Mean Proportionals by Similar Triangles
A circle with inscribed triangles finds two means between the lines 1 and 8
Continuing the doubling-of-the-cube study, Leonardo takes two given lines, 1 and 8, and constructs two mean proportionals between them using a large circle with inscribed right triangles. He finds the means to be 4 and 2, so that 8:4 = 2:1, and shows the triangles b c f and d f e to be proportional in the whole and in their corresponding sides. The paragraph breaks off mid-sentence, and further mirror-script text continues above the diagram.
On this page
Two mean proportionals between the lines 1 and 8
Given two lines, 1 and 8, in d f and f b, two other mean lines proportional to these are found, b c being 4 and d e being 2. The construction is carried out on a circle with two large inscribed triangles meeting along the vertical diameter.
Proportional triangles b c f and d f e
b f, 8, has the same proportion to b c, 4, as d e, 2, has to d f, 1. This is because the two triangles b c f and d f e are proportional in the whole and in their corresponding sides.