Mathematicae Collectione. A Federico Commandino Urbinatae In Latinum Conversae, & Commentarijs Illustratae. - [THE CULMINATION OF GREEK MATHEMATICS]

Colophon: Pisauri (Pesaro), Hieronymum Concordiam, 1588. (Having the reprinted title-page: Venetiis, Franciscum de Franciscis Senemsem, 1589). Folio. Contemporary limp vellum. Repairs to upper part of spine and small nicks to back repaired. Edges of covers with tiny loss of vellum. Covers slightly soiled. Calligraphed title on back. Title-page with and old, partly erased stamp. Woodcut printer's device on title-page. Ff (3), 334 (332) (= 664 pp). Numerous woodcut diagrams and illustrations in the text. Printed on good paper. Ff. 2-3 with an old repair to inner margin (no loss). F2 browned, but otherwise remarkably clean with only a few brownspots. A few small worm-tracts to some margins. In spite of its flaws, a very good copy of this monumental work. First edition, title-issue (with the fresh title-page stating 1589, but with nothing else reprinted and otherwise through and through the 1588-printing), of Commandino's seminal Latin translation of the work that constitutes the culmination of Greek Mathematics. This printing, which contains the complete extant text of Pappos in Latin translation is responsible for reviving ancient mathematics in the Renaissance and shaping much modern mathematics, profoundly influencing the likes of Descartes and Newton. "Pappos was the greatest mathematician of the final period of ancient science, and no one emulated him in Byzantine times. He was the last mathematical giant of antiquity." (George Sarton, Ancient Science and Modern Civilization. p.82). "Pappus of Alexandria in ab. 320 composed a work with the title Collection (Synagoge) which is important for several reasons. In the first place it provides a most valuable historical record of parts of Greek Mathematics that otherwise would be unknown to us. For instance it is in Book V of the Collection that we learn of Archimedes' discovery of the thirteen semiregular polyhedra or "Archimedian solids". Then, too, the Collection includes alternative proofs and supplementary lemmas for propositions in Euclid, Archimedes, Appolonius and Ptolemy. Finally, the treatise includes new discoveries, and generalizations not found in any earlier work. The Collection, Pappus' most important treatise, contained eight Books, but the first Book and the first part of the second Book are now lost" (Boyer, A History of Mathematics p. 205). "Each book (8) is preceded by general reflexions which give to that group of problems its philosophical and historical setting. The prefaces are of deep interest to historians of mathematics and, therefore, it is a great pity that three of them are lost [.] Book VII is far the longest book of the Collection [.] [and here], we find in it the famous Pappo's problem: "given several straight lines in a plane, to find the locus point, such that when straight lines are drawn from it to the given lines at a given angle, the products of certain of the segments shall be in a given ratio to the product of the remaining ones". This problem is important in itself, but even so because it exercized Descartes' mind and caused him to invent the method of coordinates explained in his Geométrie (1637). Think of a seed lying asleep for more than thirteen centuries and then helping to produce that magnificent flowering, analytical geometry [.] The final Book VIII is mechanical and is largely derived from Heron of Alexandria. Following Heron, Pappos distinguished various parts of theoretical mechanics (geometry, arithmetic, astronomy and physics). The Book is considered the climax of Greek mechanics and helps us to realize the great variety of problems to which the Hellenistic mechanicians addressed themselves. If Book VIII is the climax of Greek mechanics, we may say as well that the whole collection is a treasury and to some extent the culmination of Greek mathematics. [.] The ideas collected or invented by Pappos did not stimulate Western mathematicians until very late, but when they finally did, they caused the birth of modern mathematics- ana.…