# Pappus' theorem

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## 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 if

*A*,*B*, and*C*are collinear points and*A*′,*B*′ and*C*′ are also collinear points, then the intersection of*AB*′ with*A*′*B*, the intersection of*AC*′ with*A*′*C*, and the intersection of*BC*′ with*B*′*C*are collinear.A theorem of projective geometry which states that if

*A*,*B*,*C*, and*D*are fixed points on a conic and*P*is a variable point on the same conic, then the product of the perpendiculars from*P*to*AB*and*CD*divided by the product of the perpendiculars from*P*to*AD*and*BC*is constant.McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.

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