The Thirteen Books of Euclid’s Elements (vol. 2, books III-IX)

Description

Euclid's definition of ratio in Element. (l. 5.) defins. as a "similitudo duarum proportionum " is mentioned in the context of "whether mind-independent relations themselves, precisely as such, are able to found other relations." Scotus thought so (cf. Deely's Four Ages of Understanding pp. 376-7, esp. where he summarizes, on the first full quoted ¶ on p. 377, Scotus's view: "unica requirit [Scotus] solum distinctionem inter res, quæ sunt extrema, non inter rationes fundandi.D. Thomas utrumque requirit "; cf. the Summa article "Whether there is equality in God?"); St. Thomas did not. cf. John of St. Thomas's Tractatus de Signis pp. 102 line 23ff.

Euclid:

3. A ratio (Λόγος) is a sort of relation in respect of size between two magnitudes of the same kind.
6. Let magnitudes which have the same ratio be called proportional (ἁνάλογον).

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.