Finding the pole of a balance from its two weights
Dividing the beam so that a 4-pound and a 2-pound weight come into balance
A horizontal graduated beam is drawn across the top of the page, with two cords hanging down to weight-boxes (the upper suspension points lettered o and b). Leonardo explains how to locate the pole (fulcrum) of a balance carrying two unequal weights: draw a crosswise line between the two weight-cords and divide it into as many equal parts as the total number of pounds, then set the pole between the 2 and the 4. He notes that the pole lies nearer the heavier weight in proportion to how much the weights differ, and reads the point where the pole-line cuts the space between the cords to test whether the loads are equal.
On this page
Locating the pole between a 4-pound and a 2-pound weight
Once the balance is made, draw a line crosswise between the two weight-cords and divide it into as many equal parts as there are total pounds. With 4 pounds on one side and 2 on the other, the six spaces are split 2 against 4, and the pole is placed between the 2 and the 4. The pole stands nearer the greater weight in proportion to how much the weights differ.
Reading where the pole-line cuts the intercord
Draw the line of the pole up to the balance and observe where it cuts the space between the cords (the intercord), whether it falls under one cord or outside both. If it divides that space into two equal parts the loads on the two cords are equal; if the parts are unequal, divide the greater by the lesser.