Pivot friction of a crane worked out in fractions

Friction balanced by a counterpoise on a doubled arm

The friction of the 3/8 at a stands level with the weight of 3/16 at d, which is half, because its arm is double that of the friction. That weight d of 3/16 sends a quarter of its power to the friction at b, namely 3/64; these 3/64 of friction are equalled by a weight half as great, 3/120 at e, because its arm is half again the arm of the friction.

Chained fractions of friction and counterweight

The 3 at f sends a quarter into friction, namely 3/4, against which the weight of 3/4 at g is consumed, since the arms are equal and equal forces resist. Even so the weight g adds to the friction a quarter of its own weight, so 3/4 must become 4/4, which, losing 1/4, leave 3/4, the amount needed.

The pin, arms and weights of the lifting device

Here a b are 4 libbre with one libbra of friction at c; taking the force of c and that of b, worth 3 libbre, and on equal arms a n and a m giving equal weights, 3 libbre are set at e against the 3 of c b. Account is then made of the friction of that counterpoise e, so that 4/4 (one libbra) is set at f, of which a quarter goes to its own friction, leaving 3/4 clear to counterpoise the 3/4 of d, and the opposed forces rest equal about the center of the pole.

Rule: divide the pole's weight by the arm proportion

Divide the weight of the pole in the same proportion as the arm of the weight divides that of the counterpoise. When the hung weights are in the same proportion as the arms that carry them, divide the parts of the friction and of the counterpoise in that proportion, add one part to the counterpoise, multiply by the proportions, and whatever the multiplication exceeds the added part, multiply by 4 and lay upon the 'subbio' (winding beam).

Circle-and-square balance diagrams in the margins

Both margins carry a series of small circle-and-square diagrams representing the pivot, its beam and the weights hung from it, each keyed to the fraction calculations written beside them.

Facciata sinistra. Segni di abbreviazione colle lettere:

Figura colle lettere e i numeri:

Nel margine superiore:

Sotto la figura:

Sotto i numeri precedenti, figura con:

A sinistra, due figure con:

Sotto le precedenti, due figure con:

Facciata destra. Figura con:

Figura con:

Figura con: Operazione:

Left page. Abbreviation marks with letters:

Figure with letters and numbers:

In the upper margin:

Below the figure:

Below the preceding numbers, figure with:

On the left, two figures with:

Below the preceding, two figures with:

Right page. Figure with:

Figure with:

Figure with, and operation: