Dividing a triangular "pyramid" into two equal weights
A triangle a b c d e split lengthwise into four, with its parts counted as 1, 3, 5, 7 smaller triangles.
A long triangle is drawn across the top of the page with its base divided at the points a, b, c, d, e, and the note explains how to split such a "pyramid" into two equal weights. Its length is divided into four; the quarter at the tip and the quarter at the base together weigh and measure the same as the two middle quarters. A second figure at the foot of the page shows the completed decomposition, its four sections counted as 1, 3, 5 and 7 similar right triangles, with the inner and outer pairs linked by strokes marked 8.
On this page
Divide the length of the triangle into four
To halve the figure by weight, its length is divided into four equal parts. The quarter toward the pointed tip and the quarter toward the wide base are taken together, and this pair is set against the two quarters in the middle.
Tip-and-base quarters equal the two middle quarters
Leonardo claims that the quarter near the tip joined to the quarter near the base equals in both weight and quantity the two middle quarters, so that a single common measure fits them exactly.
Sections counted as 1, 3, 5, 7
The lower figure carries the labels 1, 3, 5 and 7 over its four sections, giving the number of similar right triangles into which each strip is subdivided. Curved pen-strokes marked 8 link the inner pair and the outer pair of quarters.