Pappus' theorem

Pappus' theorem [′pap·əs ‚thir·əm]

(mathematics)

The proposition that the area of a surface of revolution generated by rotating a plane curve about an axis in its own plane which does not intersect it is equal to the length of the curve multiplied by the length of the path of its centroid.

The proposition that the volume of a solid of revolution generated by rotating a plane area about an axis in its own plane which does not intersect it is equal to the area multiplied by the length of the path of its centroid.

A theorem of projective geometry which states that ifA,B, andCare collinear points andA′,B′ andC′ are also collinear points, then the intersection ofAB′ withA′B, the intersection ofAC′ withA′C, and the intersection ofBC′ withB′Care collinear.

A theorem of projective geometry which states that ifA,B,C, andDare fixed points on a conic andPis a variable point on the same conic, then the product of the perpendiculars fromPtoABandCDdivided by the product of the perpendiculars fromPtoADandBCis constant.