“Pappus’ Centroid Theorems”的概念、定义、翻译、参考文献-科学参考

Pappus’ Centroid Theorems

Mathematics

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.

单词	Pappus’ Centroid Theorems
释义	Pappus’ Centroid Theorems Mathematics 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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First TheoremSuppose 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.