Parallelograms on equal bases between parallels are equal
A proof by taking away and adding equal triangles
The page states and proves that all parallelograms made on equal bases between parallel lines are equal to one another. Working from the figure lettered g a b e f, n, h c d, Leonardo shows that parallelogram a b c d and parallelogram c d e f, on the same base between the parallels g f h d, are equal. His demonstration takes the common triangle e n b from the two triangles f d b and e c a, then adds back the triangle n c d, using the principle that equals taken from or added to equals remain equal. A marginal numeral 361 also appears.
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Theorem: parallelograms on equal bases between parallels
All parallelograms made on equal bases and between equidistant (parallel) lines are equal to one another. Hence parallelogram a b c d and parallelogram c d e f, sharing a base between the parallels g f h d, are equal.
Proof by subtracting and adding equal triangles
From the triangles f d b and e c a Leonardo removes the common triangle e n b, leaving the parallelogram a b n c and the equal figure e f n d. Adding the triangle n c d to each, and since equals added to equals stay equal, the two parallelograms are proved equal.