Ducats(?) 1020 / 86 / 12 / 172 86 / 1032 / 86 · 34 · 30 / 10 / 00 (²² 86(⁰ / 1020 / (1⁷²(1⁷² / 86 13 / 30 3⁴² / (18⁹² / (1²²(⁸⁶ / (⁶⁰ 90 / 16 / (9⁸² / (9⁶⁰ / 516 86 / 1376 / 258 86 / 120 90 / 1118 1020.

18 / 18 / 144 / 18 / 324 / 100 / 000 / 000 / 32400.

M…sto / …ello / re…ffe mane. (fragmentary, largely illegible words)

The movements are 23, and although they are of like office — that is, of doing violence to whatever opposes their courses — nonetheless they are not of one and the same nature, because the one is accidental and the other natural: the accidental, the more it moves away from its cause, the weaker it becomes; the natural, in a like course, becomes more powerful. Accidental is that which goes either upward or crosswise; natural is that in which the weight falls from high to low.

That natural movement is faster which weighs more. That accidental movement is faster which has a more powerful cause.

m — o n; m — c; r t S — n.

Proof why the wall falls toward the blow of the ball. The blow of the ball o, because it falls between equal angles where it gives the blow at the point c — there, if the ball passes inside a part of its roundness, that roundness pushes and exerts its forces between equal angles. Therefore take from its centre lines that are directed to the confines of that ball which enters into the wall, then follow them as far as m n, and you will find that, by their widening, if the entry of the ball is 1/3 of a braccio, m n makes a great increase and widening of the joints; whence for this cause it is fitting that the wall fall toward the blow.

Why does this ball m weigh more on the side above the blow than below the blow? The greater part gives no blow, and therefore the blow bears little fruit, because, that greater weight finding itself without support, it goes seeking it, and in such office it cannot exert itself without turning. Every blow desires to make its stroke between equal angles, and that blow which falls between less conformable angles makes a lesser stroke, like the ball m; and falling between the acute and the obtuse angle, it will flee by the obtuse and will give less blow, for two reasons: first, that the wall makes itself thicker to it, as appears in S c; the second is that the ball strikes a minimal part of the lower part, and the blow has a likeness to a cart-wheel turning up along the wall, and it cannot attach itself there, and from that blow until its rest it always goes turning through the air.

t v — f o — n — m — p — r q λ X. This is good for measuring towers and bell-towers and other short distances. If you wish to measure quickly any height and distance, do thus. Take a square of one braccio to a side and set it edgewise between your eye and the thing you wish to know, beginning first from the angle f to learn how far it is from q to x; and as much as o n enters into n q, so much your instrument enters into q x. Having made the measure of the plane q x, and wishing to make the height v x, set your eye below at the angle r and look at the summit v and mind your square, and as much as n p enters into p q, so much your square enters into v x exactly. And know that whenever the height t λ is as great as the distance λ q, the intersection will be at the height of the square at the point m, and as much as o m enters into m q, so much t λ enters into λ q. And if you wish to know the line m r, by as much as it is greater than r q — better said, by as much as t r is greater than r λ — so much greater is m r than q r exactly.