The Shaping of Deduction in Greek Mathematics: A Study in Cognitive HistoryThe aim of this book is to explain the shape of Greek mathematical thinking. It can be read on three levels: as a description of the practices of Greek mathematics; as a theory of the emergence of the deductive method; and as a case-study for a general view on the history of science. The starting point for the enquiry is geometry and the lettered diagram. Reviel Netz exploits the mathematicians' practices in the construction and lettering of their diagrams, and the continuing interaction between text and diagram in their proofs, to illuminate the underlying cognitive processes. A close examination of the mathematical use of language follows, especially mathematicians' use of repeated formulae. Two crucial chapters set out to show how mathematical proofs are structured and explain why Greek mathematical practice manages to be so satisfactory. A final chapter looks into the broader historical setting of Greek mathematical practice. |
Contents
The lettered d1agram | 12 |
The pragmatics of letters | 68 |
The mathematical lexicon | 89 |
Formulae | 127 |
The shaping of necessity | 168 |
The shaping of generality | 240 |
The historical setting | 271 |
The main Greek mathematicians cited in the book | 313 |
| 316 | |
| 323 | |
Common terms and phrases
angle apodeixis Apollonius Archimedean Archimedes argued Aristotle Aristoxenus arithmetic assertions Autolycus Babylonian mathematics chapter circle cognitive Conics construction context course deduction defined definiendum definitions diorismos discussion ekthesis ellipsis ematics equal Euclid's Elements Euclidean Eudoxus Eutocius evidence explicit fact Figure formula 55 formulae geometrical Greek math Greek mathematicians Greek mathematics hapax legomena Hippocrates of Chios Homeric Homeric scholarship important instance language lettered diagram lexicon logical many-lettered names mathematical proofs mathematical texts mathematicians Mueller natural noun object formula occur oral Pappus philosophical Plato possible practices predicate formula Proclus proof proposition protasis proved ratio rectangle reference relations relatively relevant repetitive role second-order seen semantically marked sense sequence significant simply spatial specific starting-points structure subsection sumperasma survey switches theorems theory tion tool-box triangle verb word-tokens word-types words ἀπὸ καὶ πρὸς τὰ τῇ τῆς τὸ τοῦ τῶν ὡς
Popular passages
Page 11 - If a straight line be cut into equal and unequal segments, the rectangle contained by the unequal segments of the whole together with the square on the straight line between the points of section is equal to the square on the half.