The Shaping of Deduction in Greek Mathematics: A Study in Cognitive History

封面
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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內容

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
Bibliography
316
Index
323
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第 11 頁 - 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.

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