Ceva's theorem

English

Etymology

Named after Italian mathematician Giovanni Ceva (1647-1734), to whom the discovery of the theorem is often attributed.

Proper noun

Ceva's theorem

(mathematics) A theorem about triangles in plane geometry, regards the ratio of the side lengths of a triangle divided by cevians.

Usage notes

In mathematical terms, the theorem states: let D, E, and F, be points on the sides BC, CA, and AB of a triangle (possibly extended). Then AD, BE, and CF are concurrent if and only if ${\\displaystyle {\\frac {AF}{FB}}\\cdot {\\frac {BD}{DC}}\\cdot {\\frac {CE}{EA}}=1.}$

单词	Ceva's theorem
释义	Ceva's theorem English Etymology Named after Italian mathematician Giovanni Ceva (1647-1734), to whom the discovery of the theorem is often attributed. Proper noun Ceva's theorem (mathematics) A theorem about triangles in plane geometry, regards the ratio of the side lengths of a triangle divided by cevians. Usage notes In mathematical terms, the theorem states: let D, E, and F, be points on the sides BC, CA, and AB of a triangle (possibly extended). Then AD, BE, and CF are concurrent if and only if ${\\displaystyle {\\frac {AF}{FB}}\\cdot {\\frac {BD}{DC}}\\cdot {\\frac {CE}{EA}}=1.}$
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