The Five Regular Bodies and the Infinite Cutting of Angles
Only five regular solids exist, while the semiregular and irregular forms are infinite
Leonardo opens this study of solid geometry with the rule that there are only five regular bodies, while the forms lying between the regular and the irregular are infinite. He explains that cutting away each solid angle exposes a small pyramidal base with as many sides as that angle had, leaving fresh solid angles that can themselves be cut without end, since continuous quantity is infinitely divisible. Three drawings accompany the note: two hatched pyramidal solids at the upper left and a fully drawn dodecahedron at the upper right.
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There are five regular bodies, but infinite intermediate ones
The regular bodies number five, but the forms partaking of both the regular and the irregular are infinite. Cutting a solid angle reveals the base of a small pyramid with as many sides as the angle had, and leaves as many new solid angles as there are sides. Because continuous quantity can be divided without end, this cutting can be repeated forever.
Drawn dodecahedron
At the upper right the sheet shows a twelve-faced solid drawn in perspective, its pentagonal faces outlined in ink. It illustrates one of the five regular bodies named in the note beside it.
Two hatched pyramidal solids
To the left of the dodecahedron stand two elongated, hatched solids resembling pyramids or cones lying on their sides. They belong to the family of pyramidal figures whose cut angles the text discusses.