The Crossbow's Diminishing Force and a Subdivided Triangle
Halving the pyramidal force (400 to 200); a right triangle split into 1, 3, 5, 7 units
Leonardo reasons about how the crossbow's force falls off as the cord is released. If a given weight draws the cord to the catch, half that weight produces more than half the motion, and five-sevenths of the weight produces three-quarters of the motion. To assign a single equivalent value to a pull that loses strength at every degree of motion, four hundred at the start and nothing at the end, he takes half of this pyramidal force, two hundred, and then reckons in the weight of the arrow. A right triangle drawn at the right is divided by parallels into tiers of 1, 3, 5, and 7 similar triangles, picturing the linearly decreasing force.
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Right triangle divided into 1, 3, 5, 7 triangles
A right triangle has three lines drawn parallel to its base at equal intervals. Each resulting tier is cut into an odd number of similar triangles and labeled with their count: 1, 3, 5, and 7.
Less than proportional loss of motion
If a certain weight draws the crossbow's cord as far as the catch, half of that weight produces more than half of the cord's motion, and five-sevenths of the weight produces three-quarters of the motion toward the catch.
Averaging a force that falls from 400 to nothing
Because the force diminishes by degrees at every degree of the cord's release, to give it a uniform value take half of the pyramidal force: if it was four hundred at the beginning and nothing at the end, half is two hundred; then calculate including the weight of the arrow.