Triangles on a common base: areas as their heights
Two proportion notes and a lettered circle-and-triangle figure on 50v; 53r blank.
The left page (50v) sets down two results on proportion. The principal note observes that the base a b is common to triangles a b c and a b d, and that among triangles of equal base the ratio of their areas equals the ratio of their heights. A second line states that the proportion b c to b a is the same as c f to a e. A lettered figure of a circle crossed by triangular construction lines accompanies the text, while the facing page 53r is blank.
On this page
Triangles of equal base compared by their heights
The base a b is shared by triangle a b c and triangle a b d. Leonardo states the general rule that triangles standing on equal bases are in the same proportion to one another as their heights. A lettered circle-and-triangle diagram illustrates the construction.
Proportion b c : b a equals c f : a e
A separate note records a proportion between line segments: the ratio that b c has to b a is the same as the ratio c f has to a e.