problems arising in middle and old age â lower limb or foot ulceration (âulcus crurisâ) â articular or joint problems like gout
251f.
His health and therapy requirements
250f., 610â613
His feeling of health deterioration (1693) â subjectively-felt pressure of work / overwork in connection with the âopus historicumâ
250f., 610
His illness pattern (1693â94) with functional health disorders â caused by stress or mental strain
251, 610
His possible psycho-vegetative disorders
251
Bodenhausenâs reaction (1694â95) to Leibnizâs health worries â his attribution of Leibnizâs indisposition to a lifetime of overwork
251, 610f.
His recommendations â dieting, exercising, resting
251, 610f.
His diagnosis of Leibnizâs biliousness â revealed though external inflammation (phlogosis), painful urination, and the after effects of medical drinks (lemon juice)
251, 611
His recommendations for the â use of mild acids in fruit drinks â use of drops of vitriol, as a remedy against infectious dysentery â intake of a vitriolic emetic, under the supervision of a physician â avoidance of all exertion
251, 611â613
Leibnizâs reaction to Bodenhausenâs proposals â propensity to try out acidic / vitriolic remedies â reluctance to try out the vitriolic emetic
251, 613
Leibnizâs interest in the health conditions of correspondents
252, 613
Crafftâs fight against gout â his quest for medication to relieve suffering â his reference (1694) to Zipffellâs âPodagrischer triumphâ
195f., 252, 263, 354, 596, 613f., 717
Leibnizâs interest in medication / medicinal products for relief of gout pains â medicaments obtained from quicklime through the spirit of wine â âSchroederâs spiritâ prepared with quicklime
195, 252, 596, 613f.
Haesâ queries regarding Moebiusâ âteinture aperitiveâ (1696) and Hoffmanâs âspiritum martis volatile striatumâ (1696)
252, 613
Leibnizâs reflections on medicine as an empirical science â a sentiment expressed to Huygens (1694) â the mainstay of medicine being empiricism and practice
263f., 614, 738f, 896
His view of the necessity of observation and applications based on observation
88, 131, 288, 473, 614, 899
His vision of a religious order of friars (Capuchins), embracing medicine as a charitable endeavor
263f., 614f., 895
Medicine (hitherto) primarily an empirical science â a view expressed to Block (1698) â most of its theories and hypotheses having been hardly reliable or useful
263f., 614, 737, 895
His recollection of Meibomâs desire that the discipline be established on an empirical foundation â his greeting of the conjectures of competent physicians
264, 737, 896
Blockâs reply and call for the institutions of medicine to reject occult speculation, and be rooted in empiricism â his doubts that medicine could be built up solely on the foundation of experience
264, 738, 896
Leibnizâs view on hypotheses and conjectures â serving as tentative solutions on the way to the establishment of the truth
264, 738, 896
His insistence on the need to separate certain from provisional knowledge
264, 738, 896
Leibnizâs deliberations on medicine as an exact science â his discourse on medical subjects with Italian physicians and scientists (1689â90) â âmediciâ with mathematical abilities (Guglielmini, Spoleti et al.)
263, 425, 895
His vision of the application of mathematics in medicine â of medicine rooted in calculus, which was essentially a form of expression in the process of reasoning, an application of rational thought â a sentiment expressed to Bodenhausen (1690)
263f., 425f., 614f., 895
Medical interests of other mathematicians â Joh. Bernoulliâs inaugural dissertation (1694) on the movement of muscles
264, 616
Leibnizâs admonition for him to continue his commitment to medicine
265, 615
Jac. Bernoulliâs sentiments (1696) on the opportunities and benefits of applying mathematics in medicine
616
Limbs â hands and hand analysis â palm reading (palmistry or chiromancy)
220, 830, 898
Medical experiment â role of the experimentalist
131f., 560
Medical observation â role of the observer
131, 473, 560
Medical observations â Pratisiusâ medical observations (1691)
261, 505
Medical organization / Organization of medicine â Leibnizâs plea to Jac. Bernoulli (1695)
266, 615f., 742, 850
Medical practice â Stisserâs âDissertatio epistolarisâ (1700)
223, 256, 837
Stisserâs passionate plea for the inclusion of chemistry in medicine / medical studies
256, 852, 896
His view of the omnipresence of chemistry in medicine â addressed to the enemies of chemistry, namely the âmisochemistsâ (âmisochymiciâ)
256, 852f.
His example of foodstuffs like bread, beer, wine being prepared with the help of chemical processes
256, 852
His suggestion that both chemical and non-chemical medicaments were likewise being prepared with the help of chemical processes
256, 852
His argumentation was founded on authorities both past (like Hippocrates) and present â and also on case studies where wrongly prepared medication had brought about undesired reactions
256, 852
Leibnizâs reply and complaint about the multiplicity of available pharmaceutical products
256, 852
His endorsement of Stisserâs opinions that â chemical medicaments had great advantages when derived from the natural world â more effective medication against illnesses that affected the body fluids would be found either by chance or as a result of advances in chemistry
256, 852f.
Wagner as physician and patient â his reports (1699â1701) to Leibniz about his own ailments â and about the injuries and illnesses he treated â and the therapies he applied
254, 855
His reports about the chronic illnesses and deaths of professors in Helmstedt (1699/1700)
254, 855
Report about the recurring hemorrhages experienced by the hemophiliac J. A. Schmidt (1699)
254, 855
Report about the pleurisy of the medical professor Meibom following infection through contact with the patient and vice rector Wideburg â the failure of a bloodletting therapy and death of Meibom (March 1700)
254f., 856
Reports about the deaths of Ilse Stisser (in childbirth) and of her husband J.A. Stisser (April 1700)
255, 856
Report about the illness and death of Cörber, the professor of eloquence (April 1700)
255, 857
Wagnerâs own short but intense illness (April 1700) â his suffering and symptoms â headache, hot flushes, lassitude, states of anxiety and fear of dying
255, 857
His recovery following consumption of large quantities of medicinal beer made from scorzonera
255, 857
Report about the case of a fourteen year old patient (1699) â with hoarseness, coughing, intense headache, and an accompanying fear of asphyxia â treatment methods for headache considered involving the opening of the temporal artery, and use of medicinal leeches (bloodsuckers)
254, 856
Report about the case of a female patient from Halberstadt (1701) with a swelling / tumor on her cheek (1701) â Wagnerâs treatment with relief, recovery and setback
254, 855
Medicine as a profession / The medical profession
4, 256, 262â265, 354, 614, 737â739, 895f.
Perfunctory / superficial attitudes â accompanying professional status â sentiment expressed to Huygens (1694)
614
Physicians and surgeons
198f., 206f., 243, 246f., 249, 257â259, 262f., 265f., 326, 350, 352, 354, 425, 500f., 604f., 737, 739, 823â825, 850, 884, 897
Practical medicine
239, 608f., 615, 846, 895f.
Practical and artisanal activity. Knowledge, Theory and Practice
Social standing of physicians â social groups and social promotion in France during the reign of Louis XIV
265f., 739f., 862
Unqualified physicians â charlatans, quacksalvers, and the academically unqualified
262, 265, 354, 739
Instances of charlatanry / charlatanism
Gedenusâ proposal of onions as an amulet against the plague (Vienna, 1680)
257, 354
Issue of the influence of the moon on the body humors (Schrader, 1681)
263, 355
Scradetzkyâs apparent cure for gout (1682)
262f., 354
Instance of a Roman charlatan and his departure from several courts (Scheffer, 1682)
263, 355
Case of an amulet presented to the Elector of Brandenburg (Elers, 1682) â claimed to be effective against pain caused by stone (kidney, ureter and urinary stone)
263, 355
Case of a blacksmithâs laborer â his claim to be able to diagnose diseases by urine observation (Scheffer, 1682)
263, 355
Medical studies and qualifications
246, 850f.
Pratisiusâ critical report (1685) from Venice about medical practice and practitioners there â his critical sentiments regarding the pharmaceutical system â also about the methods of treatment
263, 424f.
Leibnizâs advocacy of a comprehensive scientific training for physicians â his recollection (1698) of a meeting in Paris with the personal physician (Fagon) of Louis XIV â Fagonâs role in the enactment of a law requiring medics to provide evidence of their knowledge of anatomy, botany and chemistry â his efforts for the enactment of a law for the exclusion of charlatans and quacksalvers
265, 739f., 896
Molièreâs satirization of French medicine â regarding the repertoire of the treatment methods of French physicians â their limitation to the application of clysters, enemata, purgatives or cleansing enemas, and venesection (phlebotomy)
265f., 739f.
Gakenholzâs criticism of the existing system of studies and qualification (1701)
246f., 850â852
Occupational or industrial medicine
255, 500
Ramazziniâs investigation (1691) of the working conditions of laborers in the well pits and shafts of Modena â experience of suffocating vapors
255, 506
His tract on the diseases of workers and tradesmen, âDe morbis artificum diatribaâ (1700) â its announcement to Leibniz
255f., 506, 857
Leibnizâs recollection of Agricola and Stockhausen
256, 857f.
Agricola as representative of the medical profession â his works on the ailments of miners and pitmen
256, 857f.
Stockhausen, a physician from Goslar â his tract on the lung diseases of miners (1656)
256, 857
: Diseases
Organs. Pathology
Internal / deep-seated / visceral organs
260, 349f., 503, 603
Kidneys (nephrology)
198, 243, 245, 247, 260, 263, 325, 346, 355, 503, 735, 851
Diseases of the kidneys â monstrous kidneys â description of an extremely enlarged kidney (1678â1679)
198, 243, 263, 325, 346, 355
Male organs
Conduit or vas deferens â male prowess
894f.
Prostate, prostate or prostatic glands, seminal vesicles, testicles
243, 347, 894
Urinary tracts
243, 346
Urethra â external urethral / urinary orifice â the âmeatus urethrae externusâ
243, 347, 611
Pathology
Autopsies, dissections and postmortem examinations
235, 244â246, 253, 601â603, 730f., 734â736, 853, 850, 896.
Cannibalism, Corpse Medicine
Bouquetâs anatomical reports from Padua (1695) â two remarkable autopsies, representing a grotesqueness of nature
244f., 601â604
First case: a corpse with an oversized split spleen â an extension of the diaphragm, with one part pressed into the chest or breast area â the other part pressed into the abdomen
244f., 601, 603
Second Case: the corpse of a crippled / maimed man â a school master with two livers â one of normal proportions in the normal location â the other within the coverings of the diaphragm, having the size of two fists, weighing two to three pounds, with an approximately round shape, and a small lobe, and located above the vena cava
244f., 601â603
Similarities with a liver (not the heart) were deduced â based on the form and substance of the organ, the path of the vena cava, and the distribution of other veins and arteries
244, 601f.
Other anatomical anomalies â missing organs, in particular the gallbladder and the gallbladder passage to the intestines â organs of the lower abdomen were swollen, or overblown, were pressed together and pushed upwards
244f., 602f.
Bouquetâs interpretation of the deformities / monstrosities â a grotesqueness of nature which failed to provide insights into the normal functions and functioning of organs
245, 604
The postmortem examination of Bodenhausenâs corpse (1696) â Blockâs anatomical report from Florence â an abscess of the liver being the cause of his death
245f., 735f.
Monstrous births and birth deformities
Ramazziniâs report (1692) of the birth to a German woman of stillborn deformed female twins at a military camp near Modena
260, 503f.
The twins were conjoined at their breasts and abdomens but were otherwise of normal proportions
260, 503
The presentation of the remains to the ducal authorities in Modena
260, 503
The postmortem examination where the pathologist found that the twins had but a single or shared heart, a single stomach, and a single liver â each individual was found to have its own intestines and internal organs including a bladder, kidneys, spleen
260, 503
The anointment and conservation of the remains among other cimelia â undertaken by Ramazzini
260, 503f.
Ramazziniâs intelligence about the occurrence of a similar monstrous birth in Bologna
260, 504
Franck von Franckenauâs autopsy account (1697) â a postmortem examination in Copenhagen of the remains of a dead-born two-headed girl â with two arms, two legs, and nails â the mother (wife of a schoolmaster) had previously given birth to several children
245, 734f.
Duplicate organs found â trachea or wind-pipe with outgrowths, oesophagus or gullet, stomach, small intestine (with ileus and sac), spine, lungs, ribs
245, 734
Single organs found â a heart, liver, spleen, kidneys, adrenal glands, urinary bladder, uterus, pancreas, mesentery, cunt
245, 734f.
Aftermath of the autopsy â an exenteration followed by a public display â preservation of the remains in a fluid of florantibalsam (spiritus balsamicus) â deposition at the Royal Museum (Copenhagen)
245, 735
Pharmacy, pharmacists
209, 236, 246, 250, 328, 732, 850
Pharmacology â pharmacological advances
4, 247, 250, 610
Age-old conflict between physicians and apothecaries â with the production of medication in the hands of the apothecaries â Leibnizâs endorsement of the physicians
247, 350
His complaint to Stisser (1700) about an enormous multiplicity of pharmaceutical products
256, 852
Drugs and medications â adulteration of medication
250, 610.
Herbs, Paraguayan Herb
Antifebrile (antipyretic), febrifugal medicaments
252, 328, 740f.
Antiepileptic or epilepsy drug â obtained from the hearts of frogs
247, 350
Antimony preparations
247, 350
Armenian (or white Armenian) bole
248, 423
Cinchona bark
247, 350
Emetics (vomitive agents) â antimonial emetics â vitriolic emetics
248, 250f., 290, 423, 606f., 609f., 612f.
Fergusonâs skin cosmetic (âcosmeticum Fergusoniâ)
247, 350
Medication against dysentery
248â250, 423, 505f., 606f.
Medication against the pest
257, 353f.
Medicinal beer â made from scorzonera (âSchwarzwurzelnâ)
255, 857
Moxa / moxibustion
328
Peru balsam syrup
248, 422
Smelling salts (âSchlagbalsamâ)
248, 422
Sulfur as medication against cough
247, 350
Sweet almond oil
248, 422
White candied sugar
248, 422
Wound healing / sore water
328
Herbs â herbal remedies
248, 261, 414, 421, 423, 506
Proposal (Gedenus, 1680) to use onions as an amulet against the plague
257, 354
An emetic plant from south America for alleviation of nausea or vomiting (1686)
248, 423
A herbal remedy against gout (podagra) â a Chinese plant in Florence (1690)
248, 423
Medicinal cortices or barks â used as emetics and nauseants, and in the treatment of dysentery
250, 607â609
A plant root called âIpecacuanhaâ (Justel, 1691) â Leibnizâs âantidysentericumâ from America (1696) â a rhubarb-like plant used as a remedy in the treatment of dysentery and as an âemetica sine violentiaâ â previously used by the French army â Leibnizâs hope that it might also be employed by the allied forces
249f., 261, 505f., 605â609
Volckamerâs alternative recipe (1691) for the treatment of dysentery â using vegetable or herbal remedies like sorrel / common or garden sorrel
261, 506
A herb from the Indies (âherbe des Indesâ) for the alleviation of vomiting (1694) â previously recommended by Boyle
251, 290, 610
Other medicinal plants from south America â Cinchona,
Peruvian bark (âCortex Peruviana/usâ) â the Paraguayan herb (âherba Paraguayâ) â its effectivity as emetic or nauseant
250, 606â610
Other apothecary products (Wagner, 1701): crabâs eyes â dragonâs blood â prepared âmumiaâ â prepared native cinnabar â diaphoretic antimony
253, 854
Physicians â court / personal physicians
6, 210, 214, 224, 235f., 245, 247, 261f., 265, 275, 331, 339, 350, 394, 505, 731, 739, 896
Physiology
4, 239, 242, 246, 266, 742
Public health â Leibnizâs special interest in public health matters â his proposed project with Hoffmann for the collection and annual publication of meteorological-medical observational data
246, 850f., 897
Rational thought / rationalization in medicine
4, 262, 855.
Mathematization / Mathematics in Medicine
Facets of the rational and critical thought in the reign of Louis XIV â foundation of academies and institutions during his reign
265
Leibnizâs quest for the development of a rational medicine
266f., 742f, 859f., 862, 896
His correspondence (1697) with the âmedico-mathematicusâ Guglielmini
266, 742f.
His expectation for Guglielmini to assist the advancement of a rational medicine, and to help mathematics find a place in medicine
263, 266, 425, 742f.
Guglielminiâs hope of being able to deduce mathematical laws in physiology
266, 742
His skepticism regarding the possibility of the organization of medicine as an exact science â his view regarding the training of âmedico-mathematiciâ â medics were generally not versed in mathematics and not well-disposed to such ideas
266, 742
Leibnizâs belief in the higher value for medicine of rational over speculative thoughts â his opinion that plausible hypotheses should replace less certain conjectures, which were to be taken into consideration only where they were expedient or purposeful
266 743
The importance for Leibniz of keeping certain and provisional knowledge separate
264, 266, 738, 743
Leibnizâs quest (1699â1701) for the development of a rational medicine â his correspondence with the medical (Cartesian) philosopher Hoffmann â his interest in Hoffmannâs ideas on the mechanism of nature, and the representation of nature
266f., 859f., 862, 896
Leibnizâs insistence on the reduction of composite principles to simpler (or secondary) principles â firm concepts were be chosen and vague terminology avoided
267, 859f.
The outcome (after Leibnizâs death) â Hoffmannâs multi-volume work âMedicina rationalis systematicaâ (1718â34)
267, 860, 896
Sexual reproduction
240, 243, 347, 894f.
Biology
Debate about constituent parts of mammalian semen â positions of Dutch physicians and professors (van Horne / Hoorn, De Graaf, Swammerdam)
243, 347
Schelhammerâs result (1680) and Leibnizâs objection
243, 346f.
Surgery (âres chirurgicaâ) â surgery, surgeons, barber-surgeons
177, 199, 216, 249, 257, 322f., 352, 424
Therapeutics â therapeutic applications against diseases
4, 247, 250, 253, 259, 350, 422, 500f., 606, 854
Chronic diseases â Listerâs âExercitationes medicinalesâ (1696)
249, 606
Womenâs breast diseases â methods of prevention and treatment â painful operations by barber-surgeons â quest for milder treatment methods (Tschirnhaus, 1683)
249, 424
Universal remedies â cures and panaceas
249, 264f., 423f., 738f.
Ledelâs panacea against chronic diseases (1688â90)
249, 423
Blockâs belief (1698) in a form of panacea or universal remedy
264f., 738
Leibnizâs reference to the investigations of the English physician Morton â his finding that (in the case of fever patients) a remission often occurred, making it possible for the physician to save the patient â in contrast, with extreme weakness of the body recovery was no longer possible
264f., 738f.
Mortonâs inability to find a means for the procurement of a remission â Leibnizâs continued adherence to Mortonâs vision
265, 738f.
Metallurgy, metallurgists, metallurgical processes
133, 142, 152, 187, 394, 407, 857f.
American, Spanish-American metallurgy â Barbaâs âArt of metalsâ (1640)
142, 394
Boyleâs contribution to the study of metals
89, 289
Casting of metals â production of malleable cast iron
5, 151f., 273, 399f.
Rupert of the Rhineâs process for tempering iron, and the production of an alloy (Prince Rupertâs metal)
5, 139, 160, 273, 387, 806
Douceurâs cast-iron process (1679â1684) â his roasting or annealing process â technical details of the process
5, 142, 151f., 217, 225, 273f., 312, 397, 399â401, 415, 809
Tyressonâs (Falkenstjernaâs / Falkenhjelmâs) process for making iron malleable (1699)
225, 809
Foundries, metal foundries
858
Refiners of metals
187, 407
Sheet metal, sheet metal works
408
Production of canons. see Engineering, Military Engineering
Metaphors â Leibnizâs metaphor of an evil spirit / little devil
24, 449
Metaphysics. see Philosophy
Meteorology
3, 7, 99â102, 278, 299.
Physics, Geophysics
Meteorological history â Drebbelâs tract on the nature of the elements (1608) â wind, rain, storms (thunder and lightning)
190, 410, 824f., 777f.
Meteorological instruments. see Instruments
Observations â barometric / meteorological ephemerides
99, 204, 474, 775, 818, 823
Weather â rain and precipitation
100, 259, 501f.,
Weather observations â corresponding simultaneous observations â wind conditions at different locations
99, 324f.
Microscopy, microscopes. see Instruments
Mineralogy. see Geology
Mines and mining â coal mines, copper mines, lead mines, silver mines
150, 199, 201, 226, 343, 500, 802f., 891
Mining in the Harz mountains
133f., 138, 142â144, 146, 148, 151, 162, 256, 273, 275, 299, 307, 313, 356f., 386, 394f., 428, 566, 813, 857, 878â880
Corrosiveness of water in the pits
136, 311, 878f.
Slanting mine pits
151, 800
Variation of slope along the veins
151, 800
Leibnizâs involvement in the Harz ore mines â his ideas for improvement of ore production â his frequent visits and periods of absence
8, 10f., 133â135, 307â310, 357, 428, 508
Brandshagenâs role as supervisor and accountant â costs and payments for labor and materials â tradesmen, smiths, millers, material suppliers
138, 386
Leibnizâs counterparts and opponents in the enterprise
Linsenâs role in technical and engineering matters â provider of wooden models for technical designs
134f., 139, 143f., 308f., 386f., 566
Board of mines in Clausthal â local mining authority and mining officials â his main opponent, the juror Pöhler
134â137, 145f., 307â309, 384â387, 567, 569â571, 880
Court chamber in Hanover â his superiors â his reputation and influence at court
4, 11, 13, 135, 143, 145, 273, 309, 508, 565, 567, 617
Engineering techniques, processes, procedures â power supply, pumping, winding, transmission machinery
134f., 137â141, 143â146, 161, 307f., 384â388, 391â393, 407, 565â571, 810, 878â880.
Power Technology
Water-powered and water-raising machines
62, 134â136, 138f., 142, 147â150, 153, 161, 178, 299, 309f., 311, 386â388, 392, 395, 397, 570, 572f., 687â689, 695, 872, 879, 881
Vertical water wheels
62, 144, 154, 309, 312, 532, 567, 570, 698, 872
Use of water wheels for draining the mines â powered by rainwater collected in reservoirs
134, 307
Use of water wheels for hoisting ore â ore production dependent on water supply â reduced in times of drought
134f., 138, 144f., 307â311, 386, 566, 571, 685f., 879f.
Winding machinery for hoisting ore
134, 139, 143â145, 386f., 407, 565â570, 879f.
Leibnizâs most important innovation in mining â exploitation of wind power â use of windmills
46, 134f., 169, 273, 275, 308f., 311â313, 385, 813, 878;
Power Technology
His use of windmills for draining the mines â at the Dorothea Landskron colliery (1679) â at the Catharina colliery (1680)
136â138, 384â386, 878f.
Windmill project for draining mines â idea of using wind power with vertical (or horizontal-shaft) windmills
137f., 385f.
Alternative project using horizontal (or vertical-shaft) windmills
137â139, 142, 311f., 385â387, 396, 813, 878f.
Applications of windmills â the âimmediateâ and âmediateâ solutions
The âimmediateâ solution using vertical windmills â direct attachment of pump assembly â preferential trials of the direct system â protracted series of trials, with the employment of new pumps â use of control mechanisms, for more uniform operation â contemplated power transmission using compressed air
137f., 384f., 878
The âmediateâ solution using horizontal windmills â employment of pumped-storage techniques to service and replenish reservoirs, especially in times of drought
137, 162, 384f., 813, 878
Idea of Hartsinck (Hartzingk) adopted by Leibniz (1680) â deployment at the Zellbach colliery
137, 384f., 878
Trial of horizontal windmill at the Lower Eschenbach pond (1684), but not under full-load conditions â problem of erratic wind supply in the mountainous environment
137f., 385
Aspects of horizontal windmills â horizontal rotation of vanes about a vertical axis â uniform regulation of wind power â lower efficiency and lower construction costs compared with vertical windmills
137f., 385f.
Efficiency improvement of vertical windmills â by rotation of windmill sails with direction changes of the wind â by variation of inclination of the sailsâ axis with strength changes of the wind
136, 311
Leibnizâs commitment to efficiency improvement â interest in discoveries / innovations â instructions for craftsmen / tradesmen
4, 7, 135â137, 141, 143f., 188, 309, 356, 385, 392, 407, 566, 879f.
His regular visits to the mining district
135, 309
Efficiency improvement of pumping systems in the mines
4, 7f., 136, 138, 144, 146, 153, 356f., 384, 386, 407, 565f., 571, 685f., 879
Corrosiveness of water in the Harz pits â corrosion of metal components â detrimental for use of the âbucket and chainâ system
136, 311, 878f.
Use of pumps with wooden cylinders â arranged in tiers, one above the other
136, 311, 879
Reduction of friction losses with â ârag and chainâ/âpaternosterâ pumps â piston-pumps with flap valves â leather sealing of valve-pistons
141, 146, 392f., 571
Power transmission mechanisms â parts of the mechanism and frictional losses between them
141, 393, 879
Later improvement of the pumping machinery (1694â95) â construction of energy-saving pumps â reduction of friction losses â replacement of leather obturator rings â use of pump cylinders with valves
144â146, 566f., 571, 879f.
Improvement of winding / hoisting machinery â closed-loop or endless cable â powered by water wheels
138f., 144, 386f., 566, 879f.
Test of practicability and advantage, at pits in the âThurm Rosenhoferâ mountain range (1685) â repair / maintenance work at the pits (1686) â termination of the test series
138, 385f.
Proposed venture (Bornemann-Jenisch, 1693) â winding machinery to be powered by horses â employment of an endless cable / rope for weight compensation â postponement following Leibnizâs priority claims
143, 565f.
Transmission systems for power supply to the pumping machinery â iron crankshaft component â alternative construction
134, 308
Repair and maintenance work â adverse weather conditions â transport and installation difficulties
134, 138, 308, 386
Role of skilled craftsmen / tradesmen â carpenters, cabinetmakers, charburners, millers, tailors
134f., 138, 143f., 156, 212f., 308f., 386, 412f., 700, 719
Role of Leibnizâs designs â use of cogged wheels engaging lantern pinions with vertical staves â cog and rung transmission â transfer ratio value
62, 134f., 161, 308, 532, 810f., 872
Projected power transmission system (1682) â making use of compressed air
135, 137, 308, 385
Becherâs report on waterworks, water wheels
140, 391
New power transmission system â a variant of the long-established rod-engine technology â a âStangenkunstâ with rods connected to a double rotary crank mechanism â with regular (circular) motions at the ends, and an alternating linear motion in between
139â141, 391f., 879
Connection of a prime mover â supplying wind, water, or horse power with a distant load
137, 140f., 145, 162, 384, 391f., 569, 813, 879
Leibnizâs theoretical ideas regarding mining
His efforts to prove their practicality â theoria cum praxi
15, 828
His time-consuming mining involvement (1680â86 and 1693â96) â aims of improving the efficiency of the mine-dewatering pumps and the ore-hoisting winding machinery
4, 7, 144, 188, 356, 407, 566, 880
Elements of his innovation â replacement of horse power by water power â replacement of an overshot reversible water wheel by a rod-engine transmission system from a remote power source, like a water wheel on a stream
144, 392, 566, 879f.
His design of a power supply system for the joint operation of the pumping machinery and the winding or hoisting machinery
144, 566f., 880
Reduction of the overall power requirement â use of a novel tugging / towage mechanism and a switchable pinion-gear mechanism â use of an endless (closed-loop) winding cable
144f., 566f., 880
Transformation of horizontal into vertical linear motion â of above ground alternating rod motion into alternating motion of the piston rods
144, 566f.
Transformation of linear into rotary motion â of above ground alternating rod motion into closed-loop rotary winding motion
140, 391
Introduction of a switching point along the transmission line â between water wheel and pithead
144f., 566f., 569
Pithead transformation elements â a cross-shaped lever-device for the pumping machinery â a capstan or roller drive for the winding machinery
144f., 566f.
Trials of the combined system â supervision / progress reports of the trials (Reimers, Crafft)
144â146, 566â571, 880
Demonstration (February 1694) of the ore-hoisting function â subsequent dysfunctionality
144f., 566â569
Conflict with the mining office â opposition and obstruction from jurors and mining officials
145, 567f.
Damage / sabotage to the rod-engine system (April 1694)
145, 567â569
Doubts about the combined system â about its capability to meet simultaneously both requirements â the pumping and ore-hoisting requirements
145, 569f.
Issues of meeting costs incurred and suspension of trials (in 1695)
145f., 570f.
Other mining districts in Germany
Freiberg mining district
141, 391f., 879
Mining in the Erzgebirge / Ore mountains, Saxony
201, 499
Water mill near Ehrenfriedersdorf, Saxony â the water wheel âEhrenfriedersdorfer Radpumpeâ
140f., 391â393, 879
A technically-improved version, consisting of a single prime mover â a horse mill or water wheel â a piston-pump system with two or more pump stages, one above the other â a transmission mechanism with sections â comparable to rod-engine sections
141, 392, 879
A Hesse coal mining location â Papinâs employment of his Hesse pump (1699) there with a long wooden air-conduction pipe â serving for mine aeration or ventilation in the coal mine
150, 802f.
Pumps
Breathing difficulties in the pits, and the extinguishing of lamp flames there â attributed by Leibniz to inadequate air supply and circulation
150, 803
Ilmenau mining district â source of mineral ore containing fossilized plants â sent by Heyn (1690)
141f., 228, 394, 421, 891
Other mining districts in Europe and beyond
Central European mines â silver mining and minting â the mining boom
199
English mines and mining engineers â accounts of the engineer Heyn (1686â87) â his practical experience in English mining â his familiarity with English mineral ores
139, 201, 387, 499
Cornish mines â the mining district of Cornwall)
9, 139â141, 358, 387â389, 390, 392, 879
A standard scoop wheel water lifting system â referred to by Heyn (1687)
139, 387f., 879
A novel water wheel-powered pumping machine â with alternative power sources namely water, wind, horsepower, and manpower â constructed at a disused pit â designed by Becher (+1682) and reported to Leibniz by Heyn (1687)
139â141, 387â392, 879
Technical details of the Cornish âTaschenkunstâ-like machine â a Rag and chain / chain of beads pump system â consisting of a series of pump stages, with similarities to the stages of a rod-engine transmission system â provided with pumps using several pipes / pistons of different measure â operating in perpendicular or inclined shafts at depths up to 100 or more fathoms
139â141, 287â389, 879
Successful operation of the machine over a period of three years â with an investment return of 1100 Taler (250 pounds sterling) for the operating company and investors
140, 389f.
Ultimate demise of the machine â machinery at a complete standstill following vein termination and a mining accident â revelation of details of the machine offered by Heyn to Leibniz using a model of the device
140, 390
Hungarian mines
9, 188, 358, 407, 612
Paternoster pumping system â described by Agricola (1556)
139, 388f.
Scottish coal mines
136, 310f.
Paternoster pumping system with chain and buckets for lifting water from the mine pit â powered by horse mills â reported to Leibniz by Huygens (1680) â issue raised of investment versus expected return
136, 310
Spanish-American mines and mining â Barbaâs âart of metalsâ
142, 394
Swedish mines and mining
142, 151, 394, 800, 806
Copper mining at Falun â King Charles XI mineshaft (1698â99)
151, 159, 800, 804
: Furnaces
Machines of the engineer Polhammar (Polhem) â suitable for inclined or slanting pits â used for quarrying out stone â the conveyor system with conveying machinery
151, 800f.
The Swedish mining expert Odelius
142, 394f.
Welsh mining â silver mine in Wales
201, 500
Monarchy, monarch
152, 400, 497, 617f.,
Sovereign(s)
8, 11, 13, 143, 156, 177, 200, 309f., 499, 508, 565, 590, 617, 702, 715
Princes
4f., 11, 23, 27, 33, 139, 169, 175f., 183f., 191, 193f., 197, 200, 202, 213, 218f., 244, 272f., 302, 315f., 327, 387, 412, 417, 433, 483f., 497, 508, 514, 598, 601, 621, 701, 704, 713, 802, 829, 865
Subjects
184, 316f., 497
Motion, movement. see Natural Philosophy
Münden
192, 591
Münster
11, 193, 508
Muscovy. see Russia
Nature
Kingdoms of nature â animal, mineral, vegetable realms
222, 890
Secrets / treasures of nature
206, 683f., 721, 825f.
Treasures of nature â shared among many bodies / substances â example vitriol
721.
Alchemy, Chemistry
Natural history
226f., 229, 235f., 239, 419, 484, 504, 723, 729, 732, 892.
Biology and Geology
Natural philosophy
xiiâxv, 3, 50ff., 52, 57f., 87, 150, 157, 209, 219, 230, 287f., 362ff., 366, 450ff., 452, 458, 525, 646f., 703, 757ff., 870ff., 892
About nature â features, laws, philosophy, science, works of nature
55f., 60, 81, 120, 155, 219, 238, 245, 247, 267, 303, 343, 352, 363, 404, 460f., 525, 544, 604, 684, 700, 763, 798, 845, 847, 852, 859, 890f., 897, 899
Aristotelian (and scholastic) natural philosophy
xii
Natural philosophy of Descartes â his approach to the vegetal realm â the mechanical life of plants
58, 238, 458
Natural philosophy of Papin
57f., 363, 458f., 757f.
Natural philosophy in Leibnizâs correspondence
50â87, 287â307, 362â365, 450â462, 525â539, 646â682, 757â775, 870â874
Core concepts and topics (Leibniz / Papin)
Action. Bodies, Force, Motion, Movement
Action â a continuing state which exists by virtue of the movement of a body â movement per se as a kind of action
74f., 671
Action â a succession of states of a body during a change of location
672
Different terminology for the concepts
61, 65, 75, 79, 527, 648, 671, 759
Action (âactioâ, âactionâ, âWirkungâ)
66, 74â80, 646, 648, 669, 757
Actions over equal time intervals â âactions contemporainesâ
76, 676
Change, mutation â âchangementâ, âmutatioâ
75, 671
Change of location â âchangement de lieuâ, âmutationes lociâ
75, 80, 82, 671, 762, 764, 769
Changes of space â âchangemens des espacesâ
79, 758
Changed spaces â âespaces changésâ
79, 758f.
Produced changes â âmutationes loci productaeâ
78, 758
Producing changes â âmutationes loci producendaeâ
78, 758
Traversed spaces â âespaces parcourusâ
78, 677, 758
True action (Leibniz) / Intrinsic movement (Papin)
75, 673
True / veritable action estimated both by its intension
(celerity / promptitude), and by its extension (duration)
75, 673
Concepts of change â intensive or temporal change
(âintensionâ) â extensive or spatial change (âextensionâ)
75, 82, 673, 765f.
Papinâs proposal to equate action with a perseverance / persistence within the same manner of being â thus its independence of the movement
79, 759f.
Multiplication and division of an action â doubling, triplicating / halving, trisecting, etc. â instance of a body moving uniformly through a given space over one, two, three, etc. time intervals â instance of a given space being traversed in half, a third, etc. of a time interval
74f., 669f., 674f.
Leibnizâs proposition regarding action
Action proportional to â the product of path and velocity â that of time and the square of velocity
76, 674
Actions over equal time intervals proportional to squares of the velocities
76, 676
Absurdities or contradictions arise if actions be made proportional to velocities, traversed paths, times (or reciprocals of times)
76, 676
Leibnizâs principle of action â and its combination with his measure of force by which every exercise of force passes for an action â free of absurdity or contradiction
76, 676f.
His conclusion regarding his conservation law for force â the quantity of action in the world is conserved
76, 537, 675
The Cartesian interpretation
76, 81
Papinâs conception of action and force â different concept of action to that of Leibniz
75, 77â79, 87, 670f., 678, 757f., 775
Papinâs rejection of Leibnizâs proposition regarding action â his assumption an absolute indifference for every kind of manner of being â a perseverance or persistence within the same manner of being
76, 79f., 675, 761f.
The Cartesian measure of force â erroneous for Leibniz due to the confusion of the quantity of action, and quantity of movement
76, 674, 676f., 681f.
Papinâs rejection (Nov. 1698) of Leibnizâs quantity of action
77, 681
Leibnizâs two different forms of action â formal (a priori) action, where the acting force is conserved â violent or contingent action, where the acting force is consumed â both forms (âactions violentes ou contingentesâ) yield the same measure of force â essentially a connection of action and force
77, 679f.
Action proportional to â the product of force and time (Leibniz) â the product of distance and time (Papin), an embarrassing contradiction (for Leibniz)
77, 86, 679, 773f.
Distinction between force and action â action as a resistance-free movement
75, 77, 79, 671f., 681, 758
Papinâs endorsement withdrawal (Nov. 1698)
77, 681
Force always implies an action (Leibniz) â view rejected by Papin
76f., 675, 680
Papinâs view that all bodies with the same volume â be they in motion or at rest â have the same force
77, 680
Force manifestation involved both with motion with resistance and with motion without resistance, where a body is at rest
75f., 670, 673, 676, 679
Force acts on a bodyâs own mass â the body rotates around its axis â the exercise of force is conservative
75, 672
Reaction â re-action
75, 670, 682, 758
Leibnizâs action without reaction possible â with a movement that does not surmount any resistance
74f., 669â671, 681f., 758
Papinâs action â no action without reaction â action tantamount to overcoming of resistance
75, 78, 670, 682, 758
Papinâs own notion of change of place / location â more distinct for him than that of action
762
Bodies
Bodies in motion. see Motion, Movement of Bodies
Collision of bodies â laws of colliding bodies â duration of the event â bodies reduced to a state of (relative) rest â post-collision separation
58, 65f., 71f., 80, 82f., 85, 451f., 647â649, 656, 662â664, 649, 761, 766, 770f, 873
Elasticity of bodies and of their constituent parts â intervening springs between bodiesâ breaking effect of a spring â elastic resilience of a spring
59â61, 64â68, 70f., 73, 461, 527, 536, 538, 648f., 651, 654, 659â662, 666, 872
Masses and velocities of colliding bodies
69, 656
Essence / nature of bodies â a bodyâs manner of being â a general inclination for its conservation (Papinâs penchant) â an inherent / intrinsic predisposition of its being present
52, 80f., 452, 761, 763
Essence of a body (Descartes)
458
Extension / physical extension of bodies
52, 452
Forces (and mutual interaction) of bodies â forces associated with corporeal states
55f., 525
Hardness of physical bodies â assumption of perfect hardness â condition / state of perfect hardness â its conceivability without contradictions
59, 68f., 80f., 461, 652, 654, 656, 873f.
Leibnizâs view (April 1699) of a transition from movement of a body along a curve to that in a straight line â representation of a change of state
763
Example of the free-fall of a hard ball and rebound from an anvil â the movement in contrast to that along a curve â a small change in height would be scarcely noticeable â changes in the direction of oblique impact would lead to more appreciable obliquity
81, 762, 764, 874
Papinâs view (May 1699) of movement along a curve â as a concatenation of an infinite number of states
82, 764
Leibnizâs view that movement along a curve was indeed a concatenation of states â the past, future and location change were states that were being conserved â the change of direction represented a further state that was being altered
83, 766
Impact of bodies â laws of impact
64f., 536, 538
Inertia and mass of bodies. Entelechy and Inertia below
Inertia of bodies â inertia of an essential nature and always existent in a body, both at rest and in motion
81, 763
Mass â mass of bodies
51, 56, 59, 61f., 66, 69â71, 73, 75, 80, 87, 110, 287, 362f., 461, 463, 526â528, 537, 641, 647â649, 656â658, 660, 662â664, 666, 672f., 681f., 760â764, 781, 861, 871â873
Motion of bodies. see Motion, Movement
Oscillation and percussion of bodies â centers of oscillation and percussion
65, 93f., 295f., 372f., 538f.
Percussion and elastic spring
70, 660f., 872
Properties of bodies â intrinsic and extrinsic properties â possible application to movement
84, 769
States (âmanieres dâêtreâ) of bodies â rest and motion â single and compound states
80â82, 84, 86, 774, 761â766, 769, 873
Papinâs view that both states had the same amount of reality, perfection, force
774
The same amount of force was to be found everywhere and in everything
86, 771
A body in motion acts more strongly in the direction of motion
86, 774
A body at rest acts more strongly in the opposite or reverse direction
85, 770f.
Papinâs incorporation of a weakness in the opposite direction â at variance with Leibnizâs understanding of action
85, 771f.
State of motion (Papinâs view) â the movement not stronger, more real or perfect than the state of rest
84f., 770
State of rest â an apparent (or potential) state, or the true (actual or real) state â rest as such regarded as, or similar to inertia
82f., 766
Relation of the state of rest to that of motion â like the relation of zero to the positive numbers
82f., 766
Incompatibility of states (Papin)
83, 85, 766, 770
Resistance â concept of incompatibility or resistance (Papin) â external resistance
83f., 766, 769
Compatible or incompatible states â like rest and motion
82, 764
Leibnizâs distinction between the states of rest and motion
80f., 762
Natureâs (matterâs) penchant or preference for an existing state
81f, 763f.
Change of state of bodies â three states of movements â past, future and location change
83, 766.
Motion
Concatenation of states â multiple states â an infinite number of states
82f., 764, 766
Curvilinear motion â a compound state involving changes of direction â no conservation of state
83f., 767, 769
Internal and external causes â change of location (internal) â change of direction (external)
73, 75, 77, 82, 83f., 667, 671f., 681, 765f., 769
Rectilinear motion â a composite entity, involving a conservation of state
84, 109f., 542â544, 769, 876
Uniform motion â consisting of several states
76, 78, 83, 674f., 678, 758, 766f.
Conservation of states of bodies â maintenance of a state of being â actual, real or merely potential â provision by means of an entelechy â motion attributable to the intrinsic force or entelechy
80, 83, 761, 766, 873, 892.
below: Entelechy
Change of location â attributable to an internal cause
84, 769
Change of speed / velocity â attributable to an external cause
83, 766
Change of direction â attributable to an external cause
84, 769
Change of duration â duration and speed / velocity â greater perfection of rapid movement
84â86, 772f., 769
Nature of change â simple change â change of change â end of change as the external cause becomes inoperative
83f., 766
Quantity of change(s) â of changes of location â quantity of changed locations
83, 85f., 767, 772
Papinâs view of quantity of changed locations (or that of changes of location) â manifest as the product of the times and velocities
78f., 85f., 772
Leibnizâs view of an absurdity in Papinâs interpretation of duration and velocity â with mutual compensation or a reciprocal relationship between times and velocities â the entities were not always in such a reciprocal relation
86, 773
Leibnizâs comparison with the relationships between assets and liabilities (debts), possession and deprivation, knowledge and ignorance, darkness and light, states of action and rest
86, 773f.
Papinâs recapitulation of the conflicting positions (Spring 1700) â his insistence that all states were like bodies, at rest and in motion â possessing the same degree of force, of perfection, and of reality
85f., 772
Leibnizâs elaboration of his views about the for him still unanswered matters of dispute (April 1700)
86, 774f.
Stress â state of stress
60, 461
Substitutability of bodies
58f., 64, 459, 536, 647, 871
Substitution / surrogacy. see Experiments
Transferability / transmission between bodies â or a non-transferability / non-transmissibility â of the total force of a body to another â from a body of greater to one of lesser mass â or following replacement of a body by a larger body (or wall)
58â60, 70, 459â461, 647, 656f., 660, 871f.
Feasibility of a transfer / transmission between bodies â means of realizing such a transfer â practical execution of a substitution
59, 69, 460, 656f.
The elastic resilience of bodies â spring tension or spring force
61, 66, 68, 527, 649, 654
Cause(s) â cause and effect â principle of the equality of cause and effect â efficient causes (âcausae efficientesâ) â final causes (âcausae finalesâ)
56, 59, 65, 72, 87, 287, 526, 539, 664
Effect (âeffectusâ) â quantity of effect
51, 61, 364, 460f., 527
Entities â incomplete entities â substantial or absolutely real entities
56, 362, 461, 762, 770
Dynamics â Leibnizâs dynamics
50â56, 60, 64f., 87, 96, 183, 230, 363, 364, 451â456, 525f., 535, 538f., 590, 648
Fundamental concepts of his dynamics â abstract
Dynamics â concrete dynamics
51, 364f.
Parallels to the infinitesimal calculus
63f., 535
Dynamica â Leibnizâs projected work âDynamicaâ
50â58, 80, 92, 363â365, 375, 451, 453â456, 459, 525, 537, 736f.
Classification of the âDynamicaâ â content of the work
51f., 363â365
Versions of Leibnizâs dynamics â manuscript version
(âmanuscriptum dynamicumâ) â Ãlémens de dynamique (1692) â Essay de dynamique (1692)
53, 454
Specimen dynamicum (1695)
55, 60, 63, 65, 525f., 535, 538, 648
Entelechy â Leibnizâs concept of an inherent, intrinsic, purposive force â the realization or actualization of that which is merely potential through an entelechy â the concept rejected by Papin
80â83, 85, 761â764, 766, 770, 873, 892f.
Considerations about inertia and entelechy â Leibnizâs hypotheses regarding inertia and an entelechy â inertia was of an essential nature, and always existent in a body, both at rest and in motion â the entelechy in contrast was of a changeable nature
81, 763
Papinâs view of an obligation for Leibniz to prove his hypotheses regarding inertia and the entelechy
82, 764.
Inertia below
Considerations about the mass of bodies and the entelechy â mass was of an essential nature, the entelechy of a changeable nature
80, 760f., 762f., 873
Leibnizâs distinction between states of rest and motion â his concept of the entelechy being essentially a preference for the existing states of rest and motion
80f., 761â763
For Papin the entelechy meant an added complication â a multiplication of entities
81, 762
Force â âforceâ â âconatusâ â âeffortââ âpotentiaâ â âvisâ
14, 18, 50â87, 96, 101, 103, 106, 108â111, 149, 167, 183, 287, 358, 362, 366, 369f., 375, 383f., 389, 393, 451, 453â455, 458â463, 477, 481, 525â530, 532â538, 542f., 545, 549f., 563f., 589, 646â682, 692, 744, 757f., 760â764, 766, 770â772, 774f., 780f., 861, 863, 871â876, 892f.
Conceptions of force
61, 527
Active and passive forces â total and partial forces
53, 56, 453, 525
Internal force (âvis respectivaâ) and outward-operating force (âvis directivaâ)
56, 525
Metaphysical and physical forces â âvis primitivaâand âvis derivativaâ
55, 525, 648
Motive / moving forces â force in Leibnizâs Dynamica. Dynamics
Concept of force â metamorphosis of a concept
xiii, 50, 61, 527
Leibnizâs concept of force
55, 65, 538f., 648
Leibnizâs understanding of force â his distinction between force and inertia â Papinâs rejection of the distinction between force and inertia
77f., 80, 681
Force exists only when a body is in motion, and varies with velocity â force an active ability or acquirement â inertia a passive ability (âpotentiaâ)
77f., 680f.
Leibnizâs view of force as the most important property of bodies
52f., 453
Types of force â absolute and relative â living force (âvis vivaâ) and dead force (âvis mortuaâ) â real force and virtual force
14, 55â57, 61, 64, 66â68, 70â72, 450f., 525, 527, 535, 646, 648â651, 653, 658f., 661, 664, 744, 861, 871â874
Conservation of force â conservation of force requirement
60, 657
Absolute force â that produced where there is a certain determined movement â a living, productive, and spatial force analogous to areas, being the force conserved in nature â the corresponding law of âvis vivaâ â a collective law of conservation and the principle of its conservation
71, 454, 537, 661f.
Leibnizâs conservation law â product of mass and the square of the velocity â the conservation of this entity (âvis vivaâ)
87, 287, 363
Relative force â that produced for the determination / regulation of a body â preventing its advance, forcing its reversal of direction â a dead, disabled, relative, plane force analogous to lines â the corresponding law of âvis mortuaâ â a distributive law of changes
71, 661f.
Leibnizâs other conservation laws â product of mass and directional velocity â his concept of progress (âprogrèsâ), the counterpart of âforce morteââ the conservation of progress
70, 660f., 872
Papinâs conservation law â product of mass and velocity â movement, momentum and impulse â the conservation of this entity
56, 62, 71, 362, 662, 871
The conservation of force requirement â violation of the requirement
69, 657
Quantities conserved in all mechanical changes
57, 451
The âvis vivaâ controversy. Controversies and Disputes
Consumption of force â the consumption of dead force â accompanying that of living force, but In a different proportion
71, 661
Example of the tensioning of a spring â arising from the dead force â accompanied by the consumption of living force â comparison with changing areas and peripheries in geometry
71, 661
Example of the ascent of a weight against the force of gravity â similar to the tensioning of a spring
71, 661
Estimation of force â Leibnizâs estimation of force
64, 536, 682, 771
An âaestimatio viriumâ (âars aestimandiâ) â auguring additivity, homogeneity, substitutability
64, 535f.
His (real) measure of force â proofs for his measure of force, independent of experiment
66, 649
His distinction between force and action. see Action
Measure of force â Leibnizâs measure of force â Papinâs measure of force â both rooted in space and time
14, 18, 60, 66, 73f., 76â78, 80, 82, 85â87, 287, 358, 526, 536, 538, 647, 649, 666, 669, 674, 678, 679, 681, 744, 757, 761, 766, 771f., 774f., 863, 871, 873f.
True measure of force
18, 60, 66, 73, 78, 85, 358, 526, 649, 666, 757, 772, 863
Measurement of force by number of traversed springs â overcome with equal tension force / stress state of the springs
59f., 461, 647
Quantification of forces, based on the â attained heights of fall of bodies â distance covered by bodies â duration of the motion of bodies â velocity of the bodies â the product of mass and square of velocity
56, 59, 64, 71, 75, 460, 526, 536, 647f., 662, 671, 861
Transfer / transmission of force in collisions â laws of colliding bodies â force transmission between bodies
59â61, 66, 72, 527, 648, 656, 663f.
Elastic or tensioned springs â resulting from collisions or between colliding bodies
60, 64â66, 461, 536, 538, 647f., 650
Substitutability of bodies â explanation of the substitution process
67â70, 459f., 514f., 651f., 654â659
Papinâs definition of force and force transfer â attributable to very rapid percussions in a massless ether â measured by the resistance to be overcome â expressed as the product of mass and velocity
58f., 61, 71, 75f., 78, 459f., 527, 647, 672, 675, 682, 861, 871f.
Force and weakness â a force acting in a particular direction â a corresponding compensating weakness, acting in the opposite direction
84f., 770f.
Papinâs and Leibnizâs competing concepts of force, with regard to â dynamic processes â physical phenomena and their interpretation â terminology and the underlying theory
61, 65, 526f., 648
Papinâs and Leibnizâs lack of agreement regarding physical processes like â force transmission from a falling body to other bodies â in collisions of two or more bodies â in tensioning / relaxation of springs
61, 70f., 527, 648, 658, 660f.
Papinâs rejection of Leibnizâs proposition regarding â the uniform motion of a body â the concept of action
75f., 674â676
Papinâs understanding of the effect of force in terms of resistance being overcome â with the resistance not being proportional to velocity
59, 75f., 460, 647, 672, 675f.
Leibnizâs formal counter-argument
76, 676
Gravitation, gravity, force of gravity, universal gravity
19, 21f., 26, 51f., 56, 58, 61â65, 71f., 74, 76, 81, 91, 101, 103, 105, 108â111, 167, 183, 293, 358, 363, 366f., 369f., 383f., 432, 438, 441, 453, 458f., 463f., 481, 510f., 512, 526f., 532f., 536, 538â550, 577, 588f., 619f., 646â648, 661f., 665, 669, 676, 678, 762, 861, 863, 865, 867, 872, 874â878, 883
Conceptions / hypotheses of gravitation and gravity
Mechanical causes of ellipses
795
Non-uniformity of gravity
108
Cause and properties of gravity. Astronomy
Motion of a âmateria gravificaâ
108, 540
Ether percussion as the cause of gravity (Leibniz)
65, 538
Ether vortex â acting with infinite velocity (Papin) â proportional to the traversed distance, and the square of the velocity (Leibniz) â proportional to the elapsed time, and the velocity attained (Papin)
58, 103, 366, 458, 562, 646, 875
Center-of-gravity â center-of-gravity principles
65, 536, 538
Specific gravity
51, 62, 293, 363, 532, 872
Terrestrial gravity â influence of terrestrial gravity
19, 21f., 26, 56, 58, 61, 64, 81, 358, 432, 459, 463, 510â512, 527, 536, 619, 646â648, 762, 764, 863, 865, 867, 874
Fall and rebound of bodies in terrestrial gravity
81, 762, 764, 874
Leibnizâs discussion with Papin about gravity â force experienced by an ascending heavy body due to physical percussion effects (blows) â force proportional to the product of weight and height
58, 108, 459, 646f.
Papinâs alternative explanation â based on philosophical suppositions â force the effect of a resisting insensible fluid
108, 507, 539f., 877
Leibnizâs discussion with Huygens about gravity. see Physics
Inertia
73, 76â78, 80â83, 666, 676, 680f., 760â766, 873
Machines â applications of dynamics to machines â section about machines in Leibnizâs Dynamica
51f.
Magnitudes â homogenous magnitudes
51, 363
Matter â nature of matter â indifference of matter, e.g. towards states of rest and motion
52, 80â84, 453, 761â763, 767, 873
Media â resisting (resistance of) media. Physics
Motion in resisting media â problems of resisting media
112f., 372, 438
Resistance (absolute and relative) encountered by bodies in motion â arising from a bodyâs natural inertia â force required to overcome inertia â aversion / repugnance to such a force
58, 76f., 458, 676, 680
Motion / movement
Moving bodies / bodies in motion/ collision of bodies. Experiments, and Natural Philosophy, Bodies
Communication of movement â laws of communication of movement â Malebrancheâs tract (1692)
53, 454
Compound / conjoint movement â compounded movements of bodies in a single body
65, 84, 538, 608, 768
Concept of motion / movement
55, 525, 648
Impetus
51, 364
Laws of motion / movement â systematic laws of movement â laws of extended (or physical) bodies â actual (systematic) physical laws â connection with metaphysical laws â metaphysical foundations or principles
56, 60, 68, 83, 87, 287, 526, 537, 648, 652, 766, 874
Means of estimating moving bodiesâ effect as â a bodyâs gravitational ascent or descent â the overcoming of spring tension / force â the resistance encountered by bodies
58f., 61, 527
Mechanical motion â composition of motion
72, 76, 301, 664, 674, 762, 872
Perpetual motion â âmotus perpetuus mechanicusâ
58, 81, 133, 287, 459, 762f., 766f., 871, 873
Total motion/ movement in the world â a perpetual, inalterable, or invariable magnitude â an erroneous Cartesian belief (Leibnizâs view)
59, 459
Uniform motion of a body
76, 674f.
Action, Bodies, above
Varying motions â accelerating and decelerating motions
51
Velocity â magnitude of speed or velocity â with greater velocity / faster motion giving greater force, greater perfection, greater reality
84f., 769, 772
Velocity â directionality of speed or velocity
65, 539
Velocity changes or effects â absolute and relative â simple velocity, twofold velocity, etc. â infinitesimal changes
61f., 67, 77, 527f., 650, 681, 871
Resistance. Media above
Absolute resistance â relative resistance
77, 113, 680
External resistance â Internal (intrinsic) resistance
83f., 766, 769
Statics â static moment of a heavy body on an inclined plane
96, 375, 451
General problem (âproblema staticum generaleâ)
52, 451
Navigation â seafaring, shipping and navigation
108, 157, 179, 182, 194, 587, 704
Development of sea-worthy and precise clocks
182, 587
Portable watches of Leibnizâs invention (1675) â principle of their exactness
182, 587
Huygensâ completion of a new clock (1693)
182, 587
Shipbuilding and sailing â ancient and contemporary shipbuilding â Witsenâs tract âAeloude en hedendaegsche Scheeps-Bouwâ (1671)
146, 398
Methods of steering / maneuvering a sailing ship â Renau dâEliçagarayâs âDe la théorie de la manoeuvre des vaisseauxâ (1689) â Huygensâ dispute with the author
182f., 588â590.
Controversies and disputes Leibnizâs opinion regarding the dispute â his approval of the practical nature of Renauâs tract â his regret regarding the authorâs neglect of the center of gravity of the ship
183, 588â590
Matters at issue â force, speed, leeway or windward drift â Leibnizâs belief in a possible determination of a correct rule for leeway through the power of his dynamics
183, 589f.
Sailing in a fixed direction. see Mathematics, Loxodrome (Rhumbline Curve)
Global circumnavigation and observations â journeys of Dampier and Halley (reported 1701) â Halleyâs astronomical tables formerly used for computations at St Helena â Dampierâs presence at St Helena
98, 782, 794
Kirchâs astronomical table â sent by Leibniz to Sloane and Halley (1701)
118, 794
Netherlands, Holland
2, 9, 11, 20, 28, 33, 40, 43, 86, 116, 127, 129f., 132, 142, 156, 185f., 192â194, 197, 237, 250, 257, 302, 304, 306, 318, 320, 330, 349, 353, 360, 396, 408f., 428, 430, 497, 508, 518, 562, 572, 574â576, 578, 591â594, 606â608, 621f., 638, 643, 684, 702, 716, 733, 775, 786, 802, 867
Amsterdam
2, 7, 32f., 41, 128f., 132, 142, 146, 151, 153, 185, 192, 195â197, 219, 222, 250f., 271, 278, 301f., 304, 306, 318, 330, 347, 396, 398f., 524, 560, 563f., 571â573, 577, 592, 595f., 608â610, 622, 640, 716f., 719f., 802, 834f., 880
House offering medicinal beverage (1694)
610
Renowned apothecary / druggist (1696)
608
Side street / back street (âReguliers dwars straetâ)
719
St Anthonyâs Church cemetery (âSint Anthonis Kerkhofâ)
719
Antwerp
306
Breda
142, 395â397, 894
Brussels
306
Delft
x, 2, 128f., 131f., 241, 301f., 304, 306, 347, 474, 560, 576f., 682â685, 849
Delftâs âBurgomasterâ (mayor) and officials â the honor and glory of the town â the âOracle Delphiqueâ (Hugo Grotius)
132, 683â685
Dutch / Netherlandic â mathematicians, scientists, microscopists, physicians, etc.
6, 31, 91, 108, 128, 132, 137, 142f., 164f., 169, 179, 190, 196, 200, 214f., 224, 243, 249, 272, 283, 301, 312f., 327, 339, 383f., 395, 404, 410, 523f., 560, 574f., 605, 837, 848
Dutch East India company â the âVereenigde OostindischeCompagnieâ (VOC) â the companyâs Batavian Society
108, 226, 236f., 344, 732, 891
Dutch republic â Republic of the United Netherlands â Union of Utrecht (1579) â Republic of the Seven United Provinces (1581â1795) â States General of the United Provinces
132, 186, 192â194, 320, 592, 685, 716
Office of the Stadhouder (head of state of the Dutch republic)
192, 592
Reign of stadholder-king William III (1672â1702) â his accumulation of wealth â Leibnizâs and Crafftâs addressee (1694)
192â194, 592â595
Stadtholderless periods (1650â72 and 1702â1747) â Office of the Grand Pensionary of Holland â calamity year / year of disaster (1672) â murders of the de Witt brothers (August 1672)
193
The States-General / Staten Generaal
592
The Dutch slave trade
186, 320
âs Gravenhage (The Hague, Den Haag, La Haye)
2, 34, 265, 302, 466, 564, 622, 802
Groningen
32, 116, 250, 607, 786f., 867
Haarlem
2, 185, 318
Harderwijk
33, 622
Leiden
2, 43, 131, 302, 306, 347, 349, 559f., 643
Mastricht
193, 592
Rijswijk
576f.
Rotterdam
33, 621, 867
Utrecht
130, 305f., 716
Vianen (âFree cityâ)
716f.
Norway â Trondheim
236, 731
Numismatics, numismatist
8, 104, 358, 582
Nuremberg (Nürnberg)
xii, 97, 120, 128, 168, 198f., 220, 224, 261, 297, 326, 504, 564, 701, 721f., 800, 829, 839f., 884, 889
Alchemy in Nuremberg â alchemical society
xii, 220, 721f., 829, 889
Astronomy in Nuremberg â astronomical observatory â astronomical instruments
120, 799f.
Convex mirror production in Nuremberg (1695)
128, 564.
Instruments
Master craftsmen and practitioners of Nuremberg
198, 326f., 884f.
Projects
Observers
xv, 71f., 131f., 327, 380, 456, 473, 560, 662â664, 683â685, 800
Observers â their special abilities and assiduity
132, 683
Oldenburg (town)
257, 353
Osnabrück
273, 275
Optics. see Physics
Organization of science, learning and education
4, 197â208, 324, 499, 597f., 818.
Pedagogy, Projects
Paleontology and earth history. see Geology
Pansophy, pansophism. see Knowledge
Paradigms
xii, xiv, 88, 233, 288, 878
Paradox(es)
70f., 73, 336, 578, 661f., 666, 774, 778
Paradox(es) in Leibnizâs and Papinâs systems of natural philosophy with their respective concepts of force â apparent or linguistic paradoxes
70f., 661f.
Paradoxes as experienced by Papin â regarding two mutually-arresting bodies, one with double the velocity which would produce double the effect â also regarding the ability of a body at rest to bring a moving body to rest without force by virtue of its inertia
73, 666
Paradoxes as experienced by Leibniz â regarding Papinâs interpretations / explanations, which were both paradoxical and absurd, and offended against reason â even leading possibly to a âperpetuum mobileâ
73, 666, 773f.
Pathology. see Medicine
Pedagogy
32, 202f., 598f., 887
Mathematical pedagogy
32
Pedagogical projects. see Projects
Pedagogical reform â the Parisian pedagogue Ramus (16th Century)
199, 238, 597, 885, 887
Peoples and languages â origin and relatedness of peoples (and nations)
10, 231, 430, 841, 862
Language dynamics â Leibnizâs language dynamics â analogy with his dynamics in natural philosophy and physics
230
Language evolution â theory of language evolution
230
Protolanguage(s)
10, 230, 430
Sinology / Proto-Sinology
18
Search for a universal language
18
Linguistics â comparative linguistics â historical linguistics
10, 230, 430
Glossography â study of ancient words or languages
231, 841
Interrelationship of languages and alphabets
500
European Languages â history and relationship
232, 843
Matrices or unrelated languages of Europe â Basque, Finnish, Hungarian, Lappish
231, 843
Celtic / Celtic Studies / Celticization â pre-Christian Celticization
xi, 230â232, 841, 844
Languages of Great Britain and Ireland â origins of the peoples and languages
231, 841, 862
The Saxon origins of the English â the Anglo-Saxon settlement
231, 841f.
Relation of the Welsh to the Germanic tribe âCimbriâ
842
The Scots and Irish of more ancient, and of Continental European origin
842
17th-Century discussions of the development of the Celtic languages
230f., 841
Separation of Irish and Welsh (Scaliger, 1610)
231, 842f.
Relatedness of Irish and Welsh (Wallis, 1653/74), and Irish, Welsh and Breton (Wallis)
231, 843
Discussion in Leibnizâs correspondence (from 1694) â his thoughts on ancient âGaulishâ and its Germanic influences
843
His rejection of an Irish-Basque connection
231, 843
His comparison of Irish and Welsh texts â contemporary texts of the Lordâs prayer
231, 843
Division of the Celtic peoples and languages â Brythonic or Welsh (âCymraeosâ/ âCambrosâ) â Goidelic or Irish (âScotos antiquos / Hibernosâ) â referred to by Leibniz in his correspondence with Wallis (1699)
231, 841f.
Lhuydâs observations regarding Irish Gaelic (1699)
231f., 841f.
Similarity between the two linguistic families â P-Celtic (Breton, Cornish and Welsh) and â Q-Celtic (Irish, Manx, Scottish Gaelic)
231, 841
The âP-Q splitâ of the Celtic Languages â Leibnizâs reference to the split in correspondence with Wallis (1699) â first published in Lhuydâs âGlossographyâ (1707)
231f., 841
Toland as an Irish speaker â his influence on Leibniz (1701â1707)
232
Leibnizâs cooperation with Eckhart, and posthumous publication of the âCollectanea etymologicaâ (1717) â on the history and the relationships of the European languages
232, 843f.
Perpetuum mobile
58, 72f., 80, 82â84, 664, 666, 761, 764, 766, 768, 874.
Power
Persia, Persian
155, 236, 388, 700, 733
Pharmacology. see Medicine
Philosophy. Natural Philosophy
Aristotelian philosophy / natural philosophy
xii, 80
The Aristotelian entelechy concept
80
Entelechy. Natural Philosophy
Cartesian philosophy â Cartesian world view â Cartesians
xiii, 19, 21, 44, 56f., 59, 63â65, 76, 78, 81f., 85, 87, 105, 131, 233, 267, 271, 283, 287, 349, 359, 363, 369, 422, 427, 431, 451, 458â460, 463, 473, 512, 534f., 537f., 617, 620, 628, 644â647, 675f., 682, 687, 763, 766, 771, 830, 859f., 864, 871, 873â875, 878, 894
Contemplative Cartesian â antonym of a Leeuwenhoekian experimentalist â Leibnizâs critique
131, 473
History of philosophy
x
Mechanical philosophy â the mechanical view of nature â champions of this novel view (like Boyle)
91, 219, 383
Leibnizâs philosophical interests â his philosophical system â his philosophical works
56, 362, 526
Metaphysics
xiâxiv, 80, 205, 267, 647, 744, 820
Leibnizâs Discours de metaphysique (1686)
56, 362
Leibnizâs metaphysical controversy with Joh. Ch. Sturm â Its influence on Hoffmannâs mechanical world picture
266, 859
Metaphysical laws, paradigms, principles
xii, 56, 60, 103, 301, 526
Metaphysics and mechanics
xiii
Metaphysics and physics â confrontation of metaphysics and physics
80
Force conceptions rooted in natural philosophy / metaphysics
xii
Leibnizâs efforts to establish the overall
Metaphysical foundation of the laws of dynamics
60, 526, 648
Physical and metaphysical contexts of the world
647f.
Blockâs position (1699) regarding metaphysics and the disciples of that art â metaphysics in relation to reason considered by him to be a non-phantasm and non-entity of reason
830
His philosophical standpoint of not being a skeptic, but [rather] a Cartesian â doubting but not negating
830
Philosopherâs stone. see Alchemy
Philosophical assumptions, interpretations, thought â Leibniz and Papin
Papinâs views essentially shaped by Descartesâ philosophical thought
57, 458
Leibniz effort to prove that the source of error lay on the side of the Cartesians â example of the philosophical view of many philosophers â namely that the âtotal movement in the worldâ was a perpetual, inalterable or invariable magnitude
59, 459
Philosophical interpretation of biological preformation â the generation (and later death) of an animal â a transformation from a state to another state â the Leibniz-Arnauld correspondence (1686â87)
130f., 379f.
Reasoning and philosophy. see Reason, reasoning, rational thought, rationalism
Science and philosophy â Newtonian influence
xiii, 238f.
Sophism, sophistry, sophist â pansophism, pansophist
222, 224, 834, 838
Physics
Acoustics, sound â theory of acoustics and sound
3, 92
Sound production â tension and string tension â sound generation by string tension
52, 92f., 372f., 451
Sound propagation â for a given string tension, oscillations always isochronous â the same tone pitch is produced â the sound is transmitted at a constant speed
92f., 295, 372f.
Sound from a resonating body â manifest as vibrations or oscillations of tiny air particles
93, 295, 372f.
Percussion and repercussion â sound produced by a blow to a cushion â straining and state of tension of threads â a striving for restitution of the original state â possible rupture of the cushion
93, 296
Audiology, the science of hearing
93, 372
Hearing of sound â human experience of sound
94, 373.
Medicine, Anatomy of the ear Vibrations of tiny air particles carried to the ear â perceived pitch of a sound â constancy of pitch
93f., 295f., 372f.
Isochronism of elastic vibrations (oscillations)
93, 296
Different pitches transmitted in air
93, 296
Different sonorous bodies â in simultaneous resonance with the ear
93, 296
Homotony (condition of being homotonic) â being of uniform tension / tonus
242, 346
Sympathetic resonance with parts of the inner ear
93, 295
Sonority â sound level or loudness
93, 295, 372f.
Pitch, experience of pitch â related to frequency of received oscillations
94, 373
Ear consonance with all resonating bodies
94, 373
Ear drum â reproduction of corresponding sounds
94, 373
Similarity with a musical instrument, like zither or lute â different stretched strings â rendering of many different sounds â various instruments in mutual harmony
94, 373
Applied physics
Pendulum. Mathematics, Curves, Cycloid
Pendulum Clock â Huygensâcycloidal pendulum â isocrone
(double) pendulum â the âhorologium oscillatoriumâ
17, 24, 129, 284, 302, 436, 587f., 866
Richerâs âseconds pendulumâ â measurement of its length
197, 324
Experimental physics
204, 820.
Experiments and Experimentation
Mariotteâs research on the nature of an elastic collision â on the mode of operation of the wedge â on motion in a resisting medium
88, 306
Motion in a resisting medium â thoughts, theoretical considerations â mathematical treatment â experimental investigations
88, 112, 306f., 370
Fall of a body taking account of the resistance of the air
112, 306f., 370f.
Motion of a projectile â explanations of Galileo and Descartes â trajectory supposed to be a parabola â resistance of the air disregarded by Galileo and Torricelli
112, 370f.
Ballistics / science of ballistics â Blondelâs tract (1683)
88, 112, 306f., 894
Leibnizâs âSchediasmaâ (1689) on the â resistance of a medium â movement / motion in a resisting medium
21, 88, 112f., 121, 306, 370â372, 376, 406, 431, 439, 466f., 524
Motion of heavy projectiles â issue of the resistance of the air â application of the differential calculus
112f., 306, 370f., 466f.
Two forms of resistance â âresistentia absolutaâ and âresistentia respectivaâ
113, 371
Absolute resistance â proportional to the velocity
113, 371, 680
Relative resistance â proportional to the square of the velocity
113, 371, 680
Combination of the two forms in â Newtonâs âPrincipiaâ (1687) â Huygensâ âDiscoursâ (1690)
113, 371f.
Revision and extension of Leibnizâs Schediasm as an âAdditioâ (1691)
113, 372, 439, 467
Exchanges with Huygens (1690â91) â difficulties in reaching an understanding â role of the infinitesimal calculus
113, 372
Different understandings of resistance â as an effect synonymous with the resistance itself (Leibniz) â as pressure of a medium against a body (Huygens and Newton)
113, 467
Related issues â nature of an extended and resisting medium â admissibility of a perfect hardness of matter â existence of atoms in space devoid of air, matter
113f., 372
Studies of fundamental properties of air and water â compressibility (like with steam) â incompressibility (like with water) â partial or total incompressibility
101, 781f.
Density / temperature / expansion force of air â their interrelationship and proportionalities involved
101, 780f.
Elasticity and âheavinessâ of the air
101, 779f.
Laws of Physics, Boyleâs Law
Discussion with Joh. Bernoulli (1699â1701) â thought experiments and physical models
101f., 781f.
Bernoulliâs processes â based on proportionalities between densities and weights
101, 781
Discussion about incompressible parts of air â particles resisting compression â very subtle particles and their possible expulsion through the pores of the air pump
101, 781
Leibnizâs call (1700) for further experiments â to decide the matters of expansion by heat, and of contraction by cold
102, 782
Bernoulliâs measuring process â his condensation / compaction methods â differing from attenuation or rarefaction methods
101, 779f.
His claim of error reduction, and power-requirement reduction â with 3 or 4 rather than 20 cylinder strokes
779
His âDissertatioâ (1701) on the weight and elasticity of the air
101, 780
Geophysics â practical problems
97, 297f., 782
The shape of the earth â spherical or elliptical â an elliptical-spheroidal shape
107, 465f.
An elliptical-spheroidal shape of the earth â postulated excess of mass at the equator (Huygens and Newton)
107, 466
Postulated excess of mass at the poles â Eisenschmidtâs theory (1691) â Leibnizâs critical assessment â Huygensâ overall good impression, notwithstanding some doubts and reservations
107f., 465f.
Meridian(s) â line of longitude
25, 120, 381, 437, 441, 799
Meridian circle â construction
120, 799
The longitude problem â solution of the problem
97
Determination of longitude at sea â Huygensâ clocks for these measurements
97, 108
Subterranean measurements â pressure and temperature measurements
99, 476, 775f.
Modena, Subterranean wells
Earlier measurements undertaken by the Académie des Sciences â preparation of barometric ephemerides:
Possibility of an antiperistasis in observations â an illusion or false perception
99, 775f.
Gravity / gravitation. Natural Philosophy
Attraction, gravitational attraction
105, 367, 463, 875
Law of gravity â inverse-square law
105f., 109f., 367, 369f., 463, 540f., 543â545, 547, 549, 875f.
Attraction â of lead weights to the earth â of planets to the sun
463
Cause of gravity â an inherent property of matter â mechanical explanation of gravity
52, 58, 103, 108f., 366, 452f., 458, 539â542, 646, 876f.
Competing theories to explain gravity â based on assumptions of physical processes
109, 527, 542f., 876
Effects of circular motion (Huygens)
109, 542f., 876
Effects of rectilinear motion (Newton)
109f., 542â544, 876
Huygensâ theory (explanation of gravity) â his discourse on the cause of gravity (1690) â his hypothesis of matter in motion â his interpretation of gravity as a centrifugal force â deficit in the failure to yield an inverse-square law â similarities with his theory, seen by Leibniz
195f., 109f., 367, 369, 541f., 545, 547, 875f.
Newtonâs explanation / theory of gravity â his âPrincipiaâ (1687) â supposition of attraction and trajectory â lack of a law of gravity (Leibnizâs view)
102, 105f., 113, 201, 365f., 369f., 371, 462f., 542f., 548f., 874f.
His theory of gravitation â declaration of mutual attraction â the inverse-square law
109, 540f.
Constitution of the universe â consisting of empty space (for the most part)
109, 540â542, 876
Fatioâs tract on the cause of gravity (1688â90) â his mechanical explanation of gravity with two forms of matter â terrestrial matter, constituted of the smallest homogeneous particles â and an (almost) infinitely thin form of matter whose particles were the cause of gravity â subjection of the particles to high-speed rectilinear motions in all directions
108f., 542, 876
Reception of Fatioâs theory â Newtonâs approval and Huygensâ objection that matter surrounding the earth would become increasingly dense
100, 109f., 542, 545â547
Leibnizâs counter-argument â suggestion of a dissipation of surrounding matter â analogous to the activity of sun spots
110, 546f.
Varignonâs conjectures regarding gravity (1690)
110, 545
Leibnizâs supposition of gravitational attraction, and of rays of attraction
105f., 367, 369, 463, 875
Leibnizâs vortex theory â vortical motion of an ambient fluid
102, 106f., 111f., 463f., 548, 550, 552, 875.
Astronomy, Planetary Motions
Leibnizâs theory based on a circular-motion hypothesis â his conceptions of a rotating ether, and of a centrifugal force of a very subtle fluid
103, 196, 109f., 366, 369, 383, 463, 543, 875f.
Orbits of bodies rotating around the sun explained by his theory â based on the principle of equality of active force (being proportional to the square of the velocity) â all planets rotate in the same direction â a model for the derivation of Keplerâs third law, and of the law of gravity
106f., 111, 369f., 464, 548â550, 876f.
Other phenomena explained by his theory â water drops / droplets, and their round or spherical forms â the form of the terrestrial globe â parallelism of the axes of the planets with that of the earth
106, 463
Phenomena not consistent with Leibnizâs theory â constant eccentricity of planetary orbits â acceleration / deceleration along paths â movement of comets through vortices
107, 464
The trajectory of a comet â minimal impedance through a rare ether-vortex
111, 549, 877
Possible confirmability of Leibnizâs theory â possible harmonization with the other theories
106, 111, 464, 548
Huygensâ rejection of Leibnizâs theory â his insistence on the superiority of his own theory
106f., 464
Leibnizâs alternative theory based on a rectilinear-motion hypothesis
543f., 876
His notion of a fine ether vortex, where the ether particles produce gravity, and contain a compacted fine matter â analogous to a system of little air guns enshrined within a coarser matter
110, 546.
Magnetism and Electricity
Leibnizâs âexplosionâ theory of gravity â based on a rectilinear motion â with coarse matter enriched with fine matter being attracted to rarefied matter located at the center of attraction
109f., 543, 545, 876, 878
Explosion theory comparable to an incendiary or shattering process â example of the effect of a flame as a center of attraction â and of the effect of the sun as a center of attraction â with the shattering of bodies on impact
109f., 543, 546, 876
The process involving â an explosion or ignition being accompanied by rarefaction â fine matter being expelled to the periphery â re-alimentation of the coarse material there and the continuation of the cycle or process
109, 543f., 876
Comparison with the movement of light â ether particles producing light would contain a compacted fine matter
109f., 544, 546, 876
Explicability of the force of gravity as a centrifugal force â an inverse-square law for gravity â similarity with the photometric inverse-square law
109, 543f., 876
A combination of circular and rectilinear motions â in conformity with natureâs preference for an optimal, or minimum-redundancy solution
109f., 544, 876
Heat â solar heat and radiation (sunshine)
45, 848
Thermodynamics (the science of heat)
xi, 149, 696, 862, 881
Leibnizâs theory of heat
94, 373
Processes due to the motion of constituent particles of bodies â evaporation of water over a fire â liquefaction of metals in a furnace â retention of the liquid state by the power of the sun
94, 373
Effects of heat and cold in the human body â also attributed to the motion of particles â feeling of warmth evoked by the flux or movement of these particles â a sensation of cold experienced following the bodyâs debilitation and attack on its humors
94, 373f.
Elasticity as an explanatory principle
95, 242, 345, 372â374
The phenomenon that water in a vessel expands when frozen solid, and may shatter its container â attributed to a lack of convection and to the inability of the air, present in small bubbles, to form larger bubbles and exploit their elastic properties
94, 374
Analogous processes â explosion of gunpowder, by the application of fire, with scattered air pockets and the formation of larger bubbles â river flow regulation, using logging / lumbering techniques â use of large tree trunks capable of being swept away by torrential water flows, and sweeping away large obstacles, like bridges
94, 374
Leibnizâs explanatory theory for such processes â based on an assumption of the existence of small elastic particles â these being mutually obstructive while isolated, but with explosive capability when combined
94, 374
Instruments in Physics. see Instruments
Laws of Physics
Galileoâs law of falling bodies â his two new sciences, mechanics and local motion
36, 88, 296, 627, 869
Boyleâs law of the airâs elasticity â his âNew experiments physico-mechanicallâ (1660)
90, 101, 291, 780
Linusâ / Lineâs critique in (1661)
780
Boyleâs defense (1662) of his âDoctrine touching the spring and weight of the airâ
101, 780
Boyleâs observation of the role of heat in the expansion of rarefacted / rarefied air
780
Leibnizâs reference (1699) to a âcasual experimentâ of his own â his proposal for a clarifying experiment
101, 780.
Experimental Physics, Experiments
His interest in Boyleâs literary bequest and his manuscript estate
201
Keplerâs laws
103f., 366, 463, 875.
Astronomy
Law(s) of gravity
106, 110, 369f., 463, 543, 545, 875
Laws of motion
3, 56, 60, 83, 87, 287, 526, 537, 648, 766, 874
Cartesian laws of motion
87, 287.
Natural Philosophy
Newtonâs laws of motion
874
Light and optics
Theories of light
121â124
Leibnizâs supposition of a fine ether vortex â the particles of the ether produce light, and contain a compacted fine matter â analogy to a system of little air guns enshrined within a coarser matter
110, 546.
Magnetism and electricity
The corpuscular / particle theory â Newtonian corpuscular theory â Fatioâs corpuscular theory
123, 223, 554
The wave theory â Huygensâ predecessors â Ango, Pardies, Hooke
121â124, 376, 469, 556â558
Huygensâ treatise on light (1690) â âHuygensâ constructionâ â his explanation of wave propagation â his theory of light propagation â spherical wave propagation â his construction of wave fronts
105, 121, 125, 369, 376, 557
Light rays and waves â path of a ray in homogeneous media â waves orthogonal to rays
36f., 627, 630, 869f.
Mathematics, Orthogonal trajectories
Color(s) of light â theories of color â apparent and fixed colors
120â122, 124, 300, 376, 468f., 553, 556, 558
Color of blood attributed to refraction (Leibniz)
120, 306
Mariotteâs tract on the nature of colors (1679â81) â hypothesis formulated by Mariotte â no primitive constant colors of light rays â color change following refraction â his hypothesis opposite to Newtonâs views
120, 123, 306, 552f.
Newtonâs âTheory about light and colorsâ (1672) â his new experiments on the theory of colors â his seminal work âOpticksâ (1704)
121f., 124, 376, 468, 555f.
Huygensâ understanding of the nature of colors â his explanation requested by Leibniz
122, 124
Intensity of light â the photometric inverse-square law
106, 109, 369, 543f., 875f.
Movement of light â finite speed / velocity of light â Rømerâs demonstration (1676)
123, 554
Path of light â Fermatâs principle of the least time (1662) â supported by Pardies and Ango (1682) â supposition of slower motion in a denser medium
121, 125, 300f., 470
Leibnizâs minimal principle â his principle of the easiest light path (1682) â light follows the path of least resistance
120, 125, 300, 470
Leibnizâs priority over Fermat (Molyneux, 1692)
125, 470f.
His âuniversal principle in opticsâ â his claim of a shorter proof using the differential calculus â more rapid motion in a denser medium, with greater resistance of the medium leading to a greater velocity
121, 125, 300f.
Objections of Ango and Basilius Titel
120f., 300f.
Polarization of light â a phenomenon observed but not explained by Huygens
122, 124, 486, 556
Reflection of light â catoptrics â mirrors and waves â laws of reflection â Huygensâ derivation (1690)
121â123, 125, 301, 376, 469f.
The catacaustic curve. see Mathematics, Curves
Refraction of light â dioptrics
16, 26, 107, 125f., 282, 465, 470f., 558f., 704, 867, 870
Cartesian laws of refraction
87, 287
Snel(l)âs law of refraction â explanation of the law â Huygensâ derivation of the law (1690)
91, 121â123, 376, 383f., 469
Knorrâs âDe refractione luminisâ (1693)
124, 556
Phenomenon of double refraction in Iceland spar â Huygensâ explanation of the phenomenon (1690) â a critical test or an âexperimentum crucisâ
121â123, 125, 376f., 554
Leibnizâs opinion of Huygensâ treatment â merely a description, not an explanation
122, 376
Experiments with Iceland spar â samples of the mineral obtained by Leibniz â method of polishing the crystal using aqua fortis (nitric acid)
121f., 124f., 376â378, 468, 554, 556f.
Dioptrics â lenses and waves
37, 107, 125f., 465, 470f., 559, 704
Diacaustic curve
16, 282, 870.
Mathematics, Curves
Molyneuxâs âDioptrica novaâ (1692) â Huygensâ examination and critique
125, 470f.
Hartsoekerâs âEssay de dioptriqueâ (1694)
126, 558
Huygensâ (posthumously-published) âDioptricaâ
107, 125, 465, 559
Optics â mathematical science of optics
37
Leibnizâs âDe lineis opticisâ (January 1689)
121, 376
Newtonâs optical experiments â his planned work on optics
124, 555f.
Optical Instruments. see Instruments
Visuality and seeing â refulgence or luminescence
205, 822.
Scientific, educational projects,
Berlin Society, Spectacular experiments
Magnetism and electricity â phenomena of magnetism and electricity â related phenomena
98, 381
Magnetism â analogy of Leibnizâs vortex theory to this phenomenon
107, 464, 550, 877
Magnetic curl / rotation
111, 549
Leibnizâs supposition of a fine ether vortex â the ether particles produce magnetism, and contain a compacted fine matter â analogous to a system of little air guns enshrined within a coarser matter
110f., 546, 549.
Light and optics
Terrestrial magnetism
7, 43, 97f., 105, 110f., 278, 326, 369, 381f., 549f., 644, 782, 875, 877
The âterrellaâ, a small magnetized model ball â representing the planet earth
111, 550
Magnetic declination â variation of magnetic declination â gradual / non-abrupt change â spatial variation and temporal variation
97f., 297â299, 782
Law for the variation of declination â Leibnizâs heuristic continuity principle â spatial and temporal continuity
97f., 298
Cause of declination â a randomness in the earthâs make-up and structure (Descartes) â existence of a regularity (Leibniz)
98, 298
Huygensâ account (1679) of his âTraité de lâaimantâ
98, 382
Leibnizâs proposal (1681â82) for a system of corresponding terrestrial magnetic observations
198, 261, 325f., 504
Volckamerâs proposal for the creation of a âmathematical-magnetic associationâ
198, 326
J. C. Sturmâs âepistola invitatoriaâ (1682) regarding observations of terrestrial magnetic variation
7, 198, 278
Von Guerickeâs experiment with a ball of sulfur â his observation of electric sparking â Leibnizâs correspondence with him (1671â72)
98, 382
Huygensâ electrical experiments and theories
98, 383
Halleyâs research journey in the Atlantic â his study of the variation of the magnetic needle
200f., 499
Observations of the variation of the magnetic needle â observations made at sea, during Halleyâs maritime journeys (1698â1700) â Halleyâs map and observations sent to Leibniz by Sloane (1701)
98, 499, 782
Global circumnavigation and astronomical or magnetic observations. see Navigation
Mathematical physics â Leibnizâs paradigm for the advancement of mathematics and physics â organizing / carrying out a system of experiments â accumulation of empirical observations â refining calculations on the basis of experiment
88, 288
Mathematical relations for the physical world â mathematical treatment of physical themes â physical applications of the infinitesimal calculus
xiiâxv, 18, 25, 37, 88, 288, 306, 358, 437, 630, 863f., 870
Mechanics â celestial mechanics. see Astronomy
Mechanical reasoning. see Reason, Reasoning
Mechanics and mathematics â mechanics reduced to the terms of pure mathematics
151, 283, 288, 882, 884
Mechanics and physics â mathematical problems relevant for the world of physics and mechanics
271, 286, 870
Mechanics of fluids, hydromechanics. see Engineering, Science of Engineering
Newtonian mechanics â mechanistic Newtonian mathematical physics
xii
Theoretical physics
Leibnizâs âHypothesis physica novaâ (1671)
51, 55, 87, 103, 287, 364â366, 457
Discussion with Foucher (1692â93)
54f., 57, 214, 412, 451, 456f.
Physiology. see Medicine
Poland, Polish
17, 161, 226, 276, 345, 808, 892
Political economy. see Economics
Population settlement / resettlement
186, 231, 321, 841
Projected new town near Harburg (1680â81) â settlement for emigre Huguenots
185, 318
Potsdam â astronomy in Potsdam
114
Power â power and energy
Power generation / energy conversion
133, 861, 878
Power / energy source(s)
134, 144, 147, 307, 391, 566, 686f., 880
Renewable energy / power source
134
Power / energy storage â pumped-storage
137, 162, 384, 813, 878, 894
Power technology
xi, 3, 133, 146, 384, 398f., 565, 685f., 800, 877f., 894
Concept of mechanical power
133
Concept of a power technology
133, 878
Medieval / pre-modern exploration of mechanical power
133, 878
Power-conscious engineers / technicians of the late middle ages
133, 878
View of the cosmos as a reservoir of energies â vision and conception of a âperpetuum mobileâ
58, 72f., 80, 82â84, 133, 664, 666, 761, 764, 766, 768, 874
Early-modern development of power technology â accompanying social change
133f., 161, 862, 878
Leibnizâs commitment to the development of power technologies
133, 863
Power / energy transmission â rod-engine transmission
135, 137, 139â141, 144f., 308, 385, 388, 391â393, 566â569, 879f.
Mining
Power forms
Explosion / combustion power
94, 182, 374, 585, 690, 862, 878, 880
Firepower (artillery, firearms)
152, 216, 401, 576f., 894
Gunpowder â experimental investigation of its nature, power, and its constituents â air pockets contained in gunpowder were the cause of the force released in gunfire â pioneering works of Papin (1674 and 1688) â his insight that the effect of gunpowder increases with the resistance to be overcome â the explosive effect of gunpowder attributed by Leibniz (1697) to the compressive pressure of the air
94, 146f., 216, 374, 413, 686f., 695, 880
Muscle power â animal power â manpower
140, 150, 162, 388, 802, 813
Horse mills
136, 141, 144, 310, 392, 566, 573, 880
Steam / fire power. Engines, Enginery
Steam / water vapor as a power source
148â150, 689f., 692f., 696, 878, 881
Steam engines
146â150, 688, 690, 881
Vapors (other than steam) as a power source â expansion of other vapors â example of spirit of wine
146, 182, 585â587, 686, 878, 880f.
Water power. Mining
Water-powered and water-raising machines â water wheels
62, 134â142, 144f., 154f.,162, 234, 307, 309â311, 384, 386â388, 391â393, 397, 532, 566â570, 698f., 701, 872, 879f.
English waterworks â water-lifting machines
143, 397
Water-lifting machines in Copenhagen
143, 312
Water-lifting machines in Paris â the machine of Marley
143, 312, 397
Wind power. Mining
Wind power â windmills â horizontal and vertical windmills
4â6, 133â140, 142f., 162, 169, 273, 275, 307â313, 384â388, 391, 396f., 572, 813, 861, 878f., 881
Prime movers. see Engines, Enginery
Priority disputes. see Controversies and disputes
Projects â the world of projects and projectors â Leibniz as projector
12, 167, 183, 185, 214, 315, 320, 333, 338, 884â888
Leibnizâs philosophy of projects â his desire to overcome the prevailing scholar / tradesman or craftsman cleavage â his proposal (1682) for a dialog between scholars and tradesmen or craftsmen, and for an interaction of artisans, craftsmen, and practitioners with the learned / the world of learning â his desire to counteract the lack of such interaction in Nuremberg â his complaint about a certain sterility, with new and useful annotative expressions of abilities being prevalent in the population, but largely unknown among the learned â his proposal to counteract this sterile state, the practical ignorance of the learned, the bookish erudition of scholars, and the dearth of practitionersâ explanatory notes
167f. 198f., 326f., 884f.
Projects / projectors in Leibnizâs correspondence â Defoeâs âEssay upon projectsâ (1697)
12, 862
Projectors â cooperation (or lack of) between projectors â mutual trust or mistrust â agreement and recommendation, or intrigues, scheming, and withholding of information â use of cryptographic scripts or ciphers, with encrypted and non-encrypted texts â hampering of decryption by other parties, or unintentional confusion or misunderstanding, and use of vague intimations
183f., 314f.
Range of projects
Chemical projects â economic utilization of chemical processes
190, 214, 337, 409, 888
Production of a fluid gold paint (Leibniz, 1680) â used for dyeing clothing
190, 214, 338, 410
Production of ruby glass (Leibniz / Hooke, 1680)
127, 190, 214, 338, 410, 562
Preparation of gold and silver from raw materials or chemical precursors (Crafft, Elers, et al.)
190, 214â216, 218, 338f., 410, 418, 888
Efforts of chemists in Dresden to obtain gold from copper, mercury, silver (1680)
214, 339
Adolphiâs chemical secrets offered to Crafft (1680) â processes to obtain mercury from metals, and to separate sulfur and mercury â Leibnizâs intervention
214f., 339f.
Becherâs gold from sand project (late 1670s) â failed demonstrations in Amsterdam, Hamburg â witnessed by Stisser (reported 1699)
222, 834
Perfection of pearls (Crafft, Elers, 1681)
190, 214, 338, 410
Production (cementation) of silver from cinnabar (mercury sulfide) through the use of sulfur and lead (Elers, Pratisius, 1681)
214, 339
Ideas of Crafft, Rojas y Spinola, Leibniz (1682) â about obtaining silver from the liquation / segregation of Spanish copper coins
214, 339
Elersâ report to Leibniz (1682) regarding the sale of a process for obtaining gold
214, 339
Economic, techno-economic projects. Economics
Projects undertaken for national economic benefit â dependent on princely patronage, like financial support, and granting of privileges
183, 315
Futility of entrepreneurial involvement in manufactories without princely or baronial participation â expressed by Crafft (1691)
191, 497
Leibnizâs and Crafftâs brandy project (1694) â for production and marketing of brandy
196, 718
Discussions / negotiation at German and European courts â with court ministers, mercantile communities and interests, estates and social hierarchies
183f., 315
Crafftâs (and Leibnizâs) approach (1680) to the elector of Brandenburg
184, 317
Crafftâs (and Leibnizâs) approach (1680/81) to the emperor, and to imperial privy counsellors â proposals for the establishment of manufactories
184, 315f.
Leibnizâs opposition to an anti-French embargo with import barriers for French goods â his expectations for a less expensive production of domestic goods
184, 317
Prospects for export of manufactured goods â silk and wool products â proposed manufactories
184f., 316f.
Use of machinery in the manufactories
185f., 317f.
Machines, Mechanization and Social Change
Crafftâs conception of new machines for silk and wool manufacture (1680) â for textile manufacture (1681â82)
185f., 317, 321
The ribbon-loom â the âmola limbolariaâ (Bandmühle) â requisite purpose-built building â fabric production â braid and lace
162, 185, 318, 811
Proposed bag cloth and stockings manufactory â associated workhouse and orphanage in Saxony (1680)
186, 321
Proposed bag cloth manufactory in Brunswick and Lüneburg (1680)
186f., 321
Proposed steel production in the Harz district (1680)
187, 321
Manufactories considered (by Elers and Leibniz)
187, 322
Diversity of projects in Elersâ sights â a glassworks in the Weser Uplands (1681) for making of burning glasses (lenses) â a new kind of wax bleachery in Dresden (1681) â an invention to make ships unsinkable in Berlin (1681) â wallpaper made of silk, and printed with gold or silver, in Dresden (1681â82)
187, 322
Project for improvement of the luster of pearls (1684)
189, 408
Leibnizâs (and correspondentsâ) interest in engraving, punchcutting, textile printing (1683), silk and wool manufactories (1683â88), the silk trade, iron and steel production, and the wine trade (1688)
152, 184, 189, 214, 317, 321, 339, 401, 407f.
Other techno-economic / chemical projects (1680s). Chemistry
Dyeing of garments â Leibnizâs historical note (1690) on Drebbelâs discovery of scarlet dye (1608) â history of the discovery of the tincture
190, 410
Production of ruby glass
190, 410
Perfection of pearls
190, 214, 338, 410
Retrieval and extraction of gold, silver
190, 410
Phosphorus production
190, 213, 410, 412
Desalination / desalinization of sea water â Lacyâs desalination plant near Modena (1690)
190, 201, 410, 499
Chemical processing using vitriol (1689) â production of dangerous emissions
190, 410
Projected utilization of chemical substances
214, 337f., 888
Paints for the conservation of wood and stone
190, 409
Production and application of paints by Crafft, and by Heyn along the river Elbe (1687)
190, 409
Veins of iron and crude ores â yielding fine umbra and brown ocher pigments
190, 409
Projected factory / plant for processing mineral ores
190, 409
Production of paints for building and construction in Hungary and lower Austria
190, 409
Military-related projects
3, 177f.
Armor production (1681â1683)
177, 322f.
Making mail armor out of silk (Elers, 1681) â incorporating a network of brass wire â similar coats of armor produced in England and Sweden
177, 322
Testing of Swedish armor â resistance to musket balls or shot â tested on a human target, as part of an execution of a soldier
177, 322f.
Danish incendiary cannonballs (1682â83)
177, 323
Firearms (1683) â rifled gun, with automatic transfer of powder to the priming pan
177, 323
Ballistic mortars and grenades â mortar made of metal
152, 324
Mortar made of pasteboard â advantages of light weight, and easy transportability
177, 323f.
Kindred device â Bonfaâs pendulum (1679), made of pasteboard
177f., 324
Submarine development and navigation. see Submarines Military use â envisaged attacks on hostile vessels
181, 496
Scientific, educational projects â organization of science and education
3, 197, 200, 324, 499, 597, 818
Academies and learned societies â academies of sciences and arts
12, 197, 202, 508, 597, 828
Advancement of knowledge and practical skills â dedicated colleges, institutions and societies
201f., 499, 597f.
Pedagogical projects
202, 597, 862, 885, 887
Weigelâs commitment to pedagogy, learning â Leibnizâs approval and political support
202f., 599f., 887
Weigelâs school reform enterprises â his private school project (1683) â his public school project (1690) â his school of virtue, the âKunst-und Tugendschuleâ
202f., 599f., 887
Development of teaching / didactic materials
203, 599, 887
Teaching / didactic methods â possible with existing teachers or preceptors
599
Rules and mechanical instruments â a writing rule (âSchreibregelâ) â a reading rule (âLeseregelâ) â an arithmetic teaching aid
203, 599, 887
The core activity concept, with â a floating class (âSchwebeclaÃâ) or swaying movements on a suspended platform, giving a common class movement combined with individual rhythmic movements
203, 599f., 887
The dynamic instruction method â a combination of rhythmics and calculation, reading and swinging
203, 599, 887
A traditional syllabus with greater emphasis on mathematics and science â use of the vernacular as a medium of instruction
203, 599
National and international academies
Austrian academies â the âCollegium Imperiale Historicumâ in Vienna
200, 499
English academies â Royal Society of London
xv, 2, 15, 28, 46, 88f., 108, 116, 130, 150, 168, 198, 200f., 207f., 210, 214, 247, 265, 272, 278f., 289, 305, 312, 325, 327, 331, 338, 499, 517, 519, 540, 579, 597, 698, 749f., 787, 790, 802, 828f.
Royal Society appointments, membership, financial endowments â contrast with the Académie des Sciences
201, 208, 597, 829
Position of curator of experiments offered to Papin (1699) â Leibnizâs desire (1699) for the reinvigoration of the Society
207f., 828f.
French Academies â the Académie des Sciences
6, 34, 43, 48f., 53, 55, 88, 98f., 114, 116â118, 168, 197f., 200f., 208, 211f., 244, 265, 271, 276f., 306, 324f., 327, 336f., 348, 382, 412, 453f., 457, 580, 589, 597, 623f., 644, 753, 755f., 775, 783, 786f., 791f., 793f., 829, 868
Financing of the Académie â meetings of the Académie
14, 197, 324, 745
Laboratory of the Académie des Sciences â Huygensâ appointment â Papinâs assistantship (1673â1675)
57, 457
Membership and remuneration aspirations (Leibniz, Tschirnhaus)
200, 276, 327
Reform of the Académie â its restructuring (1699)
208, 829
The projects of the Académie â journeys to equatorial regions â French Guiana â journeys for map improvement
197f., 324, 397
German academies and universities â a projected âSocietas Germanaâ â the âCollegium Artis Consultorumâ (Weigelâs project, 1694), independent of royal or princely support
200, 202, 499, 597f.
Berlin â the Berlin Society of Sciences (1700) â âSozietät der Wissenschaftenâ, and the Prussian Academy of Sciences
14, 44, 47, 115, 120, 203, 262, 745f., 752, 784, 799, 818â829, 858
Financing of the Society â reputation of the Society abroad
204, 819f.
Leibnizâs presidency of the Society
14, 745
Membership of the Society â mathematicians, scientists, physicians â necessity of limiting the number of members, and restriction to the dignified and famous
203â205, 818f., 821
Projects / undertakings â construction of an astronomical observatory (1701â02) â gathering of medical and meteorological ephemerides â the medical ephemerides program â established 1701 and directed by Hoffmann in Halle
204, 206, 818, 822
Leibnizâs efforts (1701) to establish missions in remote regions â intended to help the youth gain knowledge of languages, and receive instruction in mathematics and in medical-surgical doctrines
822
Research on dyadic or binary mathematics â envisaged Journal, the âMiscellanea Berolinensiaâ (1710â)
49, 167, 204, 209, 214, 328, 413, 481, 756, 818, 820, 883
Leibnizâs efforts to communicate an enthusiasm for science at the Berlin court â by means of spectacular experiments
205, 820f.
Experiments, Experimentation
Joh. Bernoulliâs desire for financial support for his experiments, and access to a journal for publications
204, 820
Projects of the Berlin Society (1701) â a system of fire engines â a calendar monopoly enterprise â the drainage of swamps and marshlands â a German technical dictionary project
207, 827
GieÃen â University of GieÃen (1607)
201, 597
Göttingen â Grammar school
200f., 327, 597
Goslar â center in the Harz mining district â seat of the physician Stockhausen
256, 857f.
Halle â University of Halle â Thomasiusâ experimental lectures to promote a spiritualistic approach
205, 820
Academia Leopoldina, or the âAcademia Naturae Curiosorumâ, in Halle
97, 198, 201, 206, 236, 249, 260f., 298, 325f., 502, 504f., 597, 605f., 732, 822â824, 884
Hoffmannâs Lectures at the Leopoldina â project of the Berlin Society and the Academia Leopoldina
204, 820
The Medical Ephemerides Program, for annual publications following the example of Ramazzini â the collection of observational data regularly throughout a year â similarity with the joint efforts of theologians and mathematicians in the context of the calendar reform
205f., 261f., 502, 822â824
Hoffmannâs program for recording barometric, hygroscopic, and thermometric data â his goal of understanding the functioning of the barometer, and the link between weather and maladies
100f., 206, 823f.
Hoffmannâs explanation of barometric phenomena â his âObservationes barometrico-meteorologicaeâ (1701)
100f., 206, 779, 824
Leibnizâs proposal (1700) for physicians to establish a system of annual observations â a plan for a system of medical-meteorological observations, under the aegis of the Berlin Society
206, 262, 822f., 825, 858
Mandate granted (1701) for learned physicians to carry out annual observations in the provinces â a system of observations by physicians to explain the connection with illnesses â to obtain insights into epidemics, their occurrence and prevention
206f., 824â826
Mandate also to explore a possible influence of celestial bodies, or a Keplerian âAstrologia meteorologicaâ, by considering lunar and solar phases (Leibniz) and planetary aspects (Hoffmann)
207, 826
Additional observational data of â weather and illnesses â regional geographical details â living conditions and circumstances of the population â welfare of animals â condition of field crops
207, 825
Observations were to be made ideally by two physicians for purposes of mutual control
207, 825
Optional employment of instruments including barometers and thermometers
207, 825f.
Leibnizâs appeal to Sloane for emulation elsewhere (December 1701)
207, 826
Hamburg â Society of Hamburg â the âKunst-Rechnungs-liebende Societätâ
200, 499
Hanover (or Göttingen) â location for Leibnizâs proposed military academy (1680)
200, 327
Helmstedt â University of Helmstedt â the âAcademia Juliaâ (1576â1810)
14, 92, 201, 212, 219, 254, 275, 294, 337, 345f., 597, 619, 701f., 721, 729, 744f., 834, 855
Jena â University of Jena (1558)
49, 120, 202, 212, 337, 597, 729, 800
Kassel â the âCollège de Curieuxâ â the âCollegium Illustre Carolinumâ (1709)
201f., 597
Wittenberg â University of Wittenberg (1502)
91, 201, 262, 293, 329, 556f., 597, 604f.
Wolfenbüttel â Ducal library, the âBibliotheca Augusta Guelficaââ Military academy, the âAkademie Rudolph-Antonianaâ
7, 11, 156, 175, 356, 430, 486, 508, 574, 701, 838
Italian academies
Rome â âAccademia fisico-matematicaâ (1677â98)
104, 367
Venice â Sarottiâs scientific academy (1682)
200, 327
Technological projects
Technology and technological thought â an 18th-century concept (1777) â a discipline devoted to the systematic description of handicrafts and industrial arts
ixâxiv, 188f.
Development of technological thought by cameralists (from the late 17th century)
xi, 189, 407
Becher as pioneer in the development of technological ideas and thinking â his physical, mechanical, mercantile concepts and propositions (1682)
188f.
Technology and engineering sciences â philosophy of technology and the sciences
188
Technological inventions â invention reported by Tschirnhaus (1682) â a chiming repeater clock
187, 323
Proto-industrialization (The early industrial age)
xi, 149, 160
Prussia. see Berlin, Berlin-Brandenburg, Brandenburg-Prussia
Pumps. Mining
Types of pump
Ancient Greek and Egyptian technology â screw pump â Archimedesâ water-screw pump
138
Force pump â known since Hellenistic times
178
Lift pump â water lifting device â developed in Europe in the late middle ages
178
Suction pump â suction-lift pump
178
Suck and press pump â Reiselâs pump (1684 and 1690) â the âSipho Würtembergicusâ
178, 487, 886
Papinâs centrifugal Hesse pump (1689 and 1695) â the âRotatilis suctor et pressor Hassiacusâ
150, 157f., 178, 487, 494, 496, 704, 706, 803f., 886
Areas of application â air exchange in a submergible vehicle (1691â92)
150, 179, 181, 490, 493, 803.
Submarines, Submarine Development
Coal mine aeration / ventilation (1699)
150, 803
Seawater desalination
139, 150, 190, 201, 219, 387, 410, 499, 573, 803
Fuel economization in a machine â first successful experiments (1699)
150, 803
Piston pump â pump cylinder and piston â sealing techniques
138, 141, 148, 182, 385, 392f., 587, 691f.
Steam pump
146, 149, 686, 697, 801, 880.
Steam Engine
Quedlinburg
90
Reason, reasoning / rational thought
xiv, 24, 50, 61, 73f., 76, 91, 131, 229, 241f., 263, 343f., 367, 380, 425f., 466, 468, 473, 515, 527, 556, 593, 595, 649, 666â668, 674, 678, 696, 718, 725, 743, 757, 767, 770f., 778, 790, 806, 830f., 870f., 874, 895, 897, 899
Rationalism â rational scientific thought
xv, 863
Rational thought and experimental science
xiii
Rational thought and medicine â rational medicine
266f., 742f., 859f., 862, 896.
Medicine
Reasoning in dynamics
65, 538.
Dynamics
Reasoning / exact reasoning in law, morals, politics
429
Reasoning in mathematics â mathematical reasoning
482
Reasoning in mechanics â mechanical reasoning
225, 343, 890â892.
Mechanics
Reasoning in physics â physical reasoning
482
Reason and experience or experiment
61, 527, 668, 871
Leibnizâs touchstones of form and experiment â formal and virtual; form and experiment; a priori and a posteriori â establishment of a doctrine a priori, independent of sensible bodies
60, 65, 649, 767
Formalization / formalized forms of argumentation
61, 66, 83f., 527, 648, 757, 767, 770
Syllogistic reasoning, syllogisms, syllogism chains
61, 66â68, 76, 78f., 82, 86, 527, 648, 652â656, 674, 678, 757f.,765, 774f.
Syllogistic premises â major premise, minor premise, and conclusion
68, 76, 82, 86, 653, 678f., 766, 774f.
Leibnizâs syllogistic reasoning
76, 674, 678
His recourse to the method of syllogisms (1696)
66, 648.
Natural Philosophy, Vis Viva, Action, and Papinâs 13thâ17th syllogisms (1696â1697)
Regensburg â Imperial Diet / Perpetual Diet (âReichstagâ) â Protestant imperial estates (âCorpus Evangelicorumâ)
114f., 117, 162, 202, 414, 598, 782, 784, 790, 811
Rhineland district â Rhineish foot (measure)
561
Relativity (Galilean relativity) â absolute and relative
77, 113, 371, 681
Absolute action, force, resistance, velocity
67, 71, 75, 77, 113, 371, 454, 537, 650, 658â661, 673, 680f., 762
Relative action, force, resistance, velocity
66f., 71, 77, 113, 371, 536, 649f., 661f., 680f.
Religion
Biblical studies and scriptural references â the book of Moses
42, 119f., 798f., 898f.
Biblical archaeology â Burnetâs âArchaeologiae philosophicaeâ (1692)
228f., 724f., 897
Biblical narrative â its historical veracity / falsehood
xiv, 229
Creation (origin of things) out of âGodâ(1) and ânothingâ(0)
xv, 48, 753f.
Leibnizâs ânew yearâs letterâ (January 2/12, 1697)
27, 646
Creationism and Creator â divine creation â wisdom of the creator
xiv, 59, 460, 541
Mysticism, mystical theology
xv, 899
Obscurantism
798, 899
Religious heresy, heretics
xiii, 42, 232, 641
Religious rationalism â faith and reason â deistic, rationalistic theology
xiv, 219f.
Early modern theorizing about science and religion â cosmological and cosmogenic theories â geological and geomorphological theories
xi, xivf.
Compatibility of science and religion â interaction between science and religion
xi, xivf.
Early modern natural philosophy allied with revealed religion â scientist-theologians, or advocates of a physico-theology
xv
Conflict between science and religion â divorce / separation of science and religion
xvf.
Relation of science to religion â philosophical and theological issues â reflections of Boyle and Newton
90f., 219
Leibnizâs correspondence with Wedel â objections of the correspondent against heliocentricism â his view of a contradiction of the biblical account of the creation, and the story of genesis from the book of Moses
119, 798, 898f.
Leibnizâs preference for a metaphorical rather than literal interpretation of the biblical narrative
119f., 798f., 898f.
Priority for Leibniz of science, reason and rational thought over mysticism, religion and theology
899
Republic of letters. see Learning, Learned
Resistance. see Natural Philosophy, Medium, Media
Rübeland (Harz district) â nearby cave (âBaumannshöhleâ)
227, 419, 892
Russia â Muscovy / Muscovite Russia / Grand duchy of Moscow
13, 253, 618, 853
Satire, satirical writings â Becherâs satirical work (1682)
7, 140, 146, 188, 278, 390, 398, 523, 880
Savoy / duchy of Savoy (Savoie) â siege of Montmélian (1691)
175, 486
Saxony â electorate of Saxony â Saxon court
6, 19, 141, 153, 160f., 184, 186, 190, 201, 226, 257, 271, 275, 315, 321, 330, 332, 344f., 352â354, 391f., 402, 408, 499, 576, 808, 842, 857, 879, 891
Dresden
6, 146, 152, 160, 186f., 214, 257, 262, 275f., 321f., 330, 339, 352â354, 398, 401, 605, 807f.
Ehrenfriedersdorf
141, 391f., 879
Erzgebirge (Ore mountains)
201, 499.
Mining
Estates / orders of social hierarchy in Saxony
184, 315
Freiberg
141, 391f., 402, 879
Görlitz
200, 226, 249, 327, 345, 423f., 891
Kieslingswalde (near Görlitz)
161, 200, 327, 808
Königstein â Fortress Königstein
807
Leipzig â Leipzig spring fair (1697)
16, 22, 36f., 49, 58, 60, 116, 126, 130f., 141, 215, 257, 262, 280, 304, 312, 339, 341, 352, 361, 379, 394, 432, 441, 443, 458, 462, 519, 557, 559, 605, 628f., 785, 864, 869f.
Mercantile community in Saxony
184, 315
Muscau (near Görlitz)
226, 891
Schneeberg mining district â Schneeberg disease
256, 857
Torgau
262, 605
Science and the sciences, scientists
Advancement of science / the sciences
52, 128f., 132, 197, 208, 324, 452, 562, 626, 685, 827
Abstract / theoretical science(s) or scientific approach
239, 481, 575, 846
Applied /concrete / practical science(s) or scientific approach
87, 89, 92, 131, 239, 290, 294, 328, 846
Exact science(s)
4, 263, 266, 272, 425, 742, 895
Experimental science
xiii, 130, 204, 247, 380, 820, 852
Leibnizâs Idea (1701) of a âcollegium experimentaleâ, with lessons / lectures on physical-mathematical inventions and experiments â their 100-fold superior value over corresponding lessons in metaphysics, logic, ethics (Leibnizâs words to Hoffmann)
205, 744, 820
Studies in experimental science in Halle â Hoffmannâs lectures on experimental physics (1700â1701) â issue of their financing / financial support â his advocacy of an empirical science based on a Cartesian mechanical world view
204f., 820
Thomasiusâ experimental lectures in Halle â based on a spiritualistic approach
205, 820
History of science
x, xii, xiv, 7, 199, 239, 271
Natural science
xv, 236, 732
Observational science
131, 473
Observations
7, 57f., 88, 97â99, 117â120, 126, 129â132, 159, 164, 166, 198, 206f., 231, 234f., 237, 241â243, 247f., 258, 261â263, 277f., 283, 288, 294, 298, 300â305, 324â326, 333, 336, 343, 345f., 347, 351, 355, 363, 365, 379, 381f., 403, 458, 465, 473f., 477f., 480, 495, 498, 500, 504f., 557, 602, 604, 614, 646, 683â685, 694, 709, 727â731, 776f., 779, 788, 790â794, 796f., 799, 822â826, 841, 845, 847â849, 851, 858f., 890, 897, 899
Scientific rationalism. see Reason, Reasoning, etc.
Science and religion. see Religion
Scientific ideas â transformation of scientific ideas
xiii, 103
Scientific revolution(s)
xiiâxiv, 1, 104, 142, 199, 225, 238
Copernican revolution
xii
Evolution of classical science
xiif.
Newtonian revolution
xiii, 103
Paradigm of the scientific revolution
xii
Scientific societies. see Learning, Learned Societies
Unity of science
xv, 51
Scotland â draining coal mines â water power in Scotland
310f.
Shipbuilding and sailing. see Navigation
Steering and maneuvering a sailing ship. see Navigation
Slate â Mansfeld copper-slate
226, 344, 891.
see Mansfeld (Harz)
Slavery and serfdom â slave trade / slave traders
186, 320
The Atlantic slave trade â between Africa, the Americas, and Europe â the Dutch and Atlantic slave trade
186, 320
The âBrandenburg-African Companyâ (1682â1721)
185f., 319f.
Elersâ project relating to black Africans (1682) â Elersâ advocacy and Crafftâs rejection / skepticism
186, 319f.
Leibnizâs interjection regarding the Dutch slave trade â with total prohibition within the republic itself
186, 320
Elersâ insistence â that black people were being held in Holland, even by Jews there â that black laborers were hardier than their European counterparts
186, 320
Economic and demographic factors considered â demographics of Germany and of north American territories â possibility of relocation and rural settlement of black Africans in Canada
186, 320
Space. see Astronomy
Spain, Spaniards, Spanish
14, 142, 214, 220, 252, 339, 607, 723, 741, 746, 811
Spicery, spices
408
Speyer
414
Steam â steam engine / steam pump. see Engines, Enginery
Steganography. see Cryptography
Stralsund
264, 738
Strength of materials. see Materials
Submarines (submersible vessels)
3, 177â182, 487f., 490â493, 496, 584, 586, 827, 862, 885f.
Submarine development and navigation
Drebbelâs submersible vessel and his passage across the Thames (c. 1620) â speculation regarding air exchange / renewal â supply of fresh air to the vessel â possibly achieved by chemical means â possible use of a quintessence â possible beneficial effects from the burning of spirit of wine
178f., 488â490, 584â586
Papinâs âNavis urinatoriaâ/ âBatteau plongeantâ (1695)
178â181, 488â496, 584â586
His trials of the vessel on the river Fulda at Kassel
150, 488, 803, 885
His first design (June 1691) â vessel crashed and wrecked (August 1691)
179f., 490f., 496
Form and construction details of the vessel â rectangular parallelepiped tinplate box â its wooden hull and iron guide rails
179, 490f.
Use of lead ballast for submersion â lockable openings in floor and roof â upper hatch used for entry and exit, and loading of lead ballast
179f., 490f.
Bottom hatch used for offloading of lead ballast, and other under water operations
180, 490f.
Use of a ventilator pump for air exchange
179, 490, 887
Key features of the air exchange system â intake of fresh air â expulsion of foul / exhaust air
181, 490, 493
Essential role of air-exchange for the human respiratory system â and for illumination from a lamp flame
179, 490, 887
Key components of the pump system â a roof cylinder connecting inside and outside â tubing for air supply and exchange between vessel and the water surface
179â181, 488, 490â492, 494, 496, 887
Interior section of the roof cylinder â its movement within another moveable cylinder with a downward-opening valve â an up and down movement, for drawing fresh air into the vessel
180, 491
Key parameters â air pressure inside the vessel â atmospheric air pressure â hydraulic thrust
180, 491
Instruments used â a barometer (for pressure measurement) and a compass (for navigation)
180, 491
New series of trials of the vessel at Kassel (second design, springtime 1692) â successful demonstration (June 1692)
180f., 492â495
Form and construction details of the vessel â a wooden hull of oval shape â machine room places for three persons â single (upper) hatch for entry and exit â sealed side openings enabling oar propulsion of the vessel â use of water ballast tanks for submersion
180f., 492â495
Submergence and reemergence â achieved by filling and pumping out of a water tank (âbucketâ)
494f.
Key features of air exchange â use of the centrifugal (Hesse) pump, and hoses / tubing for air supply
181, 490, 492, 496
Additional features of the new design â illumination of the machine room â use of instruments for submersion and navigation (barometer, compass) â oar propulsion under water
181, 490, 493â495
Possible military use â envisaged attacks on hostile vessels
181, 496
Leibnizâs idea of using a âspirit-of-wine lampâ for illumination â dangers of the extinguishing of the flame, and of pollution of the air inside the vessel
182, 489f., 585f.
Sumatra (Indonesia)
226, 344, 891
Sweden, Swedish kings, court
2, 142, 151, 159, 176f., 220, 246, 264, 322f., 394f., 713, 723, 736, 738, 800, 804, 806, 838
Falun
151, 159, 800, 804.
Mining
Stockholm
224, 395, 800, 839
Switzerland, Swiss
24, 44, 437, 445, 746
Duillier, Municipality (Canton de Vaud)
44, 746
Technology. Power Technology, Technological Projects
History of technology
x, 139, 150
Renaissance (pre-Galilean) technology â the practical-empirical tradition
477
Galilean / post-Galilean technology â the scientific-mathematical tradition
477
Technological thought â project conceptions
xi, 314.
see Projects, Technological Projects
Textbooks â early-modern textbooks
25, 34, 43f., 238, 258, 509, 623, 868.
Mathematical textbooks
Theology, theologians. see Religion, Mystical Theology
Therapeutics, therapies. see Medicine
Thermodynamics. see Physics
Thuringia
235, 729f., 846
Gotha â Collegium Medicum
235, 729
Gräfentonna (Tonna)
235, 239, 729, 846
Tiger (panthera tigris). see Biology, Zoology
Transport, transportation
133, 146, 148â150, 154, 398, 691â694, 697, 699, 877f., 881
Leibnizâs imagined rapid transit system (before 1682) â travel between Hanover and Amsterdam in six hours â Becherâs satire (1682) on Leibnizâs vision
7, 140, 146, 188, 278, 390, 398, 880.
Controversies and Disputes
Mail-coach, stagecoach â improvement of coaches and carriages
7, 146, 278, 398
Schmidâs âschese rolandteâ (1687)
146, 398
Linsenâs work on a model for a carriage (1697)
156, 700
Leibnizâs ideas for the improvement of transportation â an engine to power a vehicle and facilitate transport â a steam engine or pneumatic engine â Papinâs plea for their publication (1698) in order to be made available for posterity
148, 690â692, 694, 881
Steam-powered transport â Papinâs conception of propulsion using steam power â his model of a vehicle powered by steam and operating on water (1698) â his vision of a marine vehicle powered by steam â its unsuitability for the propulsion of vehicles on land, due to the imperfections of existing roadways
147f., 689, 881
Tübingen
240, 847
Universe, the universe as a whole â force of the universe conservative
75, 109, 541f., 672, 876
Vienna. see Austria
Vis, Force â âvis vivaâ and âvis mortuaâ. see Controversies and Disputes, Natural Philosophy, Physics
Wales â a silver mine in Wales
201, 500
Wars in Europe (1672â1721) â Franco-Dutch war (1672â1678) â Third Anglo-Dutch war (1672â1674) â War against the Turks (1683â1689) â War of the Grand Alliance against France (1688â1697) â Jacobite / Williamite war in Ireland (1689â1691) â Palatine war of succession (1688â1697) â Denmark-Norway, and the Anti-Swedish alliance (1700) â Great Northern war (1700â1721) â War of the Spanish succession (1701â1714)
14, 104f., 177, 192f., 259f., 319, 323, 367, 502f., 508, 574, 590f., 746, 884
Trade wars â Leibnizâs envisioned trade war with France
12, 194, 591, 593, 716.
Economics, Leibnizâs / Crafftâs Brandy Project
Weather. see Meteorology
Westphalia â Neuhaus
6, 275
Wittenberg
91, 201, 262, 293, 329, 556f., 597, 604f.
Wolfenbüttel. see Principality of Brunswick-Wolfenbüttel
Wuerttemberg (Wurtemberg) â Stuttgart â âWurtemberg Siphonâ
178, 478, 487, 886.
Engineering, Mechanics of Fluids
Zeitz
120, 800
Zellerfeldt. see Clausthal (Clausthal-Zellerfeld)
Zerbst
262, 605
Zoology. see Biology