On the proportion of force and motion; crossbow questions
Whether a crossbow scaled fourfold shoots four times as far; the nature of force; suspended rods
The right column poses questions on the proportion of force and motion, asking whether a crossbow built proportionally with four times the force and size would shoot its arrow four times as far, and how arrow weight (two versus four ounces) affects the range. The left column defines force as caused by violent motion through weight, and observes that added motion doubles speed, as when a potter's wheel is helped by the foot or a moving ball is struck along its own path. At the lower left, drawings of rods suspended from supports are annotated with the repeated numbers 4 and 2.
On this page
Does a crossbow scaled fourfold shoot four times as far?
Leonardo asks whether a crossbow proportionally built with four times the force and size will cast its arrow four times the distance of one that shoots 400 braccia. He further asks how varying the bow's thickness over the same length affects range, and how far it would throw a four-ounce arrow if a two-ounce arrow flies 400 braccia.
How force is caused and doubled by added motion
Force cannot be created in bodies without force or weight together with motion, and is caused by violent motion by means of weight. If a moving thing is pushed again by a greater motion it doubles its speed, as a potter's wheel turns faster when the foot's motion is added, or a ball struck along the line of its motion hastens more.
Suspended rods marked with the numbers 4 and 2
At the lower left are figures of rods hung from supports, each annotated with the repeated pair of numbers 4 and 2. They accompany the discussion of force, weight and motion above.