The Shaping of Deduction in Greek Mathematics: A Study in Cognitive HistoryCambridge University Press, 18 de set. de 2003 - 352 páginas 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. |
Conteúdo
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 | |
Termos e frases comuns
already angle Apollonius Archimedes argued argument Aristotle assertions assumed become chapter circle claim clear cognitive common completely Conics construction contained context course defined definitions described diagram discussion equal especially Euclid's Elements evidence example explain expression fact Figure Finally formulae geometrical given Greek mathematicians Greek mathematics hand immediately important instance interesting involved known language later least less letters lexicon limited logical look marked mathematicians means mentioned names natural noted object occur oral original particular perhaps philosophical possible practices probably problem proof proportion proposition proved question reason reference relations relatively repeated repetitive represent role rule second-order seen sense shape shows significant similar simply single specific square starting-points structure survey taken theory tion tool-box triangle true whole writing written τὸ
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Página 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.