PAPPIIS of Alexandria, one of the later Greek geometers, of whose history g nothin is known; lie is said by Suidas to have lived during the reign of Theodosius the great, emperor of the east (379-395). Some writers are of opinion that he lived two centuries; earlier, but the former is much the more probable opinion. The chief work of Pappus is his _Mathematical Collections, of which the last six, out of eight books, are extant. The Collections, as their name implies, are an assemblage into one book of scattered problems and theorems, the work of Apollonius, Archimedes, Euclid, Theodosius, etc., to which he has joined his own discoveries. The first two books are supposed (on grounds) to have treated of arithmetic and arithmetical problems, but only a small frag ment of the second book is extant : the third book is a collection of problems, mostly of solid geometry: the fourth treats of curves other than the circle, according to the method of pure geometry; the fifth contains problems of maxima and minima: the sixth treats. of the geometry of the sphere; the seventh, which is by far the most important to mod ern geometers, as it is almost the sole authority Cve possess on the subject of the history and methods of the Greek geometrical analysis, treats principally of analysis; it also contains the proposition now known as " Guldinus's theorem," which was plagiarized from Pappus by father Goldin; the eighth and last book treats of machines. 'Pappus
was the author of several other works which are lost, excepting only a fragment of his Commentary on Four Books of Ptolemy's Syntaxis. Pappus, as an independent investiga tor, enjoys a high reputation, and is considered by Descartes as one of the most excel lent geometers of antiquity. Some of his problems have been looked upon with high interest by all succeeding geometers. The Mathematical Collections have been published in whole or part, at various periods, but the only complete editions are the two Latin versions, the first by Commandine (Pisa, 1588), and the second by Manolessius (Bologna, 1660), and the Greek edition of H. J. Eisenmann (Paris, 1824). The portion of the Greek text of the second book, which was wanting in Cornmandine's MS., was published (1688) in London by Dr. Wallis.