'Nothing', percussion, and the centre of gravity of a semicircle
Why point, line and surface occupy nothing; the force of impact; balancing a half-disc
An opening dominated by Leonardo's geometry of boundaries: since the surface, line and point are only the limits of a body and not parts of it, they occupy nothing, so that part equals whole and the finite equals the infinite. Between these arguments he sets two mechanical notes, one asking why a blow is more powerful a little farther from its mover than close to it, the other describing how to find the centre of gravity of a semicircle f g b by suspending it until f g hangs perpendicular and testing the third-point t with a balance. Geometric figures of circles with inscribed triangles, semicircles and arches fill the upper sheet, alongside further untranscribed mechanical sketches including a wheel and vessel at the upper left.
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Surface, line and point occupy nothing
That is said to be nothing which partakes of nothing; therefore the surface, line and point is nothing, because it is not part of its whole and occupies nothing of it. All things that occupy nothing are equal among themselves and all together equal to one, so that here the part is equal to the whole and the whole to the part, the divisible to the indivisible, the finite to the infinite.
Why a blow is stronger a little away from its mover
For what cause is percussion somewhat more powerful more remote from its mover than when it is near. This is known, that a projectile at every degree of motion acquires degrees of weakness, and its impetus grows through the wave of air that flees before it.
Centre of gravity of a semicircle f g b, found with a balance
Once the semicircle f g b is suspended so that the line f g hangs perpendicular, subtract its larger triangle f g b and give the centre of gravity to the third at t; with the balance rule you learn whether t lies a half-space in from n. Better, take the third of side b f, attach one pendant of the balance, then the second, and the pole of the balance will be the centre of gravity of that half-ball.
Two triangles on a common base are equal (a m n, a f n)
The two portions a m n and a f n have the two triangles a m n and a f n equal, being on a common base. The margin returns to boundaries: the limit of one body is the beginning of another, so limits are no part of the bodies and, occupying nothing, are themselves nothing.