They say a point is that which cannot be divided into any part.

They say a line is made by drawing the point out at length. Thus the length of the line will be divisible, but its breadth will be wholly indivisible. They say a surface is as if you extend the breadth of the line, whereby its length and also its breadth may be divided, but there will be no depth to it.

But they affirm a body to be that whose length and breadth and depth is divisible. I call a body that which is covered by the surface under aspect 1) and can be seen by light.

I call the surface of the body its outermost skin, which defines the form of the body and its edge. I call the edge of each seen surface the outermost circuit, of which the termination is the division.

Example of how force is of brief life.

Of little life, because it soon undoes itself, as appears in the bow, which if it stays too long drawn with force, there the force little by little dies out, and in the end the bow remains bent without any force. That body which by accident stays more drawn from its usual state will be capable of greater force, as happens with the bow: the more it is opened, the more it drives the arrow.

That body will maintain its accidental transformation longer where the force will consume itself by itself, as happens in a hoop for casks 2).

Of the bombard.

If the ball of a bombard were to strike another like ball which was resting against a wall, I say that, being of like stone, one will break in like manner to the other, and the blow being spent in it will do no harm to the wall. But if the stone that awaits 3) the blow be walled in among the others, I say that the violence that had to break the one that awaits and to save the neighbours entirely, this will not break it and will not save the neighbours, but rather the said violence goes distributing itself among them.

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1. That weight whose length exceeds its thickness must give of itself equal load to the supports at its 2 extremities, when the said extremities are equidistant from the centre.

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3. But if this weight be at unequal distance from the said centre, that part which comes nearer to it gives more load, and the higher part becomes lighter.

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2. But when it is in a perpendicular line, the contact of the lower extremity receives upon itself the whole weight of that body, and the upper weighs nothing on its opposite contact. Thus, if in the first proposition the said weight is shown to distribute itself in equal load to its 2 extreme contacts, and likewise in the second one receives all and the upper nothing, it follows that the third partakes of the 2 extremities, neither lying nor upright; that is, if the said body be 8 braccia and 8 braccia, 4) I say that, when it lies flat, the contacts of the 2 ends have 4 each, and when it stands by a perpendicular line, one contact has 80 and the other nothing; whence it follows that the one that is by an oblique line, partaking of the 2 extremes, gives to the lower contact a weight that is midway between 40 and 80, which is 60. Thus the low contact has 60 and the other [2]0.

: c b – e – f – d a – M z n g m

Naturally every heavy thing desires to fall to the centre, and that thing which falls by a less oblique line more quickly fulfils its desire; and that obstacle which shall oppose its course will render to its base more or less of the sum of the said weight according as it is found wholly in the whole line of the course of the said [weight]. 5)

Example.

If you raise on high one of the 2 extremities of the column [a] b, I say that its top would desire to fall to the point g, but the firmness of the base and the strength of the column, not consenting to it because of its unity, constrain the point b to make the curved course, that is e d. Thus the support e f renders to its base entirely that part of the column which bears its force upon it.

Thus if the top of the column desires to fall in d, whoever should set against it the support c M, what part would it have of the weight of the first support, that is e f?

Rule.

If half the base a b g goes 4 times into a b, the 3/4 goes into a and the rest is distributed by error 6) among the 2 supports. Now, if you wish to know how much weight belongs to each, keep this way: divide in half the base of the triangle b g d, which will be n d, which goes 4 times into b d, and thus the 3/4 remain in d of the upper weight. Then divide the base of the triangle b g M, which will be z M, which goes 3 times into b M; thus the 2/3 of the weight remain in M. Now reckon that the weight of the capital b weighs 12: in d there will be the 3/4 of 12, which is 9, in M there will be the 2/3 of 12, which will be 8. Thus of the 12 pounds of the capital ...