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 AB, the intersection of AC ′ with AC, and the intersection of BC ′ with BC 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.
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References in periodicals archive ?
The proof is the same as we have to apply Pappus' Theorem to the triads of collinear points P, T, V and K, Q, U.
The teacher can direct students to Pappus' Theorem, and the second proof shown.
According to Pappus' Theorem it follows that the points T=AN [intersection] CR, K=R[V.
Now it is enough to apply Pappus' Theorem to the triads of collinear points (A, R, [U.
Now it is enough to apply Pappus' Theorem to the triads of collinear points (A, R, U) and (C, N, V) to prove that the points T, K, D are collinear.