On Motion: a Crossbow Casting Weights of Differing Thickness
A projectile-range problem, preceded by a memorandum of three gentlemen
The upper note records three gentlemen — messer Gian Domenico and messer Giovan Francesco Mezzabarba beside messer Piero da Galerà. Below, under 'De moto', Leonardo poses a problem: if a crossbow or other force casts a one-pound body of one 'degree' of thickness 100 braccia, how far will it cast a one-pound body of half that thickness, then a quarter, then an eighth? The question probes how a projectile's cross-section governs its range.
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Three gentlemen noted
Leonardo records messer Gian Domenico Mezzabarba and messer Giovan Francesco Mezzabarba beside messer Piero da Galerà, with a cryptic phrase about being under cover and the water. It reads as a personal memorandum of people and a circumstance.
Range set against the thickness of the projectile
If a force casts a one-pound body of one degree of thickness to 100 braccia, Leonardo asks how far it will cast a one-pound body of half that thickness, then a quarter, then an eighth. He isolates cross-sectional thickness as the variable governing how far the same weight travels.
The crossbow as the launching force
The problem names the crossbow ('balestro') or another power as the agent that hurls the moving body, setting the enquiry in the field of missile weapons.
Halving the thickness: 1, 1/2, 1/4, 1/8
The successive cases halve the projectile's thickness — one degree, a half, a quarter, an eighth — framing the range problem as a proportional series.