1 Medieval representation of the cosmos through a scheme of homocentric spheres. Engraving from Hartmann Schedel’s Liber chronicarum, cum figuris et ymaginibus ab initio mundi, published in Nuremberg by Anton Koberger in 1493 7
2 The Farnese Atlas, 2nd century sculpture (Museo Archeologico Nazionale, Naples) 9
3 Diagram from the Mysterium cosmographicum by Johannes Kepler (1596) 12
4 The Mainz Globe, a Roman celestial globe of the 2nd or 3rd century CE (Römisch-Germanisches Zentralmuseum, Mainz) 14
5 “Cosmic-edge riddle” illustration, from Camille Flammarion’s L’atmosphère: météorologie populaire, Paris, 1888 22
6 Free Illustration of Plato’s astronomical system described in the Myth of Er (Republic, X, 616c–617a) 37
7 The coordinates of the celestial sphere, engraving from Christophorus Clavius’s In sphaeram Ioannis de Sacro Bosco commentarius, Rome, 1585. Sala del Tesoro, Biblioteca Nacional, Argentina 46
8 God as geometer, from the frontispiece of the Codex Vindobonensis 2554 (Österreichische Nationalbibliothek) 48
9 Per monstra ad sphaeram (By way of monsters to the sphere) is the motto on the ex libris of astronomy historian Franz Boll’s (1805–1875) personal collection 50
10 Map of Greece showing the birthplace of Plato, Eudoxus, Callippus and Aristotle 52
11 Motion a. Westward apparent motion of the sky, around the poles 54
12 Motion b. Eastward apparent movement of the planets and the sun, contained within the zodiac band 55
13 Motion c. Wandering movement of the visible planets (Mercury, Venus, Mars, Jupiter, Saturn) along their orbits 56
14 Graphic representation of Kepler’s first and second laws 57
15 Geometrical subsystem created by Eudoxus to explain the motion of the moon 62
16 Representation of the most likely layout of Eudoxian solar subsystem 64
17 Homocentric spheres arrangement showing the impossibility of describing the precession of the equinoxes phenomenon with Eudoxian-like systems 68
18 Cluster of spheres used by Eudoxus to describe the motions of Saturn, Jupiter, Mars, Mercury, and Venus 70
19 Hippopede or spherical lemniscate formed by spheres III and IV of the Eudoxian planetary subsystems 72
20 Difference in the number of spheres between the planetary models of Eudoxus and Callippus 73
21 Equinoxes and solstices according to the current duration of seasons for the Northern Hemisphere 74
22 Conjunctions and oppositions caused by the direct motion of stars (motion b) from a heliocentric and geocentric perspective 76
23 Mars trajectory generated by the callippic model of the planet 77
24 Comparison of the apparent trajectories of Mars, calculated with Callippus’s geo-homocentric planetary model (4th c. BCE) and with Stellarium software (21st c.) 78
25 The apparent trajectories of Mars, calculated with Callippus’s geo-homocentric planetary model (4th c. BCE) and with Stellarium software (21st c.) 79
26 Image showing the trajectory of the Sun and the length of the seasons, calculated with the callippic solar system 80
27 Cluster of planetary spheres designed by Eudoxus for Saturn, Jupiter, Mars, Mercury, and Venus 82
28 Representations of the three interdependent rotations of a solid in space, as defined by Euler angles 83
29 The trajectories of Saturn, Jupiter, Mars, and Mercury, produced by the four-sphere subsystems of Eudoxus and calculated through coordinate transformations based on Euler angles 85
30 Aristotle’s astronomical system 92
31 Aristotle’s circular cosmology 102
32 Analemma 109
33 Cooperation of human and celestial causalities 115
34 Linear and angular velocities in rotating spheres 134
35 A representation of the two solutions presented by Aristotle in On the Heavens, II, 8, 289b1–290a7 for the motion of celestial body 138
36 A physical explanation of the myth of Atlas, condemned by Zeus to carry the weight of the heavens on his shoulders (Hesiod, Theogony, 517) 144
37 The night sky over the Aegean Sea as seen from the Eastern coast of the Attic peninsula during March, 343 BCE, estimated with the Stellarium simulation software 148
38 Behaviour of the rewinding spheres introduced by Aristotle between Saturn and Jupiter 153
39 Aristotelian astronomical system modified by Hanson, of forty-nine spheres 156
40 Interpretations of the homocentric systems of Eudoxus, Callippus, and Aristotle 157
41 Effect produced by the rewinding of spheres introduced by Aristotle in his astronomical system 162
42 Comparative table of the current values and those apparently considered by Eudoxus, for the synodic and zodiacal periods of the stars 168
43 Schematic representation of the retardation caused by the diurnal motion of heavens on direct planetary motions 171
44 Left and right, up and down the universe 173
45 A breakdown of Aristotle’s astronomical system and its composition of motions 176
46 System of the First Heaven 177
47 Aristotle’s astronomical system understood as a superimposition of the two partial systems, the System of the First Heaven and the System of Specific Planetary Motions 179
48 The celestial spheres of the medieval cosmos according to an engraving by late-Renaissance astronomer Christopher Clavius (In sphaeram Ioannis de Sacro Bosco commentarius, Rome, 1585. Sala del Tesoro, Biblioteca Nacional, Argentina) 242
49 A Neoplatonic cosmological schema (Paris, Bibliothèque Nationale, Ms. Lat. 3236A, f. 90r) 245
50 The Rosa Celeste. Dante and Beatrice gaze upon the legions of angels in the empyrean heaven, beyond the last heaven (Paradiso, Canto XXXI) in an engraving by Gustave Doré 249
51 Regular solids made of wood by Gerardo Botteri for the Grupo de Estudio del Cielo (Facultad de Humanidades y Artes, Universidad Nacional de Rosario) 307
52 Regular solids made from clay by Roberto Casazza 307
53 Observation of the sky with the Southern Astronomical Umbrella (Botteri–Casazza, 2010) 308
54 Southern Astronomical Umbrella, designed by Gerardo Botteri & Roberto Casazza 308