Euclid, Elements
Thomas L. Heath, Sir Thomas Little Heath, Ed.

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Proposition 41.

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If a parallelogram have the same base with a triangle and be in the same parallels, the parallelogram is double of the triangle.

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For let the parallelogram ABCD have the same base BC with the triangle EBC, and let it be in the same parallels BC, AE;

I say that the parallelogram ABCD is double of the triangle BEC.

For let AC be joined.

Then the triangle ABC is equal to the triangle EBC; for it is on the same base BC with it and in the same parallels BC, AE. [I. 37]

But the parallelogram ABCD is double of the triangle ABC;

for the diameter AC bisects it; [I. 34] so that the parallelogram ABCD is also double of the triangle EBC.

Therefore etc.

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Q. E. D.