Triangular balance: a worked example with weights 3, 6, 1
Laying out each arm by subtracting the weights and dividing the remainder
Under the heading 'Example', Leonardo works through his rule for placing three weights (3, 6 and 1) on a 'triangular balance' so they hang in equilibrium. He directs the reader to subtract the smaller number from the larger and divide the remainder into equal parts to lay out each arm along the beam at points a, n and m. A ruled beam with graduated divisions is drawn across the top of the page.
On this page
Siting three weights on the triangular balance
The three given weights 3, 6 and 1 must be assigned their true positions on the triangular balance. The arm of the middle weight (3) is built from a n, and the arm of the greatest weight is n m; the arm of the smallest weight is left to a figure that follows. Leonardo defers to that next drawing for the last arm.
Subtract, then divide the remainder into equal parts
Take 1 from 6, leaving 5, and make 5 equal parts of any chosen size: these are the 5 parts of a n, the arm of the middle weight. Then take the smaller weight from the middle (1 from 3, leaving 2) and make 2 parts for the arm n m of the greatest weight, similar to the divisions of a n.