The Elements of Euclid

Viz. the First Six Books, Together with the Eleventh and Twelfth. The Errors by which Theon, Or Others, Have Long Ago Vitiated These Books, are Corrected, and Some of Euclid's Demonstrations are Restored. Also the Book of Euclid's Data, in Like Manner Corrected

Author: Euclid

Publisher:

ISBN:

Category: Geometry

Page: 518

View: 895

The Thirteen Books of the Elements

Author: Euclid

Publisher: Dover Publications

ISBN:

Category: Mathematics

Page: 464

View: 820

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.

A Commentary on the First Book of Euclid's Elements

Author: Proclus

Publisher: Princeton University Press

ISBN:

Category: Philosophy

Page: 355

View: 643

In Proclus' penetrating exposition of Euclid's method's and principles, the only one of its kind extant, we are afforded a unique vantage point for understanding the structure and strenght of the Euclidean system. A primary source for the history and philosophy of mathematics, Proclus' treatise contains much priceless information about the mathematics and mathematicians of the previous seven or eight centuries that has not been preserved elsewhere.

The Thirteen Books of Euclid's Elements

Author: Thomas L. Heath

Publisher: Cambridge University Press

ISBN:

Category: History

Page: 446

View: 219

First published in 1926, this book contains the first volume of a three-volume English translation of the thirteen books of Euclid's Elements.

The thirteen books of Euclid's Elements

Author: Euclid

Publisher: Dover Pubns

ISBN:

Category: Mathematics

Page: 443

View: 342

Volume 1 of 3-volume set containing complete English text of all 13 books of the Elements plus critical apparatus analyzing each definition, postulate, and proposition in great detail. Covers textual and linguistic matters; mathematical analyses of Euclid's ideas; commentators; refutations, supports, extrapolations, reinterpretations and historical notes. Vol. 1 includes Introduction, Books 1-2: Triangles, rectangles.

Euclid's Elements

Author: Richard Fitzpatrick

Publisher: Lulu.com

ISBN:

Category: Mathematics

Page: 548

View: 754

Euclid's Elements of Geometry, with Greek and English texts in side-by-side columns.

The Evolution of the Euclidean Elements

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

Author: W.R. Knorr

Publisher: Springer Science & Business Media

ISBN:

Category: Mathematics

Page: 374

View: 870

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.

The Elements of Euclid

viz. the first six books, together with the eleventh and twelfth; and also the book of Euclid's Data

Author: Euclid

Publisher:

ISBN:

Category: Geometry

Page: 513

View: 153