Triangles of equal height and equal-area parallelograms
Pairs of triangles between parallels, then a triangle equal in area to a parallelogram
Leonardo runs through a series of triangle pairs set between parallels: first two similar triangles 'positioned equally, directed to the same side,' then pairs of equal height with their apices joined, and six further variants before he writes 'Concluded.' Under the heading 'Parallelogram,' two parallelograms are each capped by a triangle of the same height standing on the base; drawing the parallelogram's diagonal yields a triangle equal in area to it. The sheet gathers the standard results about equal-area figures lying between the same parallels.
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Similar triangles between two parallels
Two similar triangles stand between two parallels, one based on the lower line and reaching the upper, the other the reverse. They are described as 'positioned equally, directed to the same side,' then redrawn both resting on a single horizontal line.
Triangle pairs with conjoined apices
Further pairs of similar triangles, equal in height, are drawn with their apices joined; a note 'by the adversary' frames a dialectical step, and after six more variants Leonardo writes 'Concluded.'
A triangle equal in area to a parallelogram
Under the heading 'Parallelogram,' each of two parallelograms carries a triangle of the same height on its base; the diagonal of the parallelogram produces a triangle of the same area as the figure itself.
