Weights of Pyramids on Equal Bases
Weight follows the base, and equal bases within parallels weigh alike
Leonardo relates the weight of pyramids (triangular figures) to their bases and heights. Among pyramids of equal height, the proportion of weight equals the proportion of the bases; pyramids of various lengths on an equal base weigh in proportion to those lengths, while those of equal base enclosed within parallels weigh alike. The leaf carries a row of three triangles between parallel lines, a pair of tall and slender triangles at the right, and two triangles sharing a base inside a rectangle.
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Among pyramids of equal height, weight follows the base
For pyramids of equal height, the proportion of their weight is the same as the proportion of their bases. A wider base carries proportionally more weight.
Equal bases within parallels weigh alike
Pyramids of various lengths raised upon an equal base have weights proportioned to their several lengths. But pyramids of equal base enclosed within a parallel, though of differing lengths, will all be of equal weight.
Triangles compared between parallels and within a rectangle
Three triangles of differing bases are drawn standing between two parallel lines, and two triangles sharing one base are enclosed within a rectangle. A tall triangle and a slender lozenge-like pair are set at the right for comparison of length and base.