Volume of a pyramid and the doubling of the cube
Solid-geometry problems with a large machine and the fable of the spider in the lock.
The sheet works several solid-geometry problems: finding the height of a square-based pyramid from a given board, casting a wax slab into a cylinder to recover a third of it as the pyramid, transforming a parallelepiped into a cube, and making two cubes in a given proportion (a doubling-the-cube problem). Alongside run proportion series such as 1 2 4 8 and 1 3 9 27 governing the parts of a cut drawn parallel to a triangle's base. A large machine is sketched with the note that its pole a is to be moved to b, and a lower corner carries the fable of the spider that, seeking rest in the keyhole, finds death.
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Height of a square-based pyramid found through wax
Given a board of unknown sides, a pyramid is to be raised on the given square base and its height sought. Leonardo reduces a quantity of wax to a slab and cubes it, lends it twice as much wax to form a quadrilateral cylinder with a face equal to the base, then removes the two-thirds lent so that the remaining third gives the proposed pyramid.
Making two cubes in a given proportion
From a given board of unknown thickness, width and length, two cubes are to be made in a given proportion. The note is a version of the classical duplication-of-the-cube problem, and is labelled beside its diagram.
Proportion of the parts of a parallel cut
The series 1 2 4 8 and 1 3 9 27 accompany the rule that the parts of a cut drawn parallel to the base of a rectilinear triangle stand in the same proportion to the parts of the base as the whole cut does to the whole base. Each such cut is as much smaller than its base as the base is greater than the cut.
A large machine with a movable pole a to b
A large mechanism is drawn with the labelled note that the pole a is to be moved from a as far as b. It is one of several devices sketched across the sheet.
The spider in the keyhole
In the lower-left corner, beside a small sketch of a spider inside a lock, runs the fable: the spider, believing it will find rest in the hole of the key, finds death instead.