a, x, b, p, 4, c n m f

4, 6 6, S, a, n m

wedge

The line of the mover and the line of the thing moved must always join together at a right angle.

If you raise the horizontal beam from one of its ends in such a way that at the end of its motion it stands on a perpendicular line above the plane that supports it, every degree of motion varies and produces degrees of weight. And if you wish always to know the true degrees of these weights, make the line of the cord that moves the beam and the line of the beam itself join together at a right angle, as is shown in a b c, where a b is the cord that pulls and b c is the beam pulled by that cord; and where such force joins with its resistance at the point b, there the right angle must always be.

The centre of gravity of the beam at p is what must teach the investigator of its motion the rule of its heaviness. And we say thus: if the horizontal beam c f weighs 4, f supports 2 of it and c 2. The centre of its weight is at m. Now the beam has been raised and lies on the line c b. The centre of its gravity is at p. The perpendicular from p falls at n, which has come as much closer to c as x more than when it was at m; whence it has diminished by half the weight the beam first gave to f, so that if before f supported 2, b now supports only one.

The supports n m are each in themselves 6 weights, which in their horizontal lie each of their ends weighed 3. Now, having been raised so far that they have lost a third of their horizontal lie, the front, as it is raised, has lost a third of its weight, by the 5th of the 7th of the theory; so that each front remains two weights, which joined together make 4 weights. The wedge being 4 weights as well, it seems here that the forces are used up. Now it remains that the force of the wedge does not act with its lines at right angles, together with the joint it makes with the lines of the 2 beams; and by the 7th of the ninth of the theory, that wedge lacks the weight which by that 7th is demonstrated, when one considers the diminution of the acute angle a o S, by how much it falls short of reaching the right angle.