Studies of the Balance and the Centres of Weights
Heavy bodies seek the centre; rules for proportioning weights along a beam
A faded sheet, much of it written and drawn upside down, given over to the statics of the balance. It opens with the principle that every heavy motion tends toward the centre and that the heavier a body, the faster it falls, then works through a series of balance schemes with numbered weights and rules for proportioning the centres of the weights along the beam. Several worked examples show how to divide the greater, middle and lesser weights to place them correctly on either side of the fulcrum. The numbering and diagrams recur across the sheet in different orientations.
On this page
Heavy bodies seek the centre
Every heavy motion tends toward the centre, and the heavier the body, the more swiftly it descends. This principle stands at the head of the sheet's studies of weights on the balance.
Proportioning the centres of weights
Leonardo gives a rule for balancing: divide the greater and the lesser weights joined together by the middle weight. In the worked example he joins 3 and 1 to make 4, subtracts 1 from 7 to leave 6, and takes the difference of 2 to set the arm's divisions two spaces on one side of the fulcrum and six on the other.
Proportional rule with points c, b, a
Beside another balance scheme Leonardo notes the proportion between the segments b c and b a. If b c is a triple of b a, he assigns to c a sub-triple of the amount obtained from 18 and 15; the note breaks off unfinished.