Completing the Proportional Slab with the Judicial Lines
Reading the length, width and thickness of the slab off the proportional lines K L, K v, K h
This page completes the construction begun opposite. The "judicial" proportional lines K L, K v, K h are drawn through the three terms i g x that divide the proportion of n from m, and the given lines a, b, c are laid against them to read off, in turn, the length (L v, giving S), the width (o), and the thickness (q) of the required slab. Leonardo concludes that a slab has been made whose length, width, and thickness are proportioned to those of the three given lines a b c, and so the task is done. The sheet is entirely text, with no diagrams.
On this page
The judicial proportional lines K L, K v, K h
The judicial lines of proportionality K L, K v, K h are drawn to pass through the three terms i g x, which divide the two parts of the proportion of n from m. Line a is then placed where it falls exactly among the three, at v h, so that L v has to v h the same proportion as cylinder m has to cube n, giving the length of the slab.
Reading off length, width and thickness of the slab
Line b is laid among the judicial lines at p to give the width o of the slab's length S, and line c is laid at r, with q behind it showing the thickness. Thus a slab is made with length, width, and thickness proportioned to the three given lines a b c, and the work is complete.