Cutting Many Lines in a Given Proportion
Three guiding lines from a point n divide any parallels in the same ratio
Leonardo sets out to cut any number of lines in the same ratio as a given line a b that has already been divided at c, whatever that ratio may be, rational or irrational. His device is a fan of three straight lines drawn from a single point n: two run through the ends of a b and the third through the division c, so that every line falling between the two outer parallels is cut in the same proportion. Above the construction the sheet shows tall pyramids over a base line with a small boxed cube at upper right, echoing the caption's three variously arranged pyramids.
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Cutting infinitely many lines in one proportion
The stated aim is to cut an unlimited number of lines in the same proportion as a given line, itself already cut in a given proportion. Leonardo insists the method holds whether the ratio is rational or irrational.
Three lines from point n as a proportional divider
The given line a b is cut at c into two parts. From a point n he draws three indefinite straight lines n K, n L and n m; two pass through the ends of a b and the third through the division c. Any line lying between the two outer equidistant lines is then cut in the same proportion in which a b was cut at c.
Pyramids drawn above the construction
The upper half of the page carries tall pyramids set over a base line, with a small boxed cube at the upper right. The drawing matches the caption's three pyramids variously arranged.