The Shaping of Deduction in Greek Mathematics: A Study in Cognitive History
Cambridge University Press, 2003年9月18日 - 352 頁
The 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.
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angle antiquity apodeixis Apollonius Archimedean Archimedes Archytas argued Aristotle Aristoxenus arithmetic assertions Autolycus Babylonian mathematics chapter circle cognitive Comics Conics context course deduction defined definiendum definitions diorismos discussion ekthesis ellipsis ematics equal Euclid's Elements Euclidean Eutocius evidence explain explicit fact Figure formula 55 formulae geometrical Greek math Greek mathematicians Greek mathematics hapax legomena Hippocrates of Chios Homeric Homeric scholarship important instance interesting language lettered diagram logical many-lettered names mathematical proofs mathematical texts mathematicians means Mueller natural noun object formula occur oral Pappus philosophical Plato possible practices predicate formula Proclus proof proposition protasis proved question 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 Töv triangle Trpès Trpós verb visual word-tokens word-types words written