Multiplying an Unknown Line by the Rule of Three
Rule-of-three worked on a tapering pyramid, in braccia of base and length
On this page Leonardo explains how to multiply an unknown line by the rule of three, applied to a tapering pyramid drawn hatched at the upper right. If a pyramid 2 braccia long widens by one braccio, then over 7 braccia of length it will widen by 3 and a half; he then poses the same problem 'blind,' reasoning only from the base and length of the pyramid. A long cross-hatched pyramid (cone) and a smaller triangle carry the proportional figures used in the calculation, the rest of the sheet being left blank.
On this page
Multiplying an unknown line by the rule of three
Leonardo multiplies an unknown line by the rule of three using a tapering pyramid: if in 2 braccia of pyramid it widens by one braccio, in 7 braccia of length it will widen by 3 and a half. He then poses the same reasoning worked 'blind,' knowing neither length nor width but only how much base corresponds to how much length.
Hatched pyramid and proportional figures
At the upper right a long hatched pyramid and a smaller triangle bear the proportional figures used in the rule-of-three calculation, laid out beside the tapering form.