Cones in a cube, squaring the circle, and weights on planes
Solids inscribed in a cube, cylinder and prism; the circle's area; gravity, inclined planes and the balance
The upper half of the folio treats solid geometry: the largest cone drawn from a cube is one third of it, with related claims about the lateral surfaces of a cylinder and prism, illustrated by cones and a pyramid inscribed in a cube, a cylinder and a parallelepiped. A note gives the area of the circle as half its diameter multiplied by half its circumference, under the heading 'On squaring.' The lower half turns to mechanics: a margin note 'Gravity,' weights on inclined planes labelled d c e - a - b, and a discussion of the balance in which the arms c e and c d differ fourfold. Diagrams of the solids, an inclined plane and a balance run down the right margin.
On this page
Cones and a pyramid inscribed in a cube, cylinder and prism
The greatest cone that can be drawn from a cube is one third (subtriple) of the whole cube, and the cube's lateral surface is double that of the cone; the same is said of any cylinder, faceted or not. Leonardo cautions that the cone's hypotenuse should not equal the cylinder's height, so the cylinder is smaller than that hypotenuse.
The area of the circle
Under the heading 'On squaring,' Leonardo states that the circle is equal to a quadrilateral formed from half the diameter of the circle multiplied by half its circumference.
Weights on inclined planes
Beside a margin note reading 'Gravity,' a diagram shows weights resting on inclined planes with the points labelled d c e - a - b. It sets up the analysis of how position on a slope bears on a weight's heaviness.
The balance with unequal arms
In the main column Leonardo reports an adversary's conclusion that, among equal weights, the one whose centre lies nearer the balance's centre appears lighter than the more remote, as with arms set in a wheel but not in a straight balance, where the arms c e and c d are shown to be one quadruple the other.