The mill with its water.

Why in nature does n resist m precisely? See that your rule demonstrates it with precision.

f-b4-n; S4r - c - 2 and 1/4 and 1/16 m 2 and 5/16 1/2 5/64
By the fourth of the first, b the pole, which weighs 4, returns in friction 1.
And by the sixth of the first, n, a weight of 4, again returns in friction 1.
And by the third of the second, n, a weight of 4, returns in the counter-lever f 2.
In short, at f there are found 4 pounds of weight, of which 2 are from the friction of the weights b n, which are shown only by means of motion; the other 2 are from the weight n, which is supported by the point of the support f; and these are shown both with motion and without motion.
Now the 2 pounds that n discharges at f descend again to c by the eighth of the third, (which in friction) return 1/4.
The weight of the pole r, which weighs 4, in friction returns 1.
The 2 at f in friction returns 1/4, but by the third of the second it returns to the counterweight m as one whole 1.
Now the lever and counter-lever f r S, by the ninth of the third, although they are bent, it is as if they were straightly equidistant, and the power of the resistance of the friction of f, which is 1/4, returns to the pole r, just as the weight that resists it in its lever at m; which quarter returns in friction 1/16.
Now by approximation is shown the nearness of the weight that almost resists, that is 2 and 5/16. Now this 2 and 5/16 also returns to the trial of the friction of the pole, because there it is supported, which in that friction returns 35/64; for which, for as much weight increased at m as counterweight, one must always give a quarter for the friction; and so it continues infinitely.

4

7 12 6

8—8—64
* It is impossible to give precisely the proportion by which one weight precisely exceeds the other in the balance.
* Although by mathematical discipline the powers and resistances of weights are demonstrated with precision, nonetheless in practice their makers remain confused for not understanding at least the demonstrable approximations.
* It is impossible, by experiment, precisely to give a weight that moves its opposite in the other arm of the balance.

8-64-64
The more you increase the weight, the more you increase the resistance at the pole and the friction.
* See that here 4 stands against 6, because, all the weight of the balance weighing below where the pole joins upon its support, there it makes a weight of 8, which in friction gives 1/4, that is 2. Therefore 2 added to one of the weights seems to satisfy, and with the least thing more the motion would be created. But that 2, giving its fourth part in friction, will give 1/2; and again with another half added to the 6 it seems almost to do what is needed to begin the motion. But that half too gives a quarter of itself in friction, which makes 1/4, and so on infinitely it happens in nature, or in theory.