## Mathematicae collectiones [Books III- VIII] a Federico Commandino... in latinum conversae et commentariis illustratae

FIRST EDITION of arguably the most important source book for the works of the Greek mathematicians. The magnificent Horblit copy in contemporary (probably original) boards.

Pappus of Alexandria , (fl 320AD) was "the most important mathematical author writing in Greek during the later Roman Empire, known for his *Synagoge* (“Collection”), a voluminous account of the most important work done in ancient Greek mathematics... Pappus seldom claimed to present original discoveries, but he had an eye for interesting material in his predecessors’ writings, many of which have not survived outside of his work. As a source of information concerning the history of Greek mathematics, he has few rivals."

Pappus's principal work "was the *Synagoge* (c. 340), a composition in at least eight books (corresponding to the individual rolls of papyrus on which it was originally written). The only Greek copy of the *Synagoge* to pass through the Middle Ages lost several pages at both the beginning and the end; thus, only Books 3 through 7 and portions of Books 2 and 8 have survived. A complete version of Book 8 does survive, however, in an Arabic translation. Book 1 is entirely lost, along with information on its contents... Such a range of topics is covered that the *Synagoge* has with some justice been described as a mathematical encyclopedia.

"The *Synagoge* deals with an astonishing range of mathematical topics; its richest parts, however, concern geometry and draw on works from the 3rd century BC, the so-called Golden Age of Greek mathematics... The longest part of the *Synagoge*, Book 7, is Pappus’s commentary on a group of geometry books by Euclid, Apollo Eratosthenes of Cyrene, and Aristaeus, collectively referred to as the “Treasury of Analysis.” “Analysis” was a method used in Greek geometry for establishing the possibility of constructing a particular geometric object from a set of given objects. The analytic proof involved demonstrating a relationship between the sought object and the given ones such that one was assured of the existence of a sequence of basic constructions leading from the known to the unknown, rather as in algebra. The books of the “Treasury,” according to Pappus, provided the equipment for performing analysis. With three exceptions the books are lost, and hence the information that Pappus gives concerning them is invaluable.

"Pappus’s *Synagoge* first became widely known among European mathematicians after 1588, when a posthumous Latin translation by Federico Commandino was printed in Italy. For more than a century afterward, Pappus’s accounts of geometric principles and methods stimulated new mathematical research, and his influence is conspicuous in the work of René Descartes (1596–1650), Pierre de Fermat (1601–1665), and Isaac Newton (1642 [Old Style]–1727), among many others. As late as the 19th century, his commentary on Euclid’s lost Porisms in Book 7 was a subject of living interest for Jean-Victor Poncelet (1788–1867) and Michel Chasles (1793–1880) in their development of projective geometry" (*Britannica*).

*Provenance*: Harrison D. Horblit, with his bookplate on front pastedown.

Pesaro: Girolamo Concordia, 1588.
Folio (315x220mm), contemporary (probably original) boards; old paper spine label and ink "Pappus" written on spine; "Pappi Alexandrini" written neatly on bottom edge. Soiling and light wear to boards. Early cross-out of early signature on title, very light marginal dampstaining to a few early gatherings. An outstanding copy with exceptionally wide margins.

Price: $22,000 .