But to finish what was begun on the reverse of this page: the third and last friction named was that of the pivot, which receives upon itself the weight of its own instrument to which it is joined; and upon it there also bears the counterweight that moves it. So one must make account of the resistance of such friction and draw it out of the calculation of the weight moved by such an instrument, which at every degree of motion acquires degrees of resistance.

[1] The manuscript has moso [for mosso].

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Here is treated the screw and its double or triple friction.

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Of measuring the force of the screw.

The curved wedge teaches the measuring of the force of the screw, for it too is a proper screw. But know that for such a measuring of the screw you must have notice of 6 things. The first is the obliquity of the path that the weight raised by the turns of the screw makes. The second is to know the nature of the friction that the weight makes upon the place from which it is dragged. The third is to know well the power of lever and of counter-lever. The fourth, to know the center of the weights that are raised. The fifth is the center of the force. The sixth, you must know the nature of contact. And you must know that it is as much labor to push the weight up the incline as to push the incline under the weight; as if to say it is as much to force the wedge under the weight as the weight upon the wedge. And so the turning of the screw, the weight of its nut rising upward, is like as if you turned the nut around its screw, for it is all one same thing, because the turning of the one or of the other makes one same effect and labor in the raising of weights, and the obliquity of the screw is like the wedge.

The friction that the screw here makes with its support, charged with the weight of itself together with what is moved by it, makes its motion more difficult than the drawing of the weight is. But let us say that the weight of the screw and of its lever is 27, which carries a third of 27 into its friction, which comes to 9. And because the half of its counter-lever, which lies at the quarter of the thickness of the pivot, that is at the middle of that part of the pivot which is beyond its center, enters 108 times into its lever: therefore, making 9 times 12, which is one pound, 9 times 12 is 108. Therefore one ounce of force moves the screw, charged in itself only with its own weight. Now there remains to speak of the force required for the moving of the weight. I say that you must take the measure of the line found from the middle of its thread to the center of that screw, and this measure shall be the counter-lever, which you will proportion with its lever. And you will find here that this counter-lever is 1/9 of its lever, where it stands in proportion 9 in counter-lever against 1 in lever. Now of the 27 pounds that the screw has to raise, because raising, as said, is in the screw of the nature of dragging, those 27 pounds come to 9; which 9 stand in counter-lever even with 1 in lever. And there is one ounce of the weight of the screw's pivot, which makes one pound and one ounce stand against twenty-seven of weight that is raised and 27 of the weight of the screw; to which I will further add the weight that is raised, which too, being sustained by the screw, rests upon the pivot of that screw and increases the labor for the mover.

One can make screws that shall be more difficult, by the frictions they make with their many separate nuts, than any great weight would be that could be drawn with such divided screws.