If a parallelogram has the same base with a triangle and is in the same parallels, then the parallelogram is double the triangle. | ||
Let the parallelogram ABCD have the same base BC with the triangle EBC, and let it be in the same parallels BC and AE.
I say that the parallelogram ABCD is double the triangle BEC. | ||
Join AC. | Post.1 | |
Then the triangle ABC equals the triangle EBC, for it is on the same base BC with it and in the same parallels BC and AE. | I.37 | |
But the parallelogram ABCD is double the triangle ABC, for the diameter AC bisects it, so that the parallelogram ABCD is also double the triangle EBC. | I.34 | |
Therefore if a parallelogram has the same base with a triangle and is in the same parallels, then the parallelogram is double the triangle. | ||
Q.E.D. |