Cutting from a larger triangle an area equal to a smaller one
Using two equal circular sectors, a sixteenth and an eighth of their circles
Leonardo sets out to cut off from a larger triangle a part exactly equal to a smaller triangle, so that the smaller fits entirely inside the larger. He works with two equal circular sectors, one a sixteenth of the larger circle (a b c) and the other an eighth of the smaller (d e f), taking half-portions and drawing the equidistant line L K over base h c. The top of the page shows two fan-shaped circle sectors with lines radiating to form triangles, labelled a, i, and L on the left and d, e, f, K on the right.
On this page
Equalising triangles through circular sectors
The aim is to cut from a larger triangle a part equal to a smaller triangle so the smaller enters entirely into the larger. Two equal sectors are used, a b c a sixteenth of the larger circle and d e f an eighth of the smaller; by taking the half-portion d g e and drawing the equidistant L K over base h c, Leonardo shows the triangle K h c equal to h i c.
Sectors as a sixteenth and an eighth of their circles
The two sectors stand in a doubled ratio, one being 1/16 of the larger circle and the other 1/8 of the smaller, while remaining equal in size to each other. Half of one portion is set against half of the other to make the areas match.