We gratefully acknowledge the assistance of Ms. Cynthia Graeff in editing and producing TIFFs of the illustrations listed below, and proposing a design for our book cover.
1.1 “Plan view” of Anaximander’s cosmic picture, numbers mirroring the architectural roof tile pattern for the archaic East Building on the Sacred Way 29
1.2 Left: Architect’s grid-pattern for spacing between columns in column-drum diameters. Right: Anaximander’s spacing between heavenly wheels of stars, moon, and sun, measured out in earthly, that is, column-drum proportions 30
1.3 Temple plan vs. elevation. Left: Plan, Temple of Artemis at Ephesus (after Tomlinson). Right: Elevation, Temple of Artemis at Ephesus (after Grant) 32
1.4 Left: Anaximander’s Cosmic “plan” vs. Right: elevation 32
1.5 Left: Surviving piece of a column-drum from the archaic Didymaion displaying anathyrôsis and empolion. Right: An archaic column-drum from Dipteros II, Samian Heraion also displaying anathyrôsis and empolion 34
1.6 Left: Illustration of the technique of column-drum installation displaying bosses and using pulleys. Right: An archaic column-drum displaying original boss, built into the later Artemision in Ephesus 34
1.7 Possible reconstruction of the archaic Temple of Artemis at Ephesus, after the model in the Selçek Museum 36
1.8 Left: Rendition of the Neo-Babylonian map of the world dating between the 7th and 6th centuries bce, after the artifact in the British Museum. Right: Possible reconstruction of Anaximander’s tripartite map. Both have “ocean” running around the circumference 40
1.9 Measuring the height of a Giza pyramid when shadow = pyramid height. Notice the gnomon’s set up both at the end of the shadow, and to the side, May 2013 41
1.10 Measuring the height of a Giza pyramid when shadow = pyramid height, May 2018
1.11 Pyramid measurement when shadow equals height 42
1.12 Pyramid measurement when shadow does not equal height 45
1.13 Left: An electrum statêr of Miletus ca. 600–550 bce. Right: Electrum 1/12 statêr (0.52 g), about 600–550. Obverse: lion’s head facing. Reverse: square incuse punch 47
1.14 Comparative lists of 6th century bce statêrs and sub-multiples 48
1.15 For comparative sizes, Lydian statêr and half- statêr, and Milesian 1/12th statêr and Milesian 1/96th statêr 49
1.16 Surviving examples of felts. Left: Pazyryk 5th century BCE. Right: Gordion 7th century bce 52
1.17 First the wool is cleaned by hand, and then washed 52
1.18 Then, a mat of reeds from the Meander River is rolled out – the Substrate 53
1.19 If a design is intended, the colored wool is arranged on the mat 53
1.20 Then, wool is heaped upon and over the design below 54
1.21 Next, water is sprinkled on the wool, moistening it 54
1.22 Then, the mat is rolled up tightly 55
1.23 The felters roll the mat from one side of the room to the other, compressing it as they go 55
1.24 After about 15 minutes, the felt is complete
1.25 Focusing on two steps, piling on the wool creates an unmistakable image of a cloud 56
1.26 The felter sprinkles water on the wool introducing the imagery of rain
2.1 Furnace with Tuyere. After Hauptmann 2020 89
3.1 The first plank boats 112
3.2 Rowers in a Greek Trireme 114
3.3 A ship’s plank, seen from above, with the mortise holes gouged out
3.4 Ship’s planks, this time seen from sideways on 115
3.5 Hogging and Sagging 131
3.6 Riveting 137
3.7 Plato’s triangles 139
3.8 Complex squares and complex triangles form up into three dimensional entities 140
5.1 Clepsydra with round handle 166
5.2 Clepsydra with narrow neck 166
5.3 The use of the clepsydra according to Hero of Alexandria 171
5.4 Submerging the clepsydra with the upper vent closed 174
5.5 Empedocles’ respiration 184
7.1 The sun, allegedly moving like a horizontally turning millstone above the earth 223
7.2 The paths of the heavenly bodies according to Anaximenes 224
7.3 The heavens as a felt cap and the sun at night hiding behind the northern mountains, after Graham
7.4 The sun during the seasons, supposedly circling above the flat earth 231
7.5 In the archaic Greek conception, the sun at night moves around the rim of the earth (
7.6 Greek women pounding, 6th century bce. Photography from the mid-20th century 239
7.7a Saddle-quern with charred grain 240
7.7b Egyptian statuettes (18th dynasty, about 1350 bce) of two women grinding grain with saddle-querns 240
7.8 A simple hopper-rubber (Theban Mill), found in Karanis 241
7.9 Two hopper-rubbers on a Megarian bowl, fourth century bce 242
7.10 A reconstruction of an Olynthian mill 242
7.11 A rotary hand-quern still in use in northern Jordan 243
7.12a Development and diffusion of different types of mills over the Mediterranean territory, after Martinez 2015 245
7.12b Legenda for Fig. 7.8a, after Martinez 2015
7.13 Fragment of a rotary hand-mill (?) 246
7.14 Drawing of the upper and lower side of the upper part of a rotary hand-quern found near Lake Van (dating questionable) 247
7.15a Two ‘hour-glass’ mills found in Pompei 248
7.15b Cross-section of an ‘hour-glass’ mill 248
7.16 Palestinian women crushing olives with a roller-crusher 250
7.17a Manually operated olive crusher 251
7.17b Horse-driven olive crusher 251
7.18a The excavation site of the olive oil plant in Klazomenai 253
7.18b The first (blue) and the second (orange) phases of the olive oil plant in Klazomenai 253
7.18c Reconstruction of the first phase with a hand-driven rotary mill 253
7.19 A trapetum in the Antiquarium at Boscoreale, Pompeii 254
7.20 The sun symbolized by a red dot on a vertically rolling millstone, after Martinez 2015 256
7.21 A cycloid. Drawing after Cycloid – from Wolfram MathWorld [https://mathworld.wolfram.com/Cycloid.html] 256
7.22a Crown-like circles of latitude in a stereographic projection on an astrolabe for an observer at a latitude of 30 degrees north 259
7.22b Circles of latitude cutting off millstone-like parts of northern half of the celestial sphere
8.1 Gemetrical representation of the doubled square 267
8.2 Drawing of Grecian female with dress, from Hope 1812, Plate 143
8.3 Representation of the peplos-pattern and detail with square diagram to the right 299
8.4 Pebble representation of repeat demonstrating the composition from eight triangle numbers plus one monad 299
8.5 Pebble representation of repeat with an odd number of threads 300
8.6 Pebble representation of even repeat 300
8.7 What we would write today as: 
301
8.8 How to calculate a double spiral pattern 302
8.9 Diamond twill and detail 304
12.1 Thales’ basic diagram 395