Triangles of equal height are proportional to their bases
An isosceles triangle split by its altitude into a b d and a d c
This page states the companion theorem: triangles of equal height have the same ratio to one another as their bases. Leonardo takes an isosceles triangle a b c split by its altitude a d into a b d and a d c, which, having equal heights and equal bases, are necessarily equal; and if base b c is double base b d, the corresponding triangle is double as well. The diagram shows a symmetrical (isosceles) triangle bisected by a vertical altitude from apex a to base point d, labelled b, d, c along the base.
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Triangles of equal height proportional to their bases
In triangles of equal height the same proportion holds as that of their bases. The isosceles triangle is divided by its altitude a d into a b d and a d c; with equal heights and equal bases these are of necessity equal, and if base b c is double base b d the triangle on b c is double the triangle on b d.
Ratio of areas equals ratio of bases
Where heights are equal, the ratio between two triangles equals the ratio between their bases. Doubling base b c over base b d doubles the corresponding area.