单词

Pappus of Alexandria

释义

Pappus of Alexandria

(about ad 320) Considered to be the last great ancient Greek geometer. He wrote commentaries on Euclid and Ptolemy, but most valuable is his Synagoge (‘Collection'), which contains detailed accounts of much Greek mathematics, some of which would otherwise be unknown.

Pappus' Centroid Theorems First Theorem Suppose that an arc of a plane curve is rotated through one revolution about a line in the plane that does not cut the arc. Then the area of the surface of revolution obtained is equal to the length of the arc times the distance travelled by the centroid of the curve.

Second Theorem

Suppose that a plane region is rotated through one revolution about a line in the plane that does not cut the region. Then the volume of the solid of revolution obtained is equal to the area of the region times the distance travelled by the centroid of the region.

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