Balance and Suspended Pyramids: Finding the Centre of Weight
Statics of a beam balance analysed through six equal pyramidal weights and their supports h and K
A small, closely written fragment reasoning about a beam balance and a pyramid suspended from it. Leonardo takes the line r e f as the divider of the middle of the weight, decomposing the load a b c d into six equal pyramids to show that e f falls below the central line r e of the upper balance. He then reasons about how the thirds of the pyramids fall beneath the supports h and K, concluding that because h X enters twice into X K, the support h bears two pyramids and K one. No diagram appears on this fragment; the figure it discusses is referenced by its letters.
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The line r e f divides the middle of the weight
Leonardo takes the line r e f as the middle of the weight of the balance and of the pyramid hung from it. Because e f divides six equal pyramids (a b e t f and e t f c d), it is the true divider of the weight a b c d and falls below the central line r e of the upper balance.
Supports h and K: two pyramids against one
Above the balance's arms remain three equal pyramids, a m e, b n f and c d e; the first two fall with their third part toward the base beneath the support h, while the third part of the other falls beneath K. Since h X enters twice into X K, K deserves half less weight than h X, so h carries two pyramids and K one.