The Crossbow's Force and the Motion of Its Cord
Bolt travel proportional to the charging weight, with an unequal-arm balance a-b-c
Under the heading On motion, Leonardo states that the length of travel of a bolt driven by a crossbow stands in the same proportion to the travel of the bowstring as the weight of the bolt does to the weight that charged the bow. A balance staff drawn in equilibrium illustrates the idea: a short arm a carries a large weight while a long arm c carries a small one, pivoting at b. He then names ab as the cord's charging motion and bc as its releasing motion, tied by the same proportion between weight driven and weight that created the force.
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Bolt travel proportional to the charging weight
The length of the motion made by a body driven by the crossbow bears the same proportion to the motion of its cord as the weight that is driven bears to the weight that charged the crossbow.
Charging motion ab and releasing motion bc
ab is the motion the cord made when it was charged and acquired its force; bc is the contrary motion it made when it loosed that force. The motion in acquiring force and the motion in the death of the force stand in the same proportion as the weight driven bears to the weight that created the force.
Unequal-arm balance a-b-c
A balance staff hangs in equilibrium with a suspended weight at each end. The short arm a bears a much larger sphere than the long arm c, and the beam pivots at b.