Where the arched cord separates from its pulley
Using Euclid on tangent circles to find the point of departure of a cord slung over two pulleys
This page treats the separation of an arched cord from the pulleys it is slung over, remarking that the calculation is better made without pulleys, since large pulleys would leave the reckoning no place. Invoking Euclid's Elements, that a straight line touching two tangent circles passes through their point of contact, Leonardo constructs the center d of the circle formed by the cord's curve, draws the radius d r n to the pulley, and raises the perpendicular r c to mark the point r where the cord leaves the pulley. A concluding rule places the weight b on the line a n b as the weight of the arc between the pulleys; diagrams at the right show cords over two pulleys with hanging weights.
On this page
Better reckoned without pulleys
The separation of the arched cord is better computed without pulleys, because such pulleys could be so large that the calculation would have no place. The remark frames the whole analysis of cord and pulley that follows.
Euclid on tangent circles locates the point of departure
By the Elements, a straight line touching two tangent circles passes through their contact; so the center d of the cord's circle is found, the radius d r n drawn, giving the pulley's radius r n, and the perpendicular r c raised at the point r where the arched cord separates from the pulley.
The weight of the arc between two pulleys
The weight b always lies on the line a n b, and this weight b represents the weight of the arc made by the cord interposed between the two pulleys.