Evolution of the Euclidean Elements

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

Autor: W.R. Knorr

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Oprawa: Twarda

Wydawca: Springer

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

Informacje o książce

Autor

W.R. Knorr

Język

Angielski

Oprawa

Książka - Twarda

strony

379

EAN

9789027705099

ISBN

9027705097

Enbook ID

01970233

Wydawca

Springer

Waga

1580

Wymiary

155 x 235 x 22

Pełny opis

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

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