On gravity.

i r a - e b - p - L S m - n r f o - c d h K

For the reason stated below, the balance does not have all its natural weight over the centre of its point of revolution, but so much less as is the weight that moves the upper arm to oblique motion, as is proved in this discourse.

a

a, mathematical centre; n, centre of the point of revolution.

a b

These weights a b will make stability in every position.

The suspended heavy body is wholly over the whole, and wholly in every part, of the central line of its support.

The rod placed obliquely has two kinds of weight, of which one weighs obliquely between the centre of the world and the horizon, the other weighs directly upon the centre of the world; and of these one is accidental and the other natural. And this happens where the mathematical centre is not the centre of revolution of the balance. It is proved: let the balance be a b c d and its mathematical centre be S, and the centre of revolution be f. I say, in such a situation of the balance, that the mathematical centre S is on the line that points to the centre of the world (that is, g h) just as much as the centre of revolution f; and this line g h divides the rod of the balance into two equal and similar parts, that is the part a b e f and the part c d e f; and whether one rests the balance upon the point S or upon the point f makes no difference, because both the one and the other point lie on the central line g h, which divides the weight equally.

There remains for us the oblique weight spoken of above, which lies over the centre of revolution f, that is the weight from the line n o upward, namely a b r f, to which the counterweight c d r f offers no resistance in the aforesaid oblique motion.