General Rule for Cutting a Wedge
Sections of a wedge (conio): the cut is one-third, and half of it one-sixth, of the whole
The page states a general rule for the section of a wedge (conio) and illustrates it with prism-shaped solids crossed by cutting lines. Having proved elsewhere that the cut d e c f is one-third of the wedge, Leonardo derives that the remainder is two-thirds and that any parallel cut from the face terminating at the angle c keeps the same proportion. A further proof shows that a cut from the middle of the face makes a part one-third of the remainder, its half being one-sixth of the whole wedge. Letter-labels a through h key the solids.
On this page
General rule of the cut
Since the cut d e c f is one-third of the wedge a b c d e f, the remainder a b c d e is two-thirds of the whole. It follows as a corollary that every cut made from the face a b d e with lines parallel to it, and ended by a straight line at the angle c, has the same proportion to those two-thirds as it has with the whole face a b d e.
A cut from the middle of the face, and its half as one-sixth
A cut from the middle of the face of the wedge, ending in one of the angles, makes the divided part one-third of the remainder, and half that part one-sixth of the whole. The base d e c is common to the two triangles d e c b and d e c h, but the second is twice as tall, so the part d e c b is half the pyramid a b d e c and equal to the sextile d e c h.