The Evolution of the Euclidean Elements: A Study of the Theory of Incommensurable Magnitudes and Its Significance for Early Greek Geometry (Synthese Historical Library)

W. R. Knorr

ISBN 10: 9027705097 / ISBN 13: 9789027705099

Published by Springer-Verlag Publishing, 1974

About this Item

Very Good+ in a Very Good+ dust jacket; Hardcover; Dust jacket is clean and intact with no tears, and has not been price-clipped (Now fitted with a new, Brodart jacket protector); Unmarked boards with "straight" edge-corners; The textblock edges are unblemished; The endpapers and all text pages are bright and unmarked; The binding is tight with a straight spine; This book will be shipped in a sturdy cardboard box with foam padding; Medium Format (8.5" - 9.75" tall); Dark brown and white jacket with title in black lettering; 1974, Springer-Verlag Publishing; 379 pages; "The Evolution of the Euclidean Elements: A Study of the Theory of Incommensurable Magnitudes and Its Significance for Early Greek Geometry (Synthese Historical Library)," by W. R. Knorr.

Seller Inventory # SKU-0514AI02503222

Bibliographic Details

• Title: The Evolution of the Euclidean Elements: A Study of the Theory of Incommensurable Magnitudes and Its Significance for Early Greek Geometry (Synthese Historical Library)
• Publisher: Springer-Verlag Publishing
• Publication Date: 1974
• Language: English
• ISBN 10: 9027705097
• ISBN 13: 9789027705099
• Binding: Hardcover
• Condition: Very Good

About this title

Synopsis

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.