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Books > Humanities > Philosophy > Western philosophy > Ancient Western philosophy to c 500
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The Evolution of the Euclidean Elements - A Study of the Theory of Incommensurable Magnitudes and Its Significance for Early Greek Geometry (Paperback, Softcover reprint of the original 1st ed. 1975)
Loot Price: R10,980
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The Evolution of the Euclidean Elements - A Study of the Theory of Incommensurable Magnitudes and Its Significance for Early Greek Geometry (Paperback, Softcover reprint of the original 1st ed. 1975)
Series: Synthese Historical Library, 15
Expected to ship within 10 - 15 working days
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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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