EUCLID OF ALEXANDRIA. - [EDITIO PRINCEPS OF THE ELEMENTS ...

STOICHEION BIBL. IE' EK TON THEONOS SYNOUSION. Eis tou autou to proton, exegematon Proklou bibl. d. (Greek). (Elementa geometriae). 1533.

      Basel, Johannes Herwegen, 1533. Folio. (323x220 mm). Cont. full blind-tooled calf with a broad border of ornamental rolls with corner-pieces, inside which an oblique blind-tooled parallelogram and a rectangular tooled decoration, also with corner-pieces. Professionally rebacked in old style, w. seven raised bands blindstamped ornamentations to all compartments. Corners professionally and neatly restored. (12), 268; 115, (1) pp. incl. last page with large woodcut printer's device. Numerous woodcut diagrams in the text. The last page of Grynaeus' foreword with a half-page note on Euclid, Proclus and Grynaeus in 18th century hand. One contemporary marginal note. First 3 leaves with faint finger-soiling to lower right corner. The text framed throughout by a decorative but faint ink-border. Verso of title-page with 2 small stamps. Title with woodcut printer's device. The first text-page framed with a broad woodcut border, many smaller and larger woodcut initials throughout. Internally a very fine and clean copy w. wide margins. ¶ The monumental first edition of the Greek text of The Elements. This EDITIO PRINCEPS of the original text was edited by Simon Grynaeus, professor of Greek at the University of Basle, and as such the work served as the foundation for the many later editions of The Elements. It also contains the famous commentary by PROCLUS (C. 412-485) on the first Book of The Elements, here printed for the first time! (The commentary takes up the second part of the book, pp. 1-115, and in the mathematical literature it is called the "Herwagiana", after the printer). The commentary contains historical information on ancient Greek philosophy, mathematics and geometry, not found elsewhere, and it is the first criticism of Euclid to question the "Parallel-axiom", -hereby paving the road to "NON-EUCLIDEAN GEOMETRY". "The most famous source of Greek geometry is the monumental work of Euclid of Alexandria, called the "Elements" (around 300 B.C.). No other book of science had a comparable influence on the intellectual development of mankind. It was a treatise of geometry in thirteen books which included all the fundamental results of scientific geometry up to his time. Euclid did not claim for himself any particular discovery, he was merely a compiler. Yet, in view of the systematic arrangement of the subject matter and the exact logical procedure followed, we cannot doubt that he himself provided a large body of specific formulations and specific auxiliary theorems in his deductions. It is no longer possible to pass judgement on the authorship of much of this material; his book was meant as a textbook of geometry which paid attention to the material, while questions of priority did not enter the discussion" (Cornelius Lanczos in "Space through the Ages"). PROCLUS was the first commentator to be very explicit about his objection to the Parallel axiom, as he refused to count it among the postulates. To justify his opinion he remarks that the converse (the sum of two angles is less than that of two right angles), is one of the theorems proved by Euclid (Book I. Prop. 17), and he thinks it impossible that a theorem, the converse of which can be proved, is not itself capable of proof. He says: "This (postulate) ought even to be struck out of the postulates altogether; for it is a theorem involving many difficulties, which Ptolemy, in a certain book, set himself to solve, and it requires for the demonstration of it a number of definitions as well as theorems, and the converse of it is actually proved by Euclid himself as a theorem." - Proclus' proof, taking up another axiom, was essentially correct, but he substituted one questionable axiom for another. (Se Bonola: Non-Euclidean Geometry).Riccardi 1533.1 - Thomas-Stanford No 7 - Max Steck III:29. - Adams E 980. - Dibdin I:519. - As to Proclus: Stillwell No 210.