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The Thirteen Books of the Elements, Vol. 1: Books 1-2
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About The Thirteen Books Of The Elements, Vol. 1: Books 1-2
Product Description This is the definitive edition of one of the very greatest classics of all time — the full Euclid, not an abridgement. Using the text established by Heiberg, Sir Thomas Heath encompasses almost 2,500 years of mathematical and historical study upon Euclid. This unabridged republication of the original enlarged edition contains the complete English text of all 13 books of the Elements, plus a critical apparatus that analyzes each definition, postulate, and proposition in great detail. It covers textual and linguistic matters; mathematical analyses of Euclid’s ideas; classical, medieval, Renaissance, modern commentators; refutations, supports, extrapolations, reinterpretations, and historical notes, all given with extensive quotes. “The textbook that shall really replace Euclid has not yet been written and probably never will be.” — Encyclopaedia Britannica. Volume 1. 151-page Introduction: life and other works of Euclid; Greek and Islamic commentators; surviving mss., scholia, translations; bases of Euclid’s thought. Books I and II of the Elements, straight lines, angles, intersection of lines, triangles, parallelograms, etc. Volume 2. Books III-IX: Circles, tangents, segments, figures described around and within circles, rations, proportions, magnitudes, polygons, prime numbers, products, plane and solid numbers, series of rations, etc. Volume 3. Books X to XIII: planes, solid angles, etc.; method of exhaustion in similar polygons within circles, pyramids, cones, cylinders, spheres, etc. Appendix: Books XIV, XV, sometimes ascribed to Euclid. Excerpt. © Reprinted by permission. All rights reserved. The Thirteen Books of Euclid's Elements Volume I By Thomas L. Heath Dover Publications, Inc.Copyright © 1956 Dover Publications, Inc. All rights reserved. ISBN: 978-0-486-60088-8 Contents VOLUME I., INTRODUCTION., Chap. I. Euclid and the traditions about him, Chap. II. Euclid's other works, Chap. III. Greek commentators other than Proclus, Chap. IV. Proclus and his sources, Chap. V. The Text, Chap. VI. The Scholia, Chap. VII. Euclid in Arabia, Chap. VIII. Principal Translations and Editions, Chap. IX. §1. On the nature of elements, The Elements., Book I. Definitions, Postulates, Common Notions, Book II. Definitions, Excursus I. Pythagoras and the Pythagoreans, Excursus II. Popular names for Euclidean Propositions, Greek Index to Vol. I., English Index to Vol. I., CHAPTER 1 EUCLID AND THE TRADITIONS ABOUT HIM. As in the case of the other great mathematicians of Greece, so in Euclid's case, we have only the most meagre particulars of the life and personality of the man. Most of what we have is contained in the passage of Proclus' summary relating to him, which is as follows: "Not much younger than these (sc. Hermotimus of Colophon and Philippus of Medma) is Euclid, who put together the Elements, collecting many of Eudoxus' theorems, perfecting many of Theaetetus', and also bringing to irrefragable demonstration the things which were only somewhat loosely proved by his predecessors. This man lived in the time of the first Ptolemy. For Archimedes, who came immediately after the first (Ptolemy), makes mention of Euclid: and, further, they say that Ptolemy once asked him if there was in geometry any shorter way than that of the elements, and he answered that there was no royal road to geometry. He is then younger than the pupils of Plato but older than Eratosthenes and Archimedes; for the latter were contemporary with one another, as Eratosthenes somewhere says." This passage shows that even Proclus had no direct knowledge of Euclid's birthplace or of the date of his birth or death. He proceeds by inference. Since Archimedes lived just after the first Ptolemy, and Archimedes mentions Euclid, while there is an anecdote about some Ptolemy and Euclid, therefore Euclid lived in the time of the first Ptolemy. We may infer then from Proclus that Euclid was intermediate between the first pupils of Plato and Archimedes. N
