Cutting One Regular Solid from Another
Subtracting a Platonic body so the remainder keeps the same form
Working with the five regular (Platonic) solids, Leonardo poses the problem of taking a similar body out of one of them so that the remainder keeps the same figure. He gives the pentagonal solid as an example: reduce the given and the larger pentagonal bodies each to an equivalent cube, subtract the smaller cube from the larger by the rules already given, then reshape the remaining cube back into a pentagonal body. He adds that what holds for the cube holds for every body whose vertices touch the sphere, since whatever is done in the sphere can be done in the cube. The leaf is entirely text in mirror script, with no diagram.
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Extract a similar solid, leaving the same figure
From one of the 5 regular bodies, extract a similar body such that the remainder stays in the same figure. Leonardo wants to take a given pentagonal body out of a larger pentagonal body so that what is left is still a pentagonal body, and these are to be bodies, not surfaces.
Method: cube each solid, subtract, then rebuild
Reduce the given pentagonal body to its equivalent cube, and do the same with the larger one from which the smaller is to be removed; by the earlier rules take the smaller cube out of the larger cube, then remake the pentagonal body from the remaining cube. What is said of the cube holds for all bodies whose angles touch the sphere, because whatever is done in the sphere can be done in the cube.
