f, a b, p q, g, m n

Whatever proportion the thickness of the pivot a b has to the width of each wheel a m and b n, such will be the number of whole turns the pivot gives when the said wheels give one whole turn. But make the number whole, for if there were fractions it would not come out so exactly. Even so, as regards the movement, the lines of contact are exchanged entirely at every degree of motion, and in no part of the length of such contact lines does any friction occur.

All the force of the pivot f extends in transversal, or lateral, motion, and rests upon the pivots p q, which pivots you will receive upon other wheels. And by the 5th of the 3rd, it will do good service.

This is of the same nature as the one above, except that it varies in the pivots, because the wheels of the one above turn upon the pivots, and below the wheels turn together with the pivots upon other wheels, as the drawing shows.

On the wearing of pivots placed in the position of equality.

The pivot has two contrary motions about its centre, of which one wears itself together with its support; the other wears neither itself nor its support. And the one that wears the pivot with its support is that part which, the pivot being in the position of equality, descends toward the centre of the world. But that part of the pivot which wears neither itself nor its support is the one that moves, with its revolving motion, toward the heavens.

On the wearing of pivots placed along a straight line.

Never does the pivot placed along a straight line wear its lower part, together with the support that is in contact with it.

On the motions of pivots.

The pivot has two motions about the centre of its revolution, of which one moves contrary to the other.

On the wearing of the pivot.

The pivot lying in equality wears itself together with its support, with that part of itself that descends, as, in its place, will be proved, etc.