Evolution of the Euclidean Elements

Name: Evolution of the Euclidean Elements
Brand: Springer
SKU: 9789027705099
Price: 378.86 EUR
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A Study of the Theory of Incommensurable Magnitudes and Its Significance for Early Greek Geometry

Autor: W.R. Knorr

Jazyk:

Väzba: Pevná

Vydavateľ: Springer

Dostupnosť: Skladom u dodávateľa

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378.86 €

The present work has three principal objectives: (1) to fix the chronology of the development of the...

Informácie o knihe

Autor

W.R. Knorr

Jazyk

Angličtina

Väzba

Kniha - Pevná

Stránok

379

EAN

9789027705099

ISBN

9027705097

Enbook ID

01970233

Vydavateľ

Springer

Hmotnosť

1580

Rozmery

155 x 235 x 22

Kompletný popis

The present work has three principal objectives: (1) to fix the chronology of the development of the pre-Euclidean theory of incommensurable magnitudes beginning from the first discoveries by fifth-century Pythago reans, advancing through the achievements of Theodorus of Cyrene, Theaetetus, Archytas and Eudoxus, and culminating in the formal theory of Elements X; (2) to correlate the stages of this developing theory with the evolution of the Elements as a whole; and (3) to establish that the high standards of rigor characteristic of this evolution were intrinsic to the mathematicians' work. In this third point, we wish to counterbalance a prevalent thesis that the impulse toward mathematical rigor was purely a response to the dialecticians' critique of foundations; on the contrary, we shall see that not until Eudoxus does there appear work which may be described as purely foundational in its intent. Through the examination of these problems, the present work will either alter or set in a new light virtually every standard thesis about the fourth-century Greek geometry. I. THE PRE-EUCLIDEAN THEORY OF INCOMMENSURABLE MAGNITUDES The Euclidean theory of incommensurable magnitudes, as preserved in Book X of the Elements, is a synthetic masterwork. Yet there are detect able seams in its structure, seams revealed both through terminology and through the historical clues provided by the neo-Platonist commentator Proclus.

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Evolution of the Euclidean Elements

A Study of the Theory of Incommensurable Magnitudes and Its Significance for Early Greek Geometry

Informácie o knihe

Kompletný popis

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