**Euclid's Elements: Book I: Proposition 41**

**Proposition 41: If a parallelogram have the same base with a triangle and be in the same parallels, the parallelogram is double of the triangle.**
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.

Q.E.D.