Cambridge University Press 0521622794 - The Shaping of Deduction in Greek Mathematics: A Study in Cognitive History Reviel Netz Index More information Index Index abaci – Method , , –, Aeschylus (astronomer) On Floating Bodies , –, , Alcibiades Plane Equilibria – Alcinous n. quantifiers in , n. Alcmaeon semiotics of letters in , – analysis and synthesis Sphere and Cylinder , , , Anaxagoras Spiral Lines –, –, , Anaximander status of Andron war engines of , , Anthemius see also Pheidias Antiphon , , Archytas n. , , , , , apodeixis , –, –, , , ; arguments , –, – see proof and definitions Apollonius , , , , , , diagram-based , , –, cadenza effect in intuition-based , , – Conics – , reference-based , –, – Conics , –, , , , –, , tool-box-based , , – , , , , , , Aristarchus , , Conics Aristophanes , , Conics , Aristotle , , , , Conics on age of mathematicians and his contemporaries , , Analytics – definitions in – on banausic activity – enunciations in chronology of , , literate practices of on earlier authors , quantifiers in , , , lexicon of , Arcesilaus , and generality Archimedes , , , , on geometrical objects Arenarius , , Mechanics cadenza effect in on mechanics chronology in , Meteorology , , – Conoids and Spheroids on pebble mathematics , and his contemporaries –, practice of teaching –, enunciations in references to diagrams , image of n. , , , – status of introductions of – structure of proofs in , – invention of Cochlias by use of diagrammatic letters by , –, knowledge of conic results lexicon of , – Aristoxenus , , literate practices of Aristyllus mechanical works of , arithmetic , , –; see also abaci © Cambridge University Press www.cambridge.org Cambridge University Press 0521622794 - The Shaping of Deduction in Greek Mathematics: A Study in Cognitive History Reviel Netz Index More information Index assertions semiotics of –, diagram-based see also arguments: diagram based; starting- astronomy ; see also planetaria points: diagram based Attalus , , di’ arithmDn Autolycus , –, , , , Digest – axioms , , , ; see also Common Dijksterhuis, E. J. Notions, definitions Dilke, O. A. W. Dinostratus ‘baptism’ , , –, – Diocles , Bion Diogenes Laertius Blomquist, J. n. , Dion Bourdieu, P. Diophantus n. , Brecht, B. diorismos , –, –, n. ; Burkert, W. see definition of goal Burnyeat, M. F. disambiguation – Dositheus , , cadenza Carpus Eisenstein, E. L. Carter, L. B. –, ekthesis , –, , –, n. , ; Chrysippus see setting out Cicero ellipsis , , –, , – Clagget, M. n. Empedocles , , Common Notions , enunciation , , , , , , , composition ; see protasis of abstract objects , – Epicharmus , of geometrical objects , , Epicurus , n. , of ratios , – lexicon of conclusion , , ; see sumperasma equivalence , – conic sections , –, , ; see also Eratosthenes , , , , , , , Apollonius: Conics connectors , , –, , , Euclid , , , , Conon , , , , chronology of , construction , , , , –, ; Data , , – see kataskeuB Elements –, , , – Coulton, J. J. n. Elements , , –, –, , , Crates Ctesibius n. , , Elements –, n. , –, , Cuomo, S. (formulae in , , , , , ) Cyzicus, school at Elements –, –, –, Elements , definition of goal , , ; see diorismos Elements , –, – definitions – Elements –, Democritus , , , , Elements – , – Demosthenes Elements Descartes, R. Elements Detienne, M. Elements , dia grammDn Elements diagrams – Elements , –, –, , in arithmetic –, enunciations in , fixation of reference inside –, lexicon of n. ff. graph-like – Optics , material of – quantifiers in , –, –, metonymic role of –, Sectio Canonis , perception of – see Common Notions role for generality – Euctemon 324 © Cambridge University Press www.cambridge.org Cambridge University Press 0521622794 - The Shaping of Deduction in Greek Mathematics: A Study in Cognitive History Reviel Netz Index More information Index Eudemus of Rhodes , , , Herreman, A. n. Eudemus of Pergamon , Hesiod Eudoxus , –, , , , , , hiatuses, avoidance of –, , , , Hilbert, D. , , Eurytus , , Hipparchus , , Eutocius Hippasus , references to diagrams Hippias , , , Hippocrates of Chios , , , , , Finnegan, R. , , Fodor, J. , – semiotics of letters in , , formulae Hippocrates of Cos , argumentation –, , , , , homoiDs – homonyms , –, construction –, , , , , , in formulae , , , , Housman, A. E. defined – Hoyrup, J. n. and explicit definitions , , , , , Hypatia , , Hypsicles , flexibility of –, , , lexicon of nn. ff. hierarchic structure of –, , , literate practices of – Homeric –, , , , , –, Ion Isocrates , , , , and homonyms object , –, , , , , Janus, C. n. predicate –, , , , , , Johnson-Laird, P. n. , , Jones, A. n. role in arguments – role in starting-points kataskeuB , –, see construction role in the tool-box Klein, J. second-order –, , , Knorr, W. , , n. , –, , transformations of –, , Kuhn, T. –, Fowler, D. H. , n. Lachterman, D. R. n. , n. Galen , , Lear, J. Gardies, J. L. – Leon Gellner, E. letters (alphabetic) , – Gillies, D. n. as part of lexicon Glucker, J. n. semiotics of –, – Gooding, D. n. letters (epistolary) , , – Goody, J. n. , , lexica, local , , – Gorgias Lloyd, G. E. R. –, , –, , Grattan-Guinness, I. – grid arguments –, , Long, A. A. Lord, A. B. n. Hainsworth, J. B. n. hapax legomena –, , – make-believe –, Heath, T. L. –, , Mansfeld, J. n. semiotics of letters in –, many-lettered names , –, –, –, Heiberg, J. L. , , Heraclides mathematical induction , Herman, G. , – medicine Hero , lexicon of – lexicon of nn. ff. Melissus Herodotus , Menaechmus © Cambridge University Press www.cambridge.org Cambridge University Press 0521622794 - The Shaping of Deduction in Greek Mathematics: A Study in Cognitive History Reviel Netz Index More information Index Meton , trees of –, , , , , , Mogenet, J. n. see apodeixis Mueller, I. , , –, , –, , proportion theory –, –, , , –, , ; see also Euclid: Elements , Mugler, C. , Protagoras (astronomer) Protagoras (philosopher) Naucrates protasis , –, –, , n. ; Neoclides see enunciation Nicomachus (comic author) Ptolemy n. , , , Nicomachus (mathematician) Harmonics noein – Pythagoras , non-compositionality , , , Pythagoreans and pebble mathematics Oenopides , , Pythocles Oppian orality –, –, –, , , quantifiers , –, – –, , – quipu n. Pandrosion recycling, absence of , , Pappus n. , , –, , reductio , , , , Parmenides Rips, L. J. n. Parry, M. n. , –, Ritter, J. n. Pasch axioms , , Runia, D. T. n. Peirce, C. S. , – Russell, B. , Periplous of the Red Sea Pheidias (Archimedes’ father) , Saito, K. n. , , – , Philip, J. A. , second-order discourse n. , , , , Philo of Byzantium , –, , Philolaus and first-order discourse , , , –, Philonides , , , , Philoponus Sedley, D. N. , philosophy self-regulating conventions –, , , lexicon of – –, –, , planetaria – setting out , , , –, , ; Plato , n. , , , , , , see ekthesis , Sextus Empiricus , on banausic activity , Simplicius n. on geometrical objects Simson n. lack of diagrams in Socrates , , lexicon of , nn. ff. sphaerics mathematical terminology in , starting-points – and pebble mathematics , diagram-based, –, –, , Phaedrus reference-based references to diagrams , hypothesis-based –, Republic –, implicit arguments-based –, – Timaeus intuition-based , –, Plutarch , tool-box-based, –, Poincaré, H. – Strato Polybius sumperasma , –, , ; see conclusion problems n. , , , superposition Proclus , , , symmetry –, n. , references to diagrams synonyms , –, , –, proof , , , in formulae size of – strategic vs. local – Taisbak, C. M. n. structure of – tangents –, © Cambridge University Press www.cambridge.org Cambridge University Press 0521622794 - The Shaping of Deduction in Greek Mathematics: A Study in Cognitive History Reviel Netz Index More information Index Thales , , Unguru, S. n. Theaetetus , , , Urmson, J. O. Theodorus , , , , Theophrastus , Vernant, J. P. theorems n. , , , Vidal-Naquet, P. Thrasydaeus Vitruvius , –, Thrasyllus , Thucydides Timocharis , Weitzman, K. tool-box , –, , , –, access to , – Xenophon , definition of – local n. Zeno of Elea structure of – Zenodotus toutestin – Zeuxippus © Cambridge University Press www.cambridge.org.