A Parallelogram Is Double a Triangle on the Same Base
Proved by the diagonal a d dividing parallelogram a b c d in half
Continuing his page-by-page working through Euclid's geometry, Leonardo proves that a parallelogram is double any triangle built on the same base and between the same parallels. He draws the diagonal a d across the parallelogram a b c d, which splits it into two equal triangles, a b d and a c d. Since each triangle is half the parallelogram, the whole figure is exactly twice the triangle.
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Parallelogram a b c d is twice triangle a b d
To show that a parallelogram is double a triangle on the same base, Leonardo draws the diagonal a d in parallelogram a b c d, dividing it into two equal parts. The triangle a b d is thus equal to the triangle a c d, so triangle a b d is half of the whole parallelogram. It follows that the parallelogram a b c d is double the triangle.