Weights on cords and levers: a general rule of proportion
Loads distributed between pulleys and cords, measured by the proportion of line-segments
Folio 77r sets out Leonardo's 'tested' general rule for how a hanging weight is shared between two cords or the supports of a lever. In each figure a weight suspended over pulleys is resolved so that the ratio of two segments of the supporting line equals the ratio of the two partial loads (for example t S : S v equals weight b : weight r). Diagrams of pulley-triangles, a horizontal cord marked 8, and four loaded lever-arms with weights of 8 and 16 illustrate the numerical bookkeeping. Leonardo insists the two supporting cords be taken equal in length so the calculation holds as a universal rule.
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The proportion of segments equals the proportion of loads
The same proportion that the segment t S has to S v is the proportion that the weight b has to the weight r. And the combined weight b r has to the weight f the same proportion that the space x v has to the line S x. The line-segments of the diagram thus measure how the load is divided.
Decomposition of a load among points a, b, c, m
The weight c has to the weight felt at a the same proportion that the space a b has to the space b c. Likewise the weight m has to the combined weights a c the same proportion that the line b m has to the line m c. Each partial load is read directly from the ratio of the corresponding segments.
General rule: keep the two cords equal
Remember that the two cords supporting the weight must always be taken equal. If one were far longer than the other, measure equal distances from the point where the weight's cord joins, and calculate with those measures as stated above. Done this way the method holds as a general rule.