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.

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.

VOLUME I.
INTRODUCTION.
FACSIMILE OF A PAGE OF THE BODLEIAN MS. OF THE ELEMENTS. Frontispiece
I. EUCLID AND THE TRADITIONS ABOUT HIM
II. EUCLID'S OTHER WORKS
III. GREEK COMMENTATORS OTHER THAN PROCLUS
IV. PROCLUS AND HIS SOURCES
V. THE TEXT
VI. THE SCHOLIA
VII. EUCLID IN ARABIA
VIII. PRINCIPAL TRANSLATIONS AND EDITIONS
IX.
1. ON THE NATURE OF ELEMENTS
2. ELEMENTS ANTERIOR TO EUCLID'S
3. "FIRST PRINCIPLES: DEFINITIONS, POSTULATES AND AXIOMS"
4. THEOREMS AND PROBLEMS
5. THE FORMAL DIVISIONS OF A PROPOSITION
6. OTHER TECHNICAL TERMS
7. THE DEFINITIONS
THE ELEMENTS.
"BOOK I. DEFINITIONS, POSTULATES, COMMON NOTIONS"
NOTES ON DEFINITIONS ETC
PROPOSITIONS
BOOK II. DEFINITIONS
NOTE ON GEOMETRICAL ALGEBRA
PROPOSITIONS
EXCURSUS I. PYTHAGORAS AND THE PYTHAGOREANS
EXCURSUS II. POPULAR NAMES FOR EUCLIDEAN PROPOSITIONS
GREEK INDEX TO VOL. I.
ENGLISH INDEX TO VOL. 1.