Nine cords supporting a beam: how force is shared
A statics problem on a beam held by nine cords, with fan diagrams of acute angles
The sheet poses a mechanics problem: a heavy beam whose descending head f weighs 50 pounds is held level by nine cords, and Leonardo asks how much force each cord must bear. His rule is that each of the nine cords takes the ninth part of the load it would carry if it pulled alone, and he works a case where the cord m S must exert 500 pounds. Two fan-shaped diagrams of lines radiating at acute angles, together with a lettered horizontal-beam figure, accompany the reasoning.
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Sharing a 50-pound beam among nine cords
Leonardo asks how much weight or force each of the nine cords needs to keep level with the descending head f of the beam, weighing 50 pounds. His answer is to give each cord the ninth part of the load that would fall to it if it were pulling alone.
The cord m S and the 500-pound force
If t S goes ten times into t f and the head f weighs 50 pounds, the cord m S requires 500 pounds of force. From this Leonardo derives the general rule that each of the nine cords fastened at f takes a ninth part of the weight it would sustain alone.
Motion made through acute angles
The heading names the theme of the two fan-shaped constructions, in which many lines radiate from a single point across a semicircle at successively acute angles. These angular spreads model how the cords branch off from the beam.