The Pyramidal Power of a Crossbow's Cord and Arrow
Force diminishes from base to point; two triangles compare the motor and the object moved
This page analyses the mechanics of the crossbow. Leonardo holds that the power of the released cord is pyramidal, greatest at its base and tapering to a point, so that at every degree of motion it loses speed and strength on to infinity. Two isosceles triangles, a short one labelled the pyramid of the motor (the cord) and a long one labelled the pyramid of the object moved (the arrow), compare their powers and motions. Because the arrow's pyramid is longer than the cord's, the arrow parts from the cord before the cord has stopped, while its motor is still at greatest power. A fragment at the top weighs a motion destined for four hundred braccia against one destined for a third of a braccio.
On this page
The cord's power is pyramidal, from base to point
If the crossbow's cord stayed curved after loosing an arrow, its power would at every degree of motion acquire degrees of slowness and weakness, on to infinity. This power is therefore called pyramidal, because it begins at a base and finishes at a point.
Pyramid of the power and motion of the motor
A small isosceles triangle, its vertex to the left, is captioned the pyramid of the power and motion of the motor. It stands for the driving cord, whose diminishing force is pictured as a narrowing triangle.
Pyramid of the power and motion of the object moved
Below it a second isosceles triangle of the same base and orientation, but reaching across the page, is captioned the pyramid of the power and motion of the object moved. Its greater length represents the longer diminishing motion of the arrow.
Why the arrow leaves the cord while power is greatest
Since the arrow is driven by the crossbow's cord, its motion too is pyramidal, acquiring slowness and weakness at every degree. But because this pyramid is longer than that of its motor, the arrow parts from the cord before the cord has stopped, indeed while its motor is still at its greater power.
