The Statics of a Rod Suspended Between Two Cords
How the load redistributes to the supports when one cord shifts toward the middle
The leaf works out the statics of a rigid rod (aste) hung from two cords, asking how the weight it exerts on each support changes. Leonardo states that a rod suspended level and wholly between two cords loads each cord equally, but that moving one cord toward the middle, or letting the rod overhang a cord, shifts the load in fixed proportion to the displacement. A balance schema is annotated with the weights 18, 36 and 8, and further figures carry the fractions 4-5 and 21/4, 3/4.
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Moving a cord toward the middle increases its load
The cord that is moved toward the middle of the rod acquires more weight. When one cord shifts inward, the part of the rod enclosed between the cords is no longer shared equally between the supports; the weight transferred from the fixed cord to the moved cord keeps the same proportion as the motion bears to the remaining length of the rod.
Balance schema with weights 18, 36, 8
A schematic balance is annotated with the weights 18, 36 and 8, illustrating the proportional loading of the beam discussed in the surrounding text.
A level rod loads both cords equally
A rod suspended entirely between two cords at equal height gives an equal share of its weight to each. This baseline case, annotated 4-5, is the reference against which the unequal cases are measured.
Overhang and displacement change the share of load
Two figures of rods on two cords, annotated 21/4 and 3/4, treat what happens when the rod projects beyond a cord or a cord is drawn inward. The load that passes from the immobile cord to the mobile one keeps the same ratio as the overhanging part of the rod bears to the remainder.
