Cambridge University Press 978-0-521-57162-3 — the Cambridge History of Science Edited by Alexander Jones , Liba Taub Index More Information

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Cambridge University Press 978-0-521-57162-3 — The Cambridge History of Science Edited by Alexander Jones , Liba Taub Index More Information

INDEX

Aaboe, Asger 26 external testimonies 471 abacus 613 future research 480–2 prototypes 559 historiography 469–70 Abusir papyrus 105 ingredients 474 Abydos, Egypt initiation into 479 Osireion temple 137, 139 occultism of 479–80 tomb Uj 103 origin of word 469 accounting origins 468 and development of writing 59 papyrus compilations 470 new book-keeping system (Ur) 60 and philosophy 469 Achaemenid Empire 488 processes 474 Acron of Acragas, Empiricist 332 and production of gold 474, 476 addiction, Aristotle on 313 as revealed religion 480 Adrastus of Aphrodisias 442, 443–4 sources for 470–1 Advaita Vedānta 533 texts and authors 471–4 Aelius Aristides 317 theorization of 473 Aeschylus 450 theory of transmutation 476–8 “Aetna” poem 269 and unity of matter 471, 473, 476, 477, afterlife, celestial, Egyptian 131 478 Agatharchides 410 Alcinous, Didaskalikos 262 Agathinus, Claudius 336 alembic, alchemical distillation apparatus Agathodiamon 472 475, 477 Agniveśa 543 Alexander of Aphrodisias 188, 340 Agrippa, astronomer 395 and Aristotle’s celestial spheres 283 agronomists, Roman 238 commentaries of 279, 280, 282 Ahmose, pharaoh of Egypt 113 Alexander the Great 241, 316, 455, 503 air, Anaximenes’s concept of 167 death (323 BCE) 248, 322 aither (ﬁery material), role in Stoicism 259, 260 rout of Darius III 17 Akhethotep, scribe 106 Alexandria 321 Akkadian language 60 anatomy in 325–31 alchemy, Chinese 592–3 Hippocratic Corpus at 304, 323 alchemy, Greco-Egyptian 468–82 Library 249, 323 apparatus for 475, 476 medicine in 322–5 black Corinthian bronze 472, 475, 481 Museum (Mouseion) 249, 323 chemical recipes 471–2 teaching of pagan philosophy 279 and divine water 477 algebra esoterism 479–80 cubic problems 69

617

© in this web service Cambridge University Press www.cambridge.org Cambridge University Press 978-0-521-57162-3 — The Cambridge History of Science Edited by Alexander Jones , Liba Taub Index More Information

618 Index

algebra (cont.) Anonymous of Zuretti Byzantine alchemical Greek arithmetics and algebraic thinking treatise 474 359–63 Anonymus Londiniensis 302n, 310 second-degree geometrical 61, 63, 66–8 Antikythera Mechanism 376, 377, 382, 385 symbolic abbreviations 362 eclipse predictions 396 third-degree problems 68 Antioch 322 and unknown number 362 Antiochus of Ascalon 261 algorithms Antiochus I, king of Commagene, horoscope Chinese 557, 559, 571 frieze 378 Egypt 110 Antiphon the Sophist 176 Greek 370, 397 Apollonius of Citium 326 Indian 511, 518, 521, 528, 529 Apollonius Mys, On the haeresis of Herophilus 332 Almanacs Apollonius of Perga, mathematician 351, Mesopotamian astronomical 12, 92–3 356–9, 388 Normal Star 92 Conics 357–8 Amazons 408 Cutting off a Ratio 358 Amenemhet, Egyptian official 138 and Euclid 358 Amenemope/Mapu, Egyptian scribe 115 field of analysis 357, 358 Ammianus Marcellinus 411, 467 Apollonius of Tyana 262 19 382 Ammis˙aduqa, King of Babylon Apseudes, Archon of Athens Ammonius 208, 278, 279, 281, 395 Apuleius, Apologia 414 Amphiaraus, healer 299 aqueducts 321 amulets 12, 55n Arab mathematics 72 analogy, Epicurean use of 257, 258 Arab world, alchemy in 468, 473 anatomy Aratus of Soli, Phainomena 269, 375, 383 Alexandrian tradition 325–31 Arcesilaus, head of Academy 261 and Aristotle’s knowledge of 230, 308, 324 Archagathus, doctor 317, 334 Buddhist 539 Archelaus, On the Divine Art (alchemy) 473 and dissection 230, 235, 308–9, 323–5 Archelaus, natural philosopher 176 Egyptian medical knowledge 124–5 Archidamus, king of Sparta 455 limitations of Babylonian knowledge 41, 49 Archigenes of Apamea 337 and surgery 337 Archimedes 274, 352, 353–6, 372 Vedic 537 astronomic observations 394 Anaxagoras of Clazomenae 171–3, 215 Cattle Problem 270, 274 and meteor (467 BC) 173 celebrity status 249, 263 Anaximander of Miletus, geographer 164–6, 215, On Conoids and Spheroids 355 386, 402 On the Equilibria of Planar Figures 355, 457 map of world 404 and Euclid 354 Anaximenes of Miletus 167, 215, 404 On Floating Bodies 457 Andreas of Carystus, doctor-historian 323, 333 on heliocentric hypothesis 391 Andromachus 321 and legacy 276 Anepigraph, commentator 473 Measurement of the Circle 356 animals mechanical devices 456–8 Aristotle’s classification 222–4 mechanics 355 Aristotle’s theory of reproduction 227–9 mensuration 355 constitutional hierarchy (Aristotle) 225 Method 355 heart and lung 230, 231, 234 and numbers 274, 354 likeness and difference of parts 221–2 On Spiral Lines 355 male and female contributions 228 on optics 414 necks 232 and principle of balance 355, 457 non-uniform parts 222, 226 and principle of displacement 457 physiognomic similarities to humans 53n, 53 and principle of lever 457 uniform parts 221, 226 Quadradure of the Parabola 355, 457 Ankhtifi, Egyptian nomarch 107, 109 The Sand-Reckoner 275, 354, 368, 375, 379

Index 619

On the Sphere and the Cylinder 263, 354, 355 and size of oikoumenē 408 the Stomachion 354 sublunary physics 189, 190–1, 192, 283 volume of sphere 458 systematic study of life 192–4 Archimedes Palimpsest 354 and medicine 305 architecture teleology 225, 226 laws to encourage training in 466 and Thales 164 and mechanics 462, 465–6 theory of matter 186, 197–201 Archytas of Tarentum 348, 349, 364, 447 theory of motion 204–6, 283 and diatonic tetrachord system 436–7 theory of place 208–10 mathematical harmonics 428 theory of time 210–14 mathematical mechanics 451 theory of vision 415 Ārdharātrikapaksa school 497 theory of weight 202–4 Aretaeus of Cappadocia 336 use of collected information 253, 254 Aristaeus 351 writings: Aristarchus of Samos 270, 275, 352 Categories 208–9 heliocentric hypothesis 379, 391 De sensu 415 observations 394 Generation of Animals 227–9 On the Sizes and Distances of the Sun and Moon On Generation and Corruption 199, 201, 275, 368, 375, 391 214, 280 Aristides Quintilianus 429, 432 On the Heaven 191 De musica 441, 442 History of Animals 181, 220–5, 229–31 Aristobulus 241 On the Length and Shortness of Life 185 Aristotle 181–95, 261 Meteorology 189, 192 and alchemy 477 rainbow 413 alteration and substantial change 198–9 Nicomachean Ethics 313 retention-replacement model 198 Parts of Animals 183, 185, 192, 218, 225–7, astronomical geometry 387 231–3 and calculations of size of heavenly bodies 270 and anatomy 308 celestial physics 189, 190–1, 283 On Philosophy 201 commentaries on 279, 280, 282 Physics 186, 194, 208–9 and concepts of form and matter 186 optics in 413 death (322 BCE) 248 Posterior Analytics 187, 194, 217, 218 denial of existence of void 203, 206–8 commentaries on 281, 282 forms of theoretical knowledge 184 Prior Analytics 217, 282 general and special physics 186–9 On the Progression of the Animals 185 and harmonics 439 On Respiration 233–6 and infinity 211, 212–13 On the Soul (De Anima) 193, 415, 416 and Ionian theories of matter 168 On Youth and Old Age 233 library of texts 249 zoological writings 219–20 and mathematics 352, 364 and legacy of zoological work 216–17, 236–7 on mechanics 451 philosophy of zoology 217–19 nature of light 287 Aristotle, Pseudo- on perception 287 Mechanical Problems 305, 415, 452–3 physical theory 196–214 On Plants 238 physics 184–6, 194 and physiognomy 53 on plants 245 Aristotle’s Lyceum (Peripatos) 181, 248, 252, and predecessors 196 253–6 problemata texts 255 study of medicine 305, 322 see also Peripatetics reputation Aristoxenus 332 in antiquity 182–4, 188, 194 Elementa harmonica 432 influence in Middle Ages 195 and empirical harmonics 429, 432–4, 439, 441 late ancient study of 279 arithmetic 72, 262, 278 on respiration (case study) 229–36 Egyptian applied 151–2 scientific method 217, 218–19, 224, 253, 281–2 Greek arithmetics 359–63 scope of study 182 practical Greek 360

620 Index armillary general 397–8 Chinese 605, 610 horoscopes 399 observational 396 personal 399–401 Arrian, Anabasis and Indica 241 astrology, Indian arrow, Zeno’s paradox of 213 and Greek texts 490 Ars Eudoxi 376 tājika (Perso-Arabic) 500 arsenic, as immortality elixir 593 texts 498 art astronomers, Chinese astronomical and astrological images 378 experts 605–6 in tombs 113 state officials 595, 604–5 Artemidorus 410 astronomers, Egyptian 131 śā ś 487 Artha tra text 503 astronomers, Indian (naks˙ atradara ) Ā 72 491 496 523–6 17 86–8 92 ryabhat˙a , , , Astronomical Diaries , , astronomical computations 516 astronomical prediction 13, 20, 368, 379 523 90–2 gan˙ ita chapter Babylonian planetary and sine tables 515, 516 and calculation 18–21, 397 and varga system of numeration 515 Greek 396–7 Ā 496 489 ryapaks˙a school India Asclepiades of Bithynia 333 mathematical models for 18, 21 Asclepius, cult of 38n, 299, 314–15, 339 ‘Astronomical Tables’, Seleucid texts 26 shrine on Tiber island, Rome 317 astronomical texts, Indian 485 āšipūtu (the art of healing through incantations/ astrological (muhūrta, praśna) 498 rituals) 33, 34 astronomical handbooks (karana) 497 Diagnostic Handbook 37n, 37 calendars (pañcān˙ga) 498 ‘ ’ 37 ā 490 for stroke n Gargasam˙ hit (omen) collection Aśoka, Maurya ruler 503 genethlialogy (horā,jātaka) 498 Assur Grahalāghava 497 75 ā ˙ 489 astronomical texts Jyotis˙ aved nga ā 498 exorcists 31n omens (sam˙ hit ) ā 486 state library 8 prose Br hman˙as Assurbanipal, Assyrian king 10, 16, 75, 84 siddhānta treatises Assyria, astral science tablets from 74 development 491–2 ā ā ī 503 508 492–5 As˙˙t dhy y text , structure ā ˙ ā ū ā 497 As˙˙t ngahr˙ dayasam˙ hit , Compendium being the S ryasiddh nta ā 497 Heart of the Eightfold Science tables (kos˙˙thaka or s ran˙ i) 541, 542 Vedic 486 ā ˙ ā ā 486 496 As˙˙t ngasam˙ hit , Summary of the Eightfold verse Pur n˙as , Science 541 astronomical texts, Mesopotamian astrolabes 79, 280 “Astrolabes (The Three Stars Each)” 79, 80–1 Islamic 499 compilation 88 astrology 12 Ephemerides 93, 94 celestial divination 97 influence on Greek astronomy 376 and extispicy 13 late Babylonian 13, 85–98, 379 horoscopic 97, 141, 399 Neo-Assyrian 83–5, 379 Late Babylonian 21, 28, 399 Procedure Texts 93 astrology, Egyptian second and early first millennium bce 79–83 hemerology 140–1 astronomy 74 menology 140 and geography 409 planetary and lunar tables 142 inscriptions 376 zodiacs 141–2, 399 naked-eye observations 15, 607 see also astrology, Greco-Roman 397–401 cosmology; moon; planets; sun astrologers 399 astronomy, Babylonian and auspicious days 400 calculations of phenomena 93 ephemeris 400 influence in Egypt 131 evidence for 377–8 influence in India 489

Index 621

and invention of zodiac 97 Vedic period 486–8 see also astronomical texts, mathematical 93–6 see also astronomical texts, Indian Mesopotamian; astronomy, astronomy, Mesopotamian 10–11, 13 Mesopotamian and celestial latitudes 28 astronomy, Chinese 379, 595–616 celestial observation 14–18, 26, 393 changing systems 614–15 explanation 22–5 concept of ‘twenty-eight lodges’ and explanation 23 (constellations) 608–9 measurement of degrees 20 cosmography 610–12 periodic phenomena 10 documentation 616 prediction and calculation 18–21 instruments 607–12 terminology 27 see also astronomy, Babylonian and li calendrical system 603–4, 612–14 asû (physician), Babylonia 10, 30, 38 li yuan (system origin) calculation 612–13 asûtu (the art of healing through recipes) 33, 34 and omens 602–3 diagnostic theory 40–4 pre-imperial 596, 598–601 ataraxia (freedom from anxiety) sources for 597–8 see also Hanshu; Hou Han Epicureanism 256 shu; Shi ji in Stoicism 259 star-clerks 596 Atharvaveda 537, 543 astronomy, Egyptian and calendars 131–43 Athenaeus of Attaleia 337 astronomical representations 140 Athens 322 Babylonian influence 131 calendars 381 civil calendar 133–5 Marcus Aurelius and 279 clocks 137–8 philosophical schools 251, 252 cosmography 131, 133 under Macedonian rule 181 see also Aristotle’s lunar calendars 135–7 Lyceum; Plato’s Academy northern and southern fixed stars 133 atomism 174–5, 197 orientation 132 Aristotle’s rejection of 197, 205, 214 astronomy, Greco-Roman 64, 374–97 Epicureans and 256, 257 astronomical prediction 396–7 as mechanical system 175 calendrics and chronology 381–3 and vision 415 cosmic dimensions 391–3 atoms, in Indian mathematics 521, 530 evidence for 374–8 Attalus II, at Pergamum 322 geometrical and physical modelling 386–91 Autolycus 352, 366 and Greek trigonometry 368–9 astronomy 375 mathematics and 366–7 Averroes 188 observations and measurements 393–6 Avicenna 477 reconstruction from fragmentary writings Ayurveda medical system 535 378–81 areas of medical knowledge 542 scope of 374 classical 540–8 stars and constellations 383–6 direct observation 543 teaching of 379 and early Buddhist medicine 538, 540 testimonia 379 and Indus Valley civilization 536 astronomy, Indian 485–500 materia medica 547 Babylonian links 489 medieval and early modern 548–9 Greek influence 490 modern and global 549 kalpa (aeon) 488, 491 non-ritual treatments 544 Kerala school and vākya system 499 pharmacological theory 546–7 late medieval Islamic influence 499 practitioners 541, 542 mathematical post-Vedic 488–91 rationality 544 and mathematics 506 relationship of tastes and humors 545–6 model of cosmos 487–8 ritual treatments 544 486 540–2 naks˙ atras (constellations) text sources and prediction 489 theory of food and waste 544 rival schools 496–7 and Vedic medicine 538 trigonometric calculations 490, 499 and Vedic origin myths 543

622 Index Babylon 62, 79 Buddha, sermons 489, 538 Babylonia Buddhism 503 astral science tablets from 74 in China 574, 593–4 divination 8–10, 84 see also astronomy; monasteries and inﬁrmaries 594 medicine Pali-canon text 538, 539 441 ā ū 540 Bacchius Suvarn˙ aprabh sas tra Ban Gu, Han shu (Writings on the Han) 587, 597 Byzantium, alchemy in 468, 474 Bao Huanzhi 556, 558, 559, 560 baths and bathing 336 Caelius Aurelianus 334, 335 Bel-ušezib, scholar 84 Cai Yong, astronomer 611, 615 Bellermann, Anonymi 441 Calendar of Dionysius 383 Berthelot, Marcellin 478 calendars 78–9 Collection des anciens alchimistes grecs 469 19-year cycles Bhagabatī sūtra text 522 Babylonian 21, 79, 92, 382 Bhāradvāja, seer 543 Greek 381, 383 Bhāvaprakaśa Ayurvedic text 548, 549 Babylonian civil 78–9 ā Babylonian intercalations 382 Bheda-orBhed˙ asam˙ hit , Compendium of Bheda- or Bhela 541 calculations of year 19 Bian Que, physician 589 Chinese li calendrical system 603–4, 612–14 biology Chinese luni-solar 558, 596, 598 Aristotle’s physical science 184, 280 Chinese sixty-day cycles 598 developmental 227 see also anatomy; animals; Egyptian civil 133–5, 136 body Egyptian lunar 135–7 birds, Aristotle’s correlations 224 Egyptian solar 131, 134, 383 al-Bīrūnī, on Indian mathematics 501, 505 Greek 381–3 BītReš temple 75 hours of day and night, Egypt 137–8 blood Indian Vedic 485, 488 circulation of 125 intercalary months 78, 381–2 as uniform part 226 lunar months 78 blood letting 330 Papyrus Cairo 139 blood vessels 324, 326, 329, 330 schematic 79 see also year body Callippic Periods 383 Chinese view of relationship with nature 578 Callippus of Cyzicus 383 Greek engagement with 295, 304 astronomical modelling 388 heart valves 328 Callistus, freedman 319 as living organism 329 Cambyses, Achaemenid ruler 18 as microcosm (China) 588–9 Candragupta, Gupta kingdom 503 nerves 324, 327 Candragupta Maurya, Indian monarch 503 pulse 327, 337 Canopus, Decree of 135 systematic observation of 307–9 see also Cantor, Georg 286 ā respiration Carakasam˙ hit , Compendium of Caraka Boethius 436 541, 542 and texts on harmonics 429 Catalogus Codicum Astrologorum Graecorum 377 Bolus of Mendes 319, 471 Cato, M. Porcius (the Elder) 238, 317 Borchardt, Ludwig 136, 143 Cattle Problem 270, 274 botany 238–47 Celsus, Cornelius 325, 331 Antinoopolis illustrated herbal 244 on Methodists 335 Greek knowledge of 239, 241 Chaldean Oracles 280 – ū 518 life of plants 244 6 Chandah˘ s tra text medicinal herbs 319 see also plants Chang Hong, diviner 600 Bower manuscript, Buddhist medical text 540 China Brahmagupta 72 accounting books 560 Brāhmasphutasiddhānta 492, 496, 526–7 administrative regulations 560, 561, 562–5 ā 496 astronomy 379 Br hmapaks˙a school Brugsch, Heinrich 143 Buddhist monasteries and inﬁrmaries 594

Index 623

Buddhist texts in 540 comets, Chinese observations 601 canonical literature 554, 577, 587, 590 commentaries centralization and standardization 576, 595 on Greek mathematics 350, 370–3 Chinese empire 553, 576 on Indian mathematics 510–11 Daoism 591 on Plato and Aristotle decision-making 614–15 “harmony thesis” 280 Discourse on Salt and Iron 589 late ancient 278, 280 education system 554, 606 modifications of Aristotelian conception of Han dynasty 574, 596 science 281–2 see also Porphyry; historical narrative 574–5 Proclus; Simplicius imperial bibliographies 587 compositional hierarchy, Aristotle 199, 202 importance of calendrical astronomy 603 compositional reductionism 198 Northern Wei dynasty 556 Confucian canons 554, 569 Northern Zhou dynasty 557 Confucius, on calendar error 599 official written texts 554–7 conquest, and botanical knowledge 241 printing culture 591 Cosmas, Byzantine alchemist 474 rise of religious cults 591–2 Cosmas Indicopleustes 406 School of Mathematics 555, 556, 559 cosmic balance 166 significance of number eleven 583 cosmic cycle, Empedocles 173 spirit presences 576 cosmogony, Anaximander’s 166 spread of Buddhism 574, 593–4 cosmography Spring and Autumn annals 600, 607 Chinese 610–12 zheng shi histories 597 see also astronomy; Han gai tian (heaven as chariot-umbrella) 610–11 dynasty; mathematics; medicine; Qin hun tian (heavens as rotating disk) 611 dynasty; Tang Dynasty Egyptian 131 chōrographia, Strabo 410 cosmology, early Greek 163–80 Christian authorities Eudoxus’s mathematical model of heavens 179 and late ancient philosophy schools 279 Parmenides 169–70 and origin of universe 285 post-Parmenidean 171–6 Christian Philosopher, the, commentator 473 cosmology, Indian Chrysippus of Soli, Stoic 259, 328, 364 siddhānta 491–2 Chunyu Yi, Historical Records 583 Vedic 487–8 Cicero, Marcus Tullius 261, 263, 269 cosmos on Academy 261 estimates of dimensions 391–3 and Greek medicine 318 as finite, Aristotle 207 knowledge of Greek 267 geometric relationships of earth, moon and Claudius Marcellus, Marcus 353 sun 392 Claudius Menecrates, Tiberius 336 Hesiod’s 403 Cleanthes of Assos, Stoic 259 homocentric spheres 387 Cleombrotus 322 role of mathematics 262 Cleomedes 274 two-sphere model 350, 386–8 Cleonides, Introduction to Harmonics 441 Crateuas the Root-Cutter 238 Cleopatra of Egypt 322, 472 creation Cleostratus of Tenedos 384 and eternity, late ancient tradition 285–6 clocks temporal 285 Egyptian 137–8 creationist accounts, Plato 178 Ramesside star 138 Croesus, king of Lydia 164 shadow clocks 139 Ctesibius 458 star clocks 137 see also sundials; water clocks cuneiform writing 8, 58 Cnidos, medical school 303 Cuvier, Georges 237 Codex of Justinian 465 Cyllene, Mt 273 Codex of Theodosius 465 Cyriades, senator 465 cognitive powers, human 291 Columella, L. Iunius Moderatus 238, 245 Damocrates, Servilius 321 combinatorics 363–4 Dante Alighieri, and Aristotle 195

624 Index Daoism 591 dissection 324 Celestial Masters 591 Matters of Health 312 Shangqing school 592 Diocles, mathematician, Burning Mirrors 359, 414 Darius III 17 Diocletian, emperor, destruction of books on Darwin, Charles, on Aristotle 217, 237 alchemy 471, 479 David, head of Alexandria philosophy school 279 Diodorus 369, 455 days Diogenes of Apollonia 175 24-hour, Egypt 139 Diogenes of Babylon 440 calculation of duration of daylight 20, 80 Diogenes Laertius 452 sexagesimal hours and minutes, on the Academy 261 Babylonian 139 on Archytas 451 De rebus bellicis 466 on Epicureanism 256, 257, 269 Deir el Medina, Egypt 105 Lives and Opinions of Eminent Philosophers 182, Delphi, as centre of world 403 254, 260 Demetrius of Ephesus Poliorketes, king 455, on Posidonius 276 460, 467 on Theophrastus 253, 254 Demetrius of Phalerum, archon of Athens Diogenes of Oinoanda, Epicurean 252, 256, 264 454, 455 Diognetus of Rhodes 460 demiurge, cosmic Dionysius of Alexandria (Periegetes) 410 postulated by Plato 178, 285 Dionysius, tyrant of Syracuse 454 Proclus and 290 Dionysodorus of Melos 271 Democedes of Croton 299 Diophantus 360–3 Democritus 215, 408 Arithmetica 72, 360, 361–3 atomism 174 Porisms 360 cosmology 175 dioptra (sighting instrument) 273 optics 415 dioptrics (refraction) 423–7 Democritus, Pseudo-, Phusika kai mustika 471 analysis of 424 demons, as cause of disease 44, 49 Ptolemy and 423–7 Dendera temple, Egypt 141 Dioscorides, Pedanius, of Anazarbus 240 dental practice, Egypt 128 classification of plants 242 Diagnostic Handbook (Babylonian) 37n, De Materia Medica 238, 242, 318, 319 37, 46–9 disease causality in 49–51 and anatomical nomenclature 41 description of symptoms 48 causes of 31, 40, 43, 49–51, 296, 306, 331 and divine influence 47, 51 description of symptoms 40, 48 theoretical nature of 48 divine aetiology of 11, 47, 51 diagnostic theory and dreams 314 and decision on treatment 311 early Greek theories of 310 early Greek 309 Egyptian concepts of anatomy and physiology in Egyptian medicine 126 124–5 and prognosis, Galen and 343 Egyptian medicine 122–3 within asûtu 40–4 epidemic 300 Diaries four humours theory 43, 310, 329 astronomical (Mesopotamian) 12, 16, 17, 26 Greek definitions of 300 goal-year predictions 20 Greek representation of 294 Dicaearchus of Messina, geographer 408 modern identifications 42 on measurement of mountains 272 non-anatomical 41 Didymus 440 physiognomic omens 46 Dieuches 312 prevention and prophylaxis 311–12 Digest of Tang law 555, 557 treatment of 31, 54 Digesta 465 and treatment of terminal cases 47 digestion diseases in ayurvedic medicine 545, 547 asthma 336 in Egypt 123, 125 cancer, Egypt 122 Diocles of Carystus 306, 309 epilepsy 37, 42, 55, 306

Index 625

infectious 42 Egypt 131 leprosy 42 Greece 163, 165, 175 migraine, Egypt 123 India 487 parasitic, Egypt 122 as drum 404 skeletal deformities, Egypt 123 estimates of circumference 270, 408 spinal tuberculosis 122 fictional journey to centre 271 ‘stroke’ 37n, 42 as moving body 176 tetanus 126 rotation of 491 tropical, Egypt 122 as spherical 274, 405, 406 dissection 230, 235, 308–9, 339 India 491 of animals 308, 322, 326 Parmenides 170, 405 human 308, 324, 325 Plato 178 distances, to heavenly objects 270 earthquakes 175 divination Egypt by analogy 15 administration 104, 109, 110, 134 Babylonian 8–10, 84 archaeological finds 105 celestial 97 chronology 145n and Chinese medicine 576 elites 103 in India 489 First Intermediate Period 107–9 integration of celestial and terrestrial 12, 21 Greco-Roman Periods 116–19, 141 and role of observation 14, 26 Greek astronomical observations 394 divination expert (bārû) 10 Late Period 116 Divine Farmer (Red Emperor, Yandi) 577 literacy and numeracy 102 Shennong bencao jing 578, 592 Middle Kingdom 109–12 divine judgments, Mesopotamia 9 New Kingdom 113–16 division Old Kingdom 104–7 Chinese procedure 568, 570 predynastic 103 Egyptian technique 147 scribes and the king 107, 111 Djoser, king of Egypt 133 Second Intermediate Period 112 doctors temples and astrology 399 Greco-Roman 338 Third Intermediate Period 116 see also travelling (archaic Greece) 299 alchemy, Greco-Egyptian; Alexandria; women 338 see also physicians astronomy; mathematics; medicine Dorotheus of Sidon 377 Egyptian texts 101 doxographies (collections of opinions) 165, 254–5 Abusir papyrus 105, 156 of Stoics 260 Akhmīm papyrus 158 ’ 542 132 Dr˙d˙habala, and Caraka s compendium Book of the Dead dreams, and disease 314 ‘Book of Nut’ 137 drugs Cairo Demotic mathematical papyrus 117 compound 318 Carlsberg Papyrus 136 in Egyptian medicine 129 Ebers Papyrus 121, 136 herbs 318, 319, 327 grammatical forms 110 new Greek 318 handbooks 105 numbers in recipes 321 Illahun archive 136 opiates 319 medical texts 110 secret names for plants or minerals 55 Middle Kingdom 109 treatment by opposites 54 see also Middle Kingdom Coffin Texts 132 pharmacology Moscow mathematical papyrus 144 Duhem, Pierre 284 Old Kingdom Pyramid Texts 132 Dunhuang cave-temple 560, 567 Papyrus Anastasi I 115, 145 dynamics, Aristotle and 206 Papyrus Cairo 139, 141 Papyrus Lansing 114 earth Rhind mathematical papyrus 112, as disk 403 118, 144 Anaximenes 167, 404 Stobart planetary and lunar tables 142

626 Index Eleatic school 171 Eratosthenes of Cyrene 409 geography 405 Archimedes and 355 elements, earth, water, air and fire 173, 191, 197 estimate of size of earth 271, 409 and Aristotle’s account of mixture 201 and large numbers 274 Aristotle’s theory of change 199 Letter to King Ptolemy 264, 270 and contraries, Aristotle 200 map 409 natural positions 201 Platonicus 440 Eliade, Mircea 470 size of oikoumenē 408 Elias, head of Alexandria philosophy school 279 use of term geography 402–3 embryology 227 Erotian, scholar 35n Empedocles of Acragas, Sicily 173–4, 197, 215, Esagil-kīn-apli, Babylonian scholar 34 299, 386 corpus of medical texts 35, 36n, 53 astronomy 174 Esarhaddon, Assyrian king 10, 16, 75, 84 and elements 173 Ešnunna, mathematical texts from 62 On Nature and Purifications 173 eternity, and creation 285–6 optics 415 Euclid 281, 351–3 empirical investigations Catoptrics 414, 420 Aristotle’s 187 codification of mathematical knowledge 351 Epicurean 257 Conics 353 Presocratic advances 180 Data 353 Empiricists, medical sect 332–3 Division of Figures 353 and case histories 332 Elements 281, 351–3 primacy of experience 332 Elements II 71, 72 Enūma Anu Enlil 10, 12, 15, 75 and equal-angles law of reflection 420 celestial omen series 80, 81–2, 85 field of analysis 353 Tablet 14 (lunar visibility) 17, 19, 80, 81 Optics 414, 417 Tablet 63 (Venus) 18, 27 Porisms 353 Enūma Eliš creation epic 79 and ray analysis 427 Ephorus, world map 406, 407 and refraction 423 Epictetus, Handbook 280 Solid Loci 353 Epicureanism 252, 256–8 spherical astronomy 366 and ataraxia (freedom from anxiety) 256 Euclid, Pseudo-, Sectio canonis treatise on compared with Stoicism 259 harmonics 438–9 and epistemology 256 Euctemon 382, 384, 385 influence of 259, 269 Eudemus, anatomist 324 Epicurus Eudemus of Rhodes 348, 351 Diogenes Laertius’s account of 269 History of Geometry 347, 348 and Garden school 252, 256 Eudoxus of Cnidos 265, 349, 408 Key Doctrines 257 homocentric spheres 387, 390 Letter to Herodotus 257 Phainomena 269, 383 Letter to Pythocles 257 Plato’s Academy 179 and multiple explanations 258 spherics 366 optics 415 Euenor of Athens 322 on speed of light 292 Eutocius of Ascalon, head of Alexandrian school use of analogy 257, 258 279, 372 Epimachus of Athens 460 Exorcism catalogue, Mesopotamia 37n, 38n Epimenides of Crete 299 exorcist (āšipu) 10, 11 episteme (scientific knowledge) 217, 252 healing incantations 44–5 epistemology, Epicurean 256 LÚ.KA.PIRIG 38 equinoctial rings 266 medical role of 31 Erasistratus of Ceos 324, 325, 327–31 explanation and body as living organism 329, 331 astronomical texts 23 influence 330 of computational methods 24 and optics 416 in cuneiform scholarship 22–5 and vacuum process 330 and elucidation 22

Index 627

of omens: protasis and apodosis 9, 22 Gaozou, Emperor 554 and scientific method 25 Garden of Epicurus 252, 256–8 text series 25 Gaudentius 441 extispicy 10 Gaza, Theodore, Libri de animalibus edition of and astrology 13 Aristotle 216 Gellius, Aulus 337 Fabianus 274 Gelon, king of Syracuse 275 famines, Egypt 108, 122 Geminus Fan Ye, Hou Han shu (Writings on the later astronomical phenomena 390 Han) 598 Introduction to the Phenomena 272, 375, Farnese Atlas 383 379, 382 fire, rings of (Anaximander) 165 pure and applied mathematics 365 Firmicus Maternus 377 “Geminus parapēgma” 384, 385 Flavius Josephus 463 geography, Greek and Greco-Roman 402–12 fountains, in cities 321 ethnographic model 407 fractions, Egyptian 146, 147, 149–51 and mountains 273 aliquot parts 156 oikoumenē (inhabited world) 406, 408, 410 multiplication 148 origin of term 402 tables of 148 Parmenides’ zones 405 fumigation 12 geometrical analysis, Euclid and 351 funerary texts, Egyptian, astronomy in 132 geometry in Chinese mathematics 571 Gaius Curio, revolving theatres 455 circle calculations 117 – Galen 35n, 48n, 263, 339 44 in Indian mathematics 519 in Alexandria 120 and mechanics 456 on Alexandrian anatomy 325 and natural philosophy 290 astronomy 378 pole-against-a-wall problems 117, 158 – career 339 41 solid 352 fi and classi cation of plants 242 synthesis and analysis forms of proofs 281 dissections 342 and theorems 281 drug recipes 318 geometry, Egyptian and Empiricists 333 area computations 153 on Erasistratus 328, 329 circles 153 Examining the Physician 338 computation 153–4 on Herophilus 327 influence on Greek geometry 159, 164 and Hippocrates 336, 342 techniques 154 and Hippocratic Oath 320 trapezium 153 library 340 triangles 153, 155 and logic 341 geometry, Greek Method of Healing 341 Egyptian influence on 159, 164 and Methodists 335 and geography 404, 411 and non-medics 337 in Hellenistic period 350–9 and optics 416 spherics 366–8 and Plato 342 and trigonometry 368–9 public anatomy displays 340 geometry, Mesopotamian 65–6 – reputation and legacy 340, 343 4 angles 65 Simples 242 area computations 60, 65 and surgery 338, 339 circles 66 theory of humours 340, 342 trapezium 60, 65, 66, 118 – theory of medicine 342 3 volumes 66 writings 341 Germanicus, Iulius Caesar 269 Galileo Galilei 206, 284 gēs periodos (description of the known Gan Gong (Gan De) 601 world) 402 Gandhi, Mahatma 533 globe, first 404 Ganeśapaksa school 497 Glycon, healing god 317

628 Index gnomon 404 Hattusas, Hittite capital 79 China 599, 607 healing cults India 489 Greece 299 goal-year periods 11, 20, 24, 27, 85 in Italy 317 mathematical calculations 96 health planetary 91 and diet 312 gods early Greek theories of 310 Egyptian 132 Greek interest in good 295, 297 Epicureans and 256 human control over 296, 315 Greek 163, 314 and prevention and prophylaxis 311–12 and Indian mathematics 507–8, 518–20 heat role in disease and healing 313, 317 in animal generation 228 in Stoicism 259 and cooling function of respiration on Gorgias of Leontini, Sicily 176 heart 234 Grand Classic of the Yongle period 556 Hecataeus, geographer 402, 406, 407 Greek Anthology (Anthologia Graeca) 270 Heliodorus 395 Greek science On the Divine Art 473 continuing influence of 180 Hellenistic science 248–61 Latin translations 267 Hephaestion of Thebes 377, 398 writings 267–70 Heqanakhte, Egyptian priest 108 Gregorius 395 Heracleopolis, Upper Egypt 107 Gula, healing goddess 39 Heraclides of Pontus 261 gynaecology and obstetrics Heraclides of Tarentum 332, 333 Egyptian medicine 128 Heraclitus of Ephesus Greek 327 and Ionian predecessors’ theories 168 and river riddle 168 Hahnemann, C. F. Samuel 533 Heraclitus of Rhodiapolis 320 hairesis (choice, sect) 248 herbs 318, 319, 327 and sectarian medicine 331 Hermes 472 Hammurabi, king of Babylonia 61 Herodotus 241, 402 Law Code 30 on Babylonian medicine 29, 56 Han dynasty 574, 577, 596 on mechancial devices 450 history writers 577 on Thales 396 mathematical manuscripts 560 Heron (Hero) of Alexandria 345, 372, 460–2 ‘hand of a god/ghost’, as cause of disease 50, 51 Automata 461 Hanshu (Writings on the Han, Han History) 587, Belopoietics 460 597, 602, 605, 608 Catoptrics 414, 420, 423, 460 Harappan culture 502 Dioptra 273, 460 Harkhuf, scribe 106 and equal-angles law of reflection 420 harmonics 428–48 five mechanical powers 462 and acoustics 439 laws of force and motion 461 diatonic system 436–7 Measurements 356 empirical 428 Mechanics 460, 461 classical period 431–4 mechanics 365, 460–2, 464 Roman period 441–2 Pneumatics 460 Hellenic period 440–1 Herophilus of Chalcedon, Greek anatomist, mathematical 428 Alexandria 120, 324, 326–7 classical period 434–9 dissection of criminals 325 Roman period 443–8 naming of parts 326 and number theory 443 and optics 416 reason and perception 443, 445–6 Hesiod status as science 428, 443 and geography 403 theorists (harmonikoi) 431–2, 441 Theogony 163, 166 theory of sound 435 see also music Work and Days 163, 384, 397 harmony, of limiter and unlimited 176 Hesy-ra, Egyptian doctor or dentist 123

Index 629

Hierakonpolis, Egypt 104 Hou Han shu (Writings on the later Han) 598, hieratic script 118, 145 602, 604, 606 Hieron II, king of Syracuse 353, 456, 457 Huai nan zi, astronomical book 598, 607, 608 Hierotheus, On the Divine Art 473 Huan Tan, astronomer 611 Hinduism, and modern yoga 533 humours, bodily Hipparchus of Nicaea 266, 269, 274, 363, 409 Galen and 340, 342 “Against the Geography of Eratosthenes” 409 Greek theory 43, 310, 329, 336 calculation of year length 383 Huzirina, astronomical texts 75 ˘ calculations of distances 270 Hyksos rulers, of Egypt 112 chord tables 369 Hypatia 372 epicyclic and eccentric models 389 Commentary to the Arithmetics 361 Exposition of the Phenomena of Aratus and hypothesis Eudoxus 375 method of 177 observations 394 theorems from 281, 290 and predictive astronomy 368 Hypsicles, mathematician 359 Hippias of Elis 176 On Polygonal Numbers 360 Collection 164 Hippocrates 293, 302 Iamblichus 279, 472 Hippocrates of Chios, mathematician 348 Ibn al-Haytham 427 Hippocratic Corpus 35n, 302–4, Ibn Sahl 427 Airs Waters Places 303, 339 imitation, alchemy as 471, 476 Ancient Medicine 303, 306 immortality elixirs, China 593 disease taxonomy 42 impetus theory 204, 206, 283–4 Diseases 304, 336 Inanna, goddess 14 drugs 318 incantations 12 embryology in 227 in Babylonian medicine 43, 44–5 Epidemics 303, 307, 309, 384 indexes, to drug recipe books 319 Fractures 303 India Joints 303, 326 centrality of grammar 506 Nature of Man 303, 306, 336 earliest settlement 502 On the Heart 328 foreign incursions 503 On Prognosis of Acute Diseases 47n geographical region 502 On Regimen 312, 314 Gupta kingdom 503 On the Sacred Disease 37n, 49n, 51, 216, intellectual legacy 501–2 303, 306 Mauryan kingdom 503, 522 and role of gods 313 medieval continuity 503, 527 and origins of zoology 215–16 Ministry of AYUSH (medicine) 532–3, 549 Ś 538 Prognosticon 303, 309 raman˙a religions Hippocratic Oath 320 trading contacts 502, 503 Hippocratic physician, as craftsman 33n Vedas (sacred texts) 517 Hippodemus of Miletus 190 Vedic culture 502 see also astronomy; Hippolytus, on cosmic distance 393 mathematics; medicine historia, inquiry into facts (Aristotle) 221 Indus Valley civilization 486, 535 homeomers and anhomeomers, Aristotle 199 inﬁnity 286 homeopathy 533 in Jainist mathematics 521 Homer inscriptions and geography 402–3 astrological 378 mechanical devices 450 astronomical 376 mētis (resourcefulness) in 449 scientiﬁc 264–5 references to healers 298 instruments Honigberger, Johann Martin 533 for astronomical observations and Hori, Egyptian scribe 115 measurements 396 horoscopes, personal 377, 400 for Chinese astronomy 607–12 horoscopic astrology 97, 141, 399 for Indian astronomy 495

630 Index instruments (cont.) and temples to healing gods 317 surveying 460 see also musical instruments; life, origins of (Anaximander) 166 scientific instruments life expectancy, Egypt 122 Ionian Presocratics, view of world 403 light Isis 472 as movement 287, 289 itineraries 409 nature of 286–9 speed of 292 Jainism 503 literacy and Indian mathematics 511, 520–2 Egypt 102, 104 Jerusalem, siege of 463 Hellenistic period 249 Jia Kui, state official 605, 616 and non-specialist science 250 Julian calendar 134 Littré, Émile, edition of Hippocrates 303 Jung, Carl Gustav 470, 472 Liu An, Han prince 598 Justinian, emperor, and late ancient philosophy Liu Hui 558, 571 schools 279 Liu Xiaosun 558 śā 505 507 jyotih˘ stra (exact sciences), India , logic, in Stoicism 259, 260 logos (reason) 260 75 Kalh˘u, astronomical texts longitude, astronomical 399 Kallaneos the Indian 265 Loyalist Teaching, Egyptian text 111 Kamose, pharaoh of Egypt 113 Lucian of Samosata 271 Kassite tribe, conquest of Old Babylonia 62 A True Story (journey to the Moon) 251 āś ā āś 541 K yapasam˙ hit , Compendium of K yapa Lucretius Kepler, Johannes 255 Epicureanism 252, 258 Kerala school, South Indian astronomy 499 On the Nature of Things 258, 259, 269 kerotakis, alchemical apparatus 475, 476 optics 415 Khalid ibn Yazid 473 lunar calendars al-Khwārizmī 72 Egyptian 135–7 al-Kindi 427 stellar-based 136 Kleon, and waterlifting machines 456 lunar eclipses 10, 81, 86 knowledge and opinion, Plato 178 compilation texts 88 Kuhne, Louis 533 Egypt 142, 143 India 490 Lahun, Egypt 105, 112, 118 method of predicting 89 ‘ ’ lamentation priest (kalû) 10, 76 nature of 172 land, measurements of area 146 Saros eclipse period 88–90 Lang Yi, astronomer 606 siddhānta treatises 493 languages lunar light, from sun 164, 170, 172, 386 Akkadian 60 Lunar Six time intervals Greek-Latin bilingualism 267 observations 18, 86 – Sanskrit 485, 502, 508 9, 515 prediction 90 Sumerian 60 Lyceum see Aristotle’s Lyceum (Peripatos) Vedic 508 Lycus of Macedon 339 Laozi, Daoist deity 591 Largus, Scribonius 316, 320 Maadi culture, Lower Egypt 103 index to drug recipes 319 machinator, meanings 450 latitudes, lunar and planetary 28, 396 Mādhavanidāna Ayurvedic text 548 Letter from Isis to Horus (alchemy) 479 magic Leucippus, atomism 174 in Egyptian medicine 125 fi Li Chunfeng, of cial Tang historian 554, 555, in Mesopotamian medicine 32, 34, 43 556, 559 Mahābhārata epic 503 and measurement units 563 Mahāvīrā, mathematician 506, 520, 530–1 Ten Canons of Mathematics 555 ā 72 530 Gan˙ ita-S ra-Sangraha , libraries and zero 530 ’ Galen s 340 Maishu medical manuscript, China 579, 581 Hellenistic period 249, 323 māmītu-disease (caused by violation of oath) 43

Index 631

Manilius, Marcus, Astronomica 269, 377 trisection of angle 350 see also algebra; ‘mantic’ texts 35, 37 geometry; zigzag functions and acute diseases 47 mathematical texts, Babylonian, training 61, 68 Diagnostic Handbook 46–9 mathematical texts, Chinese physiognomic omens 46, 52–4 Mathematical Canon continuing the maps 412 Ancients 558 by Anaximander 404 Mathematical Canon of Five Administrative by Ephoros 407 Departments 557 by Eratosthenes 409 Mathematical Canon of the Gnomon of the by Hecataeus 407 Zhou 558, 569, 570 and itineraries 409 Mathematical Canon of Master Sun 557, Ptolemy’s cartographic innovations 411 563, 566 Marcellus of Side 323 Mathematical Canon of the Sea Island 558 Marcianus Graecus manuscript, alchemy Mathematical Canon by Xiahou Yang 558, 566 470, 474 Mathematical Canon by Zhang Qiujian 558 Marcus Aurelius, emperor 279, 340 Mathematical Procedures for the Five Canons Maria the Jewess 472 558, 570 Marinus 326, 339 Mathematics (Shu), Chinese manuscript 561 Martialis (Martianus) 339 Records on the Procedures of Numbering Left Martianus Capella 429 Behind for Posterity (China) 556, 559 see mašmaššu (exorcist) also mathematics, China Late Babylonian 31–2, 35, 38 mathematical texts, late antique Greek 370–3 role as priest 38n, 76 mathematicians, celebrity status 249, 263 materia medica mathematics Ayurvedic 547 and mechanics 465 Babylonian 39 pure and applied 365 Chinese immortality elixirs 593 role in cosmos 262 see also algebra; geometry; Shennong bencao jing (Divine Farmer’s) 578, trigonometry 592 see also plants mathematics, China 553–73 mathematical astronomy see astronomy, abstraction 572 Babylonian; astronomy, Greco- canonical corpus 557–9 Roman counting rods 557, 568, 613 mathematical problems management of grains 562–5 chords (of circles) 366, 367, 369, 525 manuscripts from archaeological excavations determination of unknowns 526 560–2 doubling the cube 348, 349, 350, 459, 465 measurement units 557 in Greek poems 270 multiplication tables 560 incommensurability 349, 352 numerical tables 565, 567–8 metrical units 519 official written texts 554–7 multiplication tables 118 place-value decimal notation 569 negative quantities 528 procedures 557, 568, 572 notation and layout 528–9 theoretical work 569, 571 see also mathematical number theory 352 texts ratio theory 350, 352 mathematics, Egyptian 144–59 sine function 369, 425 applied arithmetic 151–2 Indian 369, 490, 515, 524, 525 compared with Old Babylonian 156 square roots 519, 528, 569 cultural context 101 squaring the circle 348, 350, 519 Demotic developments 158–9 step functions 21, 23, 77, 94 geometrical computation 153–4 theory of congruency 353 influence of Babylonian mathematics on 157–8 theory of congruency of spherical triangles influence from Western Asia 158 367–8 numbers and metrology 146–59 theory of conic sections 356–8 numerical patterns and techniques 147–51 theory of parallelism 352, 353 origins and development 155–7

632 Index mathematics, Egyptian (cont.) numbers 63–5 problems 112, 115, 117 problems 117–18 distribution problems 151 matter pesu (pfśw) (baking ratio) problems 152 Aristotle’s theory of 186, 197–201 sources 144–6 coming-to-be of the world 165, 169, 281 mathematics, Greek 345–73 Ionian theories of 168 arithmetics and algebraic thinking 359–63 prime, Aristotle’s 200 collections and commentaries of Stoic view of continuous nature of 259, 260 knowledge 350 unity of (in alchemy) 471, 473, 476, 477, 478 combinatorics 363–4 ‘universal mixture’ axiom 171 see also atomism defined 346 Mawangdui, China, tombs, medical manuscripts exact sciences 364–70 579–81 geometry in Hellenistic period 350–9 measurement late antique commentaries and expositions Chinese units for weight and volume of grains 370–3 563–4 literary theoretical texts 345–6 Egyptian techniques 146, 154 numerical tables 369–70 Greek calculations 270–4 origins of 347–50 Greek theories of mensuration 365 and philosophy 346, 373 Hellenistic work on 250 for professions 345, 360 Mesopotamian units of 76 quadratic equations 569 of weight 203 spherics 366–8 mēchanē, positive and negative connotations theoretical geometry 72, 159 449–50 trigonometry 368–9 mechanical devices use of Egyptian fractions 159 see also algebra; attack tower (helepolis) 455, 467 geometry automata 460 72 501–31 452 mathematics, Indian (gan˙ ita) , balances Ā 523–6 466 467 ryabhat˙ a ballista , and astronomy 506 catapults 454, 456, 459, 460 Bakhshālī manuscript 528–30 cog-wheels 456, 461 Brahmagupta 526–7 for displays of power 454 in classical age 522–7 hodometer 459 context and role of 505–8 hot air devices 460 flexible terminology 510 hydraulic organ 459 format of texts 509–11 levers 450, 453 Greek influence 522 pumps 456 Jainism and 520–2 revolving theatres 455 notion of divisibility 518 self-moving devices 451 numerals and numeration systems 511–17 sickle chariots 466 overview 504–5 siege engines 450, 455, 463, 466 place-value system 64, 511, 521 siphons 461 post-classical 527–31 surveying instruments 460 Siddhānta texts 523 use of steam (Heron) 461 textual sources 508–9 war machines (belopoietics) 458, 460, 466 in Vedic India 517–18 waterlifting machines 455, 459 verses for oral learning 509–10 mechanics 449–67 written commentaries 510–11 and architecture 462, 465–6 mathematics, Mesopotamian 58–72 and concentric circles 452 algebra 61, 63, 66–9 definitions 452, 464 in astronomical cuneiform texts 26, 76–7 in Hellenistic kingdoms 454–6 computations 69–70 Heron of Alexandria 365 geometry 65–6 late Roman Empire 465–7 influence on Egyptian mathematics 116, 157–8 laws to encourage training in 466 influences of 71–2 and mathematics 465

Index 633

properties of circle 453 diagnosis and prognosis 309 Pseudo-Aristotle’s Mechanical Questions 452–3 and general culture 337 Roman war technology 463 Hippocratic Corpus 35n, 302–4 study of 451 pharmacology 318–21 and utility 454, 461, 462, 467 and philosophy 304–5, 306 medical education prevention and prophylaxis 311–12 Alexandria 322 professionalization 298 Egypt 124 role of non-experts 297 medicine and scientific theory 305–7 modern complementary and alternative 532–5 sectarian medicine 331–7 see also Greek medicine surgery 337–9 medicine, Babylonian 29–57 theories of health and disease 310 changes in thinking 51 therapeutics 310–11 competing disciplines 32, 33 and Unanani Tibb (South Asia) 534 pharmacology 54–6 and urbanisation 321–2 recipes 38–9 medicine, Indian 532–49 and zodiac 97 early Buddhist 538–40 medicine, Chinese 35n, 574–94 feelings (bile, phlegm and wind) 539 540 acupuncture 580, 581, 586, 588 humors (dos˙ a) aphrodisiacs 585 and karma 539, 540 Canon of Difficult Issues 590 in prehistoric South Asia 535–6 development of orthodoxy 586–7 Vedic medicine 536–8 see also Ayurveda and gender differences 583 Mehrgarh, Pakistan, prehistoric settlement 535 literacy of medical practitioners 577, 579 Melissus, Eleatic school 171 mai channels 580, 581–3, 589 on void 205 medical manuscripts 579, 590 Menaechmus 349 “Medicine of Systematic Correspondence” 589 Menelaus 369 moxibustion (heat treatments) 580, 581 astronomy 375, 395 qi flows 578, 580, 583, 585–6, 588, 589 Spherics 367–8 and sensory world 585 mental health, Greek interest in 295, 312–13 sexual cultivation 583–6 Mentuhotep Nebhepetre (Mentuhotep II), king spirit healing 580 of Egypt 109 traditions of healthcare 578 Meru, Mount, as centre of earth 487 wuxing (“Five Agents”) 578 Mesopotamia Yin and Yang 578, 580, 583 bureaucratic state 59 medicine, Egyptian 120–30 literacy and numeracy 102 concepts of anatomy and physiology 124–5 modern nomenclature of astrological and dental practice 128 astronomical texts 25–8 doctors and practitioners 123–4 scholarship and wisdom 7 see also astronomy; Ebers Papyrus 121 mathematics; medicine, Babylonian Edwin Smith Surgical Papyrus 121 Mesopotamian cuneiform, writing system 58 foreign influences 120 metaphysics gynaecology and obstetrics 128 Aristotle’s first philosophy 184, 196 ophthalmology 129 and Indian super-mundane 507, 520 pattern of disease 122–3 Neoplatonic 289 practice of 126–9 meteor, near Aegospotami (467 BC) 173 Sallier IV papyrus 141 meteorology schools of medicine 124 Aristotle 189 surgery 127 and celestial physics 190 texts 110, 120–2 explanation of phenomena 166 medicine, Greek 293–315, 316–44 Methodists, medical sect 333–5 anatomical observations 307–9 ‘common conditions’ 334 archaic and early classical period 298–300 mētis (resourcefulness) 449 development of technē 296–8 Meton of Athens 379, 382, 394 developments 293–6 Metrodorus 328

634 Index Michael Psellus, Byzantine alchemist 474 musical scores, notation 429 Miletus 403 musicians, Greek 428, 434 calendar 383 methods of instruction 431 parapēgma 384 teaching manuals 441 scientific inscriptions 265 tuning systems 446 mirrors 422, 460 myrrh 241 Mithradates VI, King of Pontus 238, 322 mythography, Greek 163 Mnesitheus of Athens 306, 309, 312 monism 175 Nagada, Upper Egypt 103 486 Ionian 168, 169 naks˙ atras (constellations) monuments, stone, scientific inscriptions 264–5 use as unit of arc 489, 490 moon Narmer, king of Egypt 104 estimates of dimensions 391 natural philosophy estimates of distance to 270 late ancient questions of 279 mathematical calculations 93 Proclus and 290 periods of visibility 17, 18, 19, 81 natural science, in Aristotle 184 India 490 nature as spherical 172, 386 concept of (phusis) 306 systems of calculation 96 see also lunar study of 252, 289–91 calendars; lunar eclipses naturopathy and Nature Cure 533 moral behaviour, as cause of disease 50 Nearchus 241 Morienus (Marianus) 473 Nebamun, Egyptian scribe 113 mosaics, Plato’s Academy (Pompeii) 250 Nechepsos, King of Egypt 401 motion Needham, Joseph 476, 575 Aristotle’s theory of 204–6 Nemrud Dag, horoscope frieze 378 projectile 204, 283 Neo-Babylonian period 62 through void 205 neo-Pythagoreanism 261–3, 281 time as measure of 211 Neoplatonism, in late antiquity 278 and velocity 206 Neugebauer, Otto 25, 71, 143 mountains, estimates of height 270, 272–3 Newton, Isaac 283 MUL.APIN “Plow Star” compendium (Middle newts (kordulos), gills 231, 235 Assyrian) 15, 17, 75, 80, 82–3 Nicander of Colophon 319 multiplication Nicephorus, Byzantine alchemist 474 Chinese tables 560 Nicolaus of Damascus 244, 245 commutativity of 149 On Plants 238 Egyptian technique 147 Nicomachus of Gerasa of fractions 148 and harmonics 429, 436, 444–5 Mesopotamian 64 Introduction to Arithmetic 262, 278 tables 118 and Pythagoras 262, 445 mummification, Egypt 120, 124, 325 Nimrud, state library 8 music Nine Chapters on mathematical procedures 558, concords 429 569, 570 division of tone 436, 439, 444 and regulations on grains 563–4 keys 430, 447 Nineveh melody 433 astronomical texts 75, 84 musical identity of notes 433–4 state library 8, 10 octave and intervals 429, 431 Nippur 18, 79 pitch 430, 433, 434, 435 nomarchs, Egypt 107 and role of ears (hearing) 431, 432 Normal Star Almanacs 92, 93 scales 430, 433 Normal Stars (ecliptical stars) 17, 87 singing voice 433 number theory 352, 443 tetrachords 430 numbers theory of 278 see also harmonics Greek numerical tables 369–70 musical instruments 431, 433 Hellenistic work on large 250, 274–5 and ratios and intervals 434–5, 445, 446 numbers, Egyptian 104, 146–59

Index 635

capacity unit 146 historical overview 413–14 decadic notation 146 intromission 415 fractional 146, 147 and perception 416 length 146 ray theory 413, 427 patterns and techniques 147–51 spatial perception 417 numbers, Indian and visibility 418 base-ten place-value system 511, 517 visual clarity 417 ū ā 512–13 fl 415 418 423 Bh tasam˙ khy (object-numerals) visual ux , , glyphs and zero 528 and visual illusions 418 ā ā 513–15 415–17 kat˙ apay di (vaky phrase system) visual perception nāgarī numerals 511, 512 visual-ray theory 417–19 see also reflection; numerals and numeration systems 511–17 refraction varga system 515–17 Orphic Poems 280 verse for long-strings 512 Ostanes, Persian magus 319, 472 numbers, Mesopotamian 63–5 Ouroboros 478 accounting measures 59 Ouyang Xiu, and New History of the Tang calculating board 64 Dynasty 555, 557 place-value system 63, 76 Owen, Richard, anatomist 216, 237 sacred numbers of the gods 63 sexagesimal notation 19, 59, 63, 76 Pammene 472 units of measurement 76 Pamphilus of Alexandria 319 Numisianus, doctor 339 Panaetius, Stoic 260 ā 503 508 P n˙ini, Sanskrit grammarian , Ogle, William, translation of Aristotle 217 Pappus of Alexandria 371–2, 410, 411 oikoumenē (inhabited world) 406 Collection 371, 464–5 size of 408 Collection II on Apollonius 356, 371 Strabo’s 410 on Euclid 351 Old Babylonian period 61 on field of analysis 372 Olympiodorus 264, 479 Little Astronomy 372 in Alexandria 279 parapēgma (inscription) 265 commentary on Zosimus 473 astronomical texts 384–6 Olympus, Mt 272 for predictions 396 as centre of world 403 Parker, Richard A. 136, 143 omens Parmenides of Elea 169–71, 336 abnormal birth 10 Aristotle and 198 application to human fortune 12, 21 earth as spherical 170, 405–6 astral 10, 80, 81–2, 85 and Heraclitus 169 Chinese astronomy and 602–3 and lunar light 170, 386 explanation 9, 22, 398 Truth and Opinion 169 India 490, 498 and Venus 170 lists of 9 Pelagius 472 planetary 11 perception prognostic 47n and experience 289 symptoms as 46, 52–4 see also astronomical and knowledge 289 prediction theory of 286 ophthalmology, Egypt 129 Pergamon (Pergamum) 322 optics, Greek 413–27 library 249 binocular vision 419 period relations, mathematical tool 20, 26, 77 catoptrics 420–2 Peripatetics (Aristotle’s Lyceum) 252, 253–6 and color 416, 418 medical treatises 305 complementarity 416 problemata texts 256, 305 dioptrics (refraction) 423–7 periploi (charts of sea routes) 409 extramission 415 Persian empire, expansion to India 503 fate of 427 Peseshet, Egyptian female physician 123 and Governing Faculty 418, 419 phainomena, Aristotle’s use of term 187

636 Index

phantasia (impression), and truth 260 Egypt 155 pharmacology in Indian mathematics 513, 519 Babylonian medicine 54–6 Pibechius 472 Egypt 129 Pindar 403 Hellenistic and Greco-Roman 318–21 see also Pin˙gala 518 drugs place, Aristotle’s theory of 208–10 Philinus of Cos, Empiricist 332 planetary observations Philip II of Macedon 181 Diaries 87 Philo of Byzantium predictions in compilation texts 90–2 Belopoietics (war machines) 458, 459 planets Mechanical Syntaxis 458–9 complex motions 179 Philolaus of Croton 176, 348 eccenter and epicycle models 388–90, 492 and harmonics 435–6 Jupiter periodic visibility 94, 397 Philoponus, John 208 longitudes of 493, 499 on Aristotle’s Posterior Analytics 281 Mercury periodic visibility 94 and classical dynamics 278, 283–4 periods of visibility 15, 81, 494 on eternity of cosmos 285–6 planetary omens 11 and impetus theory 204, 206, 283–4 as solid and massy 172 on nature of light 287, 288 synodic cycles 11, 17, 87, 93 On the Astrolabe 280 systems of calculation 94–5 on Plato’s Timaeus 285 Venus periodic visibility 19, 91 philosophers, celebrity status 249, 263 Wu xing zhan treatise on motion 600 philosophical schools, Hellenistic 248 and zodiac 12 allegiances 252–3 plants commentaries on Plato and Aristotle 278, 280 Aristotle and 192 curriculum 279–80 artemsia vulgaris (mugwort) 580, 581 in late antiquity 278–92 botanical description 243 Latin authors 252 Chinese medical 578, 580 loyalty to 252 classification and description 242–4, 578 publicity for 256 diseases of 246 philosophy first-hand knowledge of 240 and alchemy 469 folk system of classification 243 and Greek medicine 304–5, 306 generation of 245 and mathematics 346, 373 hellebore 327 and study of heavens 183 illustrations of 244 teaching of 279 life of 244–6 physicians in materia medica 39, 54 asû (Babylonia) 10, 30, 38, 56 for medical preparations 240, 244 Ayurvedic 541, 542 nomenclature 243 Chinese 579, 590–1 oral accounts of 240 Greco-Roman 338 and pollination 246 ś 539 245 raman˙ a (India) propagation of technitēs (Greece) 297 rituals of gathering 241 Vedic 538 see also doctors sensations of 245 physics specialist users 240 Aristotle’s celestial and sublunary 189–92 utility of 239, 244, 246–7 Aristotle’s general and special 186–9 Vedic medicinal 537 Aristotle’s natural philosophy 184–6 written sources 241 see also botany Epicurus on utility of 257 Plato 177–9 and mechanics 452 and Anaxagoras’ theory 177 and medicine 305 and Anaximenes’ theory 169 Stoics and 259, 261 and harmonics 437–8, 439 physiognomic omens 46, 52–4 late ancient study of 279 physis, Aristotle’s concept of 185 and mathematical harmonics 428 π (pi) on mechanics 456

Index 637

and mental health 313 celebrity status 249 “Myth of Er” (Republic) 386 contemporary fame 263 nature of light 287 and distances to sun and moon 270 On Nature 178 potentiality, existence in, in Aristotle 197, optics 416 201, 202 Phaedo 177 Prajāpati, creator god 518 on plants 245 Praxagoras of Cos 309, 324 and quadrivium of mathemathics 364 prediction see astronomical prediction; omens Timaeus 178, 262, 281, 285, 386 prescriptions, 2nd person singular verbal form and diatonic scale 438 39, 45 Plato, Pseudo-, Epinomis 375 Presocratics Platonism, and neo-Pythagoreanism 262 natural philosophy 215 Plato’s Academy 181, 252 view of world 403–4 mathematicians 349 Problemata (question-and-answer texts) mosaic of 250 255, 305 and neo-Pythagoreanism 261–3 Proclus Pliny the Elder 13, 272 commentaries 281, 372, 375 and circumference of earth 271 Commentary on Elements Book I 347 classification of plants 242 Elements of Theology 280 and Greek medicine 317 and Euclid 281, 354 index to drug recipes 319 and natural philosophy 290 on lack of scientific inquiry 275–6 nature of light 288 on large numbers 275 Procopius 465, 467 Natural History 238, 267, 267, 390 proportionality on planets 390 canonical system 154, 155 on plants 239, 244, 246, 319 in Egyptian mathematics 149 on revolving theatres 455 Ptolemaïs of Cyrene 440 Plutarch Ptolemy, Claudius 134, 143, 276 and the Academy 262 Almagest (Mathematical Syntaxis) 264, 266, on Archimedes 456 369–70, 379, 390 on Archimedes’ tomb 263 astronomical observations 393 on catapult 455 map of constellations 384 and combinatorics 363 Analemma 369 Life of Aemilius Paulus 272, 274 astrology 377, 401 on mechanics 451 astronomical texts 375, 378, 397 On the Face of the Moon 250, 255 and binocular vision 419 Placita philosophorum (attrib.) 255 Canobic Inscription 264, 392, 393 on Timaeus 443 and celestial spheres 283 Plutarch, Pseudo-, Philosophers’ Opinions on and equal-angles law of reflection 421 Nature 260 Geōgraphikē Hyphēgēsis 402, 410–12 pneuma (breath) on geography 410 in arteries 327, 329, 330 Handy Tables 395 in optics 416 Harmonics 278, 365, 442, 445–7 role in Stoicism 259, 260 on Hipparchus 394 Pneumatists 336 mathematical astronomy 391 poetry models for planets 390 medical 320 Optics 414, 418–19, 427 scientific 250, 263, 267, 269 visual cone 418 Polybius 410 Phaseis 385 Pomponius Mela 410 Planetary Hypotheses 391, 393 Pontus, medicine at 322 Planisphere 369 Porphyry and refraction 423–7 commentary on Ptolemy’s Harmonics 447–8 Tetrabiblos 377, 398 and theory of music 278, 440 on theoretical sciences 365 Posidonius of Apamea, Stoic 260, 272, 410 trigonometry 369–70

638 Index Ptolemy I, ruler of Egypt 322, 325 Roman empire and Library of Alexandria 249, 323 astronomy as Greek science 374 Ptolemy II Philadelphus 452, 454 and Greek medicine 316 and Library of Alexandria 249 horoscopes 399 pyramids 450 Rome 321 geometry of 155 Greek philosophy in 259 orientation 132 healing cults and temples 317 Pythagoras 262, 262, 299, 347 lack of scientiﬁc inquiry 276 Pythagorean theorem 65, 353 medicine in 318 in Chinese mathematics 570 and Methodist medical sect 333 in Indian mathematics 509, 519 public sundials 266 Pythagoreans rope stretchers, mensuration 154 geography 405 Ruelle, Charles-Émile 469 and mathematical harmonics 435–7 Rufus of Ephesus and anatomy 339 Qin dynasty 553, 576, 595 Buying Slaves 338 Qin Statutes in eighteen domains 562 The Layman 338 Qinshi Huangdi, Emperor 576 Medical Questions 338 Qizil fragment, Buddhist medical text 540 Russell, E. S., The Interpretation of Development Quintus, doctor 339 of Heredity 228

rainbow 413 Sachs, Abraham 26 Rāmāyana epic 503 Sardinian Sea, estimates of depth 273 Ramesses IV, king of Egypt, tomb 137 Śā ˙ ā 548 rngaharasam˙ hit , Ayurvedic text Rationalists (Dogmatists), medical sect 336–7 Saros eclipse period 88–90 reflection 420–2 Ś ā 518 atapathabr hman˙ a, text concave mirrors 422 497 Saurapaks˙a school convex mirrors 422 scholarly professions, Mesopotamia 10 equal-angles law of 414 scholarship and wisdom, Mesopotamia 7, 8–14 image location 421, 422 scientific inscriptions, stone 264–5 refraction 423–7 scientific instruments, for measurement of atmospheric 425, 426 mountains 272 image distortion 426, 427 scientific objects, public displays 249, 263–6 Ptolemy and 423–7 scientific theory, development of Greek 179 religion scientific writings, Hellenistic and Roman in Egyptian medicine 125 267–70 and Greek medicine 313–15 histories of science 267 Reports, Assyrian texts 16 non-specialist interest in 267 reproduction, Egyptian knowledge of 125 Scipio Africanus 463 respiration scribal profession, Egypt 104 Aristotle on (case study) 229–36 careers 106 Aristotle’s explanation of activity of 233–6 First Intermediate Period 107–9 Aristotle’s explanation of parts 231–3 mathematical training 156–7 epiglottis 230, 232 Middle Kingdom 109–12 and gills 231, 233, 234 New Kingdom 113–16 and heart 230, 231 and numbers 104 larynx 232 Old Kingdom 104–7 lung 230, 232 relations with kings 107, 111 analogous with gills 235–6 Second Intermediate Period 112 oesophagus 230, 232 self-depiction 106, 110, 111, 116, 118 organs of 229–31 superiority of 113–14 windpipe 230, 232 teaching texts 111 Rhind mathematical papyrus 112, 118 scribal profession, Mesopotamia 60 ri shu (day books) 604 astronomy 74–6 Roman army, and treatment of wounds 337 ‘humanism’ 61, 70, 156

Index 639

sea, estimates of depth 270, 273 Skythians 408 ‘secret of the great gods’, cuneiform knowledge Socrates of Athens 176–7 as 7 in Plato’s Phaedo 177 sectarian medicine, Hellenistic and Greco- solar eclipses 396 Roman 331–7 Babylonian method of predicting 89, 164 Empiricists 332–3 China 600 Methodists 333–5 India 490 Rationalists 336–7 nature of 172 Seleucid period, mathematical texts 63 Saros period 89 Seneca, Lucius Annaeus 268–9 siddhānta treatises 494 Natural Questions 260, 267, 268 Thales’s prediction of 164, 396 Senenmut, Egyptian official 140 solstices sensory experience dating of 381–2, 394 Epicurean 257 measuring 599 and perception 289 sophists, Greek 176, 177 Serapion of Alexandria 319 Soranus of Ephesus 334, 335 Against the haeresis 331 Gynaecology 334 Seti I, king of Egypt 137 Sosicrates, doctor 318 Sextius Niger 238, 319 Sowa-Rigpa (gSo ba rig pa), Tibetan Sextus Empiricus 332 medicine 534 Shang period, China 574, 576, 596 Speusippus, head of Plato’s Academy 181 Shi ji (Records of the Historian) 597, 605 spherics, and Greek astronomy 366–8 Shi Shen 601 square roots 519, 528, 569 Shu jing (Book of Documents) 603 Śrīpati, mathematician 506 Shuangbo shan, China, figurine 581–3 star clocks 137 Shuihudi, China, medical manuscripts 579 diagonal 137 Siddha medicine 534 transit 137 siddhānta treatises 492–5 stars calculations of moon’s crescent 494 Chinese observations 599 conjunctions of planets and stars 494 and constellations 383–6, 486, 608–9 instruments 495 fixed 133, 274, 392 lunar eclipse 493 and gods, Egypt 140 lunar shadow 494 helical risings 20, 80 mean motions 493 and markers of natural year 384 planetary visibility 494 as solid and massy 172 solar eclipse 494 ziqpu (“culminating”) 84 “Three Questions” 493 Statilius Attalus 341 true motions 493 Statilius Criton 341 sight step functions 21, 23, 77, 94 theories of 415 see also optics Stephanus of Alexandria 480 silphium 241, 245 Lectures 473 Sima Qian 601, 608 Sthānān˙gasūtra, Jainist text 521, 522 Shi ji (Records of the Historian) 597 Stoa (Porch), Athens 252, 259–61 Simplicius 208 Stobaeus, Excerpts 260 astronomical geometry 387 Stoics 252, 259–61 astronomical modelling 388, 390 influence of 259 commentaries 280, 375 Strabo 273, 410 Commentary on Aristotle’s Physics 348 chôrographia 410 sine function 369, 425, 490, 515, 523–6 on Ephorus 406 Ā ’ 524 525 260 273 ryabhat˙a s verse table , on Posidonius , Sanskrit terminology 524 Strassmaier Cambyses 400 tablet 11, 18 Sirius (Sothis), heliacal rising in Egyptian Strato of Lampsacus 330 astronomy 134, 136 and Mechanical Questions 452 Sīvaka, Buddha’s discourse with 539 sublunary physics Skymnus, Pseudo- 410 Aristotle’s conception of 189, 190–1, 192, 283

640 Index sublunary physics (cont.) mathematical textbooks 556 and celestial motion 284 Records on the Procedures of Numbering Left Suda, tenth-century Byzantine lexicon 182 Behind for Posterity 556, 559 Śulbasūtras mathematical text 518–20 The True Meaning of the Five Canons 554 Šulgi, king of Ur 60 Zhui shu mathematical canon 556, 558 Sulla, siege of Athens 463 Tao Hongjing 592 Sumerian language 14, 60, 61 The Teaching of Amenemope 115 sun Teaching of Ptahhotep 106, 111 continued existence at night 172 teaching texts, Egypt 111 Empedocles’ view of 174 temples, Egypt 103, 118 estimate of size of 271, 391 Testament of Hippocrates 336 estimates of distance to 270 see also solar texts eclipses astrological papyri (Egypt) 377 Sun Simiao, physician 592 Byzantine manuscript tradition 377 sundials collection of, Hellenistic period 249 Egypt 139 doxographies 165, 254–5 Greco-Roman 266, 376 on harmonics 429 portable 377 question-and-answer (problemata) 255, 305 see surgery also astronomical texts Ayurvedic 541 texts, Greco-Roman astronomical 374–6 Egypt 127 astronomical tables 397 surveyors papyrus from Egypt 376 area computations 60, 65, 66 texts, Greek literary, disease and medicine in 300 line-of-sight techniques 415 texts, Greek medical 301–4 riddles 68, 71 rhetorical character 301 Susa, mathematical texts from 62 for teaching 301 ś ā ś 541 301 Su rutasam˙ hit , Compendium of Su ruta vocabulary see also Hippocratic Corpus sūtra, concept of (“string” or rule) 517 texts, Indian 518 537 sutures, Egypt 127 ˙Rgveda, Vedic hymns , syllogistic proof, Aristotle’s 217, 236, 281–2 Vedas (sacred texts) 517 Synesius, Commentary on the Books of Thales of Miletus 163, 164, 183, 215, 396 Democritus 472 mathematical proofs 347 Syracuse 454 Theaetetus 349 Athenian campaign (413 bce) 398 Thebes, tomb of Senenmut 140 sack of (212 bce) 353 Themison of Laodicea, Methodist 333 Syrianus 281, 288 Theodorus, mathematician 349 Theodosius 372 tablets, Mesopotamian 8 Spherics 366 archaeological contexts 74–5 Theologoumena arithmeticae 72 catalogue (medical) 35, 36 theology 290 classification systems 26 Theon of Alexandria 372, 395 classified as secret 13 Theon of Smyrna 375, 378, 443 explanatory texts 25 Mathematics useful for Reading Plato 262, 442 late Babylonian 85–98 and physical astronomy 391 MUL.APIN series 15 Theon “the mathematician” 395 planetary observations 17 Theophrastus, alchemist, On the Divine Art 473 second and early first millennium bce 79–85 Theophrastus of Eresus 165, 241, 245, 322, 328 study of 73 see also Enūma Anu Enlil Aristotle’s Lyceum 210, 249 Taizong, Emperor 554 Causes of Plants 245 Tale of the Eloquent Peasant (Egypt) 110 classification of plants 242 Tamil Nadu, Siddha medicine 534 and doxographies (collected opinions) 253–5 Tang dynasty 553, 574 Enquiry into Plants 238, 240, 253 canonical literature 554 and harmonics 440 Mathematical Canon by Xiahou Yang 556 writings on natural science 253

Index 641

theorems, from hypotheses 281, 290 cosmology 487–8 therapeutics hymns 518, 537 early Greek 310–11 medicine 536–8 Greco-Roman 334 religion 536 Thessalus of Tralles 335 sacrificial rituals 536, 537 Thucydides 396, 398, 450 texts 517, 537 Tian wen zhi (Record of celestial patterns) 602 Vegetius 466 Tiberius, emperor 323 velocity Tibet and motion 206 Ayurvedic medicine 542 relative 203 Sowa-Rigpa (gSo ba rig pa) medicine 534 Venus Tiloyapan˙n˙att, Jainist text 521 as morning and evening star 170 time periodic visibility 19, 91 Aristotle’s theory of 210–14 Vettius Valens 377, 378 and infinity 211, 212–13 Vienna Dioscorides 242, 244 and intervals 213 Virasena, Dhavaklā 520 as measure of motion 211 Vitruvius 459–60 and now 211, 214 On Architecture 266, 267, 459 Timocharis, astronomer 394 and sundials 266 tombs void artwork of 113 Aristotle’s denial of existence of 203, 206–8 depictions of metrological systems 105 Epicureans and 256 Egyptian nomarchs 107 Heron and 461 elite burials, Egypt 103 motion through 205 grave goods 108 Philo on 458 triangles volcanoes, Plato 178 Aristotle’s general treatment of 187 vortex 175 Chinese mathematical procedures 559, 570 motion of primordial condition 172 Egyptian geometry 153, 155 and streams of atoms 174 in Plato’s cosmology 179 trigonometry 368–9 Wang Xiaotong 558 in astronomical prediction 397 water clocks (clepsydra) 376 chord tables 369 in Chinese astronomy 609 Indian astronomy 490, 499 in Indian astronomical measurement 489 Indian mathematics 527 outflow 138 tabular 368 water cycle, Xenophanes’s view of 167 Trilokaprajñapti, Jain text 521 water supply, aqueducts 321 truth, and impressions (phantasia), in weight Stoicism 260 Aristotle’s theory of 202–4 measurement of 203 Unanani Tibb medicine 534 and relative velocity 203 Unity of Heaven and Humanity, theory of 592 Weni, scribe 107 Ur, Third Dynasty 60 wisdom see scholarship and wisdom urbanisation, and medicine 321–2 witchcraft, Babylonian, as human agency 45 Uruk 14 women astronomical texts 75, 94 as doctors 338 and Epicurean school 256 vacuum process, Erasistratus and 330 writing, evolution of Egyptian 104 ā 541 V gbhat˙a, Ayurvedic compendia writing system Varro, M. Terentius 238, 240 Mesopotamian cuneiform 58 Vedic culture 502 protoliterate 59 astronomy 486–8 Writings on Mathematical Procedures 561, 562–3, Atharvaveda 537 566–7 calendars 485, 488 wu (diviners, shamans) 576

642 Index

Wu xing zhan treatise on planetary motion 600 Zhang Jue (Jiao), Yellow Turbans sect 592 Wuwei, China, medical manuscripts 579 Zhang Zhongjing, Treatise on Cold Damage 590 Wuzong, Emperor 594 Zhangjiashan, China Maishu medical manuscript 579, 581 Xenagoras 272 Yinshu writings 586 Xenophanes of Colophon 167–8 Zhao Shuang 558 Xenophon, Stertinius 316 Zhen Luan 557, 558, 570 Xiahou Yang 556 Zhou bi, astronomical book 598, 610 Xu Yue 556 Zhou dynasty 576, 577, 596 Zhui shu mathematical canon 556, 558 Yang Xiong, astronomer 611 zigzag functions Yao, Emperor 603 in astronomical predictions 19, 20, 21, 27, 521 Yativr˙˙sabha 77, 81 year in Indian astronomy 489 Egyptian civil calendar 133 for synodic arc calculations 94 – Greek calculations 382 3 “Three Stars Each” 80 Indian ideal 486, 488 ziqpu (“culminating”) stars 84 – intercalary months 78, 381 2, 486 zodiac leap day (Egypt) 135 and astral medicine 97 Mesopotamian calculations 19 and astrology 97 natural 384 and celestial positions 88 numbering 383 Egyptian 141–2 Yellow Emperor (Huangdi) 577, 578 and Greco-Roman astrology 398 Inner Canon of the Yellow Emperor 587 and Greek constellations 384 Basic Questions 587, 588, 589 and mathematical astronomy 97 Grand Basis 588 and planets 12 Numinous Pivot 588 zodiac boards 378, 400 yoga, modern 533 zoology Yongle, Emperor 556 Aristotle’s legacy 216–17, 236–7 Aristotle’s norms of zoological inquiry Zabarella 189 218–19 Zeno Aristotle’s philosophy of 217–19 Eleatic school 171 ‘Presocratic’ natural philosophers 215 see also paradox of the arrow 213 animals; birds; ﬁsh paradoxes of divisibility 174 Zosimus of Panopolis 472, 475, 479 paradoxes of motion 212, 213 Final Quittance 472, 479 and Stoa school 252, 259 Visions 470, 472 Zenodorus 372 Zu Chongzhi 556 zero, in Indian mathematics 528, 530 Zuo Zhuan chronicle 600