The Balance: Choosing the Site of Weights by Proportion
Triangular balance schemes and the proportional division of weights in quarters
The verso continues the study of the balance with triangular balance schemes and the rule that the position (site) of each weight on the beam is chosen according to its proportion. Leonardo works an example in which, because 1 is one-fifth of 5, the line n o is divided into six parts with one part given to n r and the rest to r o. Further notes, worked in fractions of quarters, divide a middle weight of 8/4 among weights of 20/4 and 4/4 so that each receives its fitting share. A large lettered quadrilateral with tick-marked lines fills the lower half of the sheet.
On this page
The site of a weight chosen by its proportion
The position of each weight on the beam is chosen according to its proportion. Since 1 is one-fifth of 5, the segment n r stands to r o in the same way; Leonardo therefore divides the line n o into six parts, giving one to n r and the remainder to r o.
Dividing the mean weight among three (fractions in quarters)
Working in quarters, Leonardo has 20/4 in front and 4/4 behind and wants to divide the middle 8/4 so that the 20 and the 4 each receive a fitting part. He divides the mean number into the total of the three weights and distributes 5/4 and 3/4 accordingly, leaving the sites to be sought.
Halves and wholes on the beam
A further scheme distributes 1/2 and 3 1/2 among whole units. The half is given to the one whole and the 3 1/2 to the three whole.