PAPPUS, or PAPPOS (Let., from Gk. My roc) (c.300 A.D.). An Alexandrian mathema tician. He is said to have written on geography and astrology, to have composed a commentary on the Almoagest of Ptolemy. and to have been the head of a school. His principal work, how ever, was a mathematical Synagog,' (collection) in eight hooks. the first and half of the second of which are lost. To this work we owe inch of our knowledge of Greek mathematics, and its translation by Commandin (1583) had a power ful influence on the Renaissance of geometry in the seventeenth century. In particular, the geometry of Descartes had for one of its prin cipal objects the solution of a problem of Pappus, viz.: given 2a straight lines. to find the locus of points such that the product of the dis tances of each of these to n of the line: (or more generally of straight lines at given angles to the o lines) shall have a given ratio to the product of the distances (or lines at given angles) to the other o. Pappus was the la.t. of the great Greek
mathematicians, but the value of his work is largely due to the fact that it gives to us mine-r oil: extracts from the lost writings of his pre decessors. The most important theorem due to him is the one often called by Guldin's name, viz.: the volume of a solid of revolution is equal to the product of the area of the revolving plane figure and the length of the path of its centre of gravity. Numerous minor propositions bear his name, such as the Pythagorean theorem as generalized for an oblique-angled triangle, in which the squares on the sides are replaced by parallelograms. The text of Pappus has been edited by Hultsch (3 vols., 1s76-78, Greek and Latin).