Winds and Projectile Motion: The Path of an Arrow
Generation of winds from the elements; simple motion; why an arrow's flight is never truly straight
The right column treats the generation of winds: the elements convert one into another, and wind arises when air turns to water, drawing surrounding air into the void, or when water turns to air and displaces the air it fills. Leonardo refutes the notion that the stars could drive the wind around the earth in 24 hours, and cites 'Albert' on vapor driven crosswise between heat and cold. The left column argues that transverse projectile motion is never truly straight: an arrow deviates imperceptibly as its natural weight pulls it toward the center of the world, and a numerical proof divides a 500-braccia shot into a thousand degrees to show the downward deflection is about a thousandth of a half-braccio, 'like a hair'. A doubling series 1, 2, 4 ... 4096 is written at the foot of the column as a number endlessly halvable without fractions.
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Winds generated by the conversion of the elements
When air converts into water at its cold region, it draws the surrounding air with fury into the vacated place, and this rush is the wind; conversely, when water converts into air, the displaced air flees with impetus to make room, and this too is the wind. Leonardo concludes the north wind would generate all the winds at one and the same time.
A moving body never outruns its mover
Of simple motion: the moving body can never be swifter than its mover in an equal time. Therefore the wind supposedly moved by the stars cannot have the speed to circle the earth in 24 hours as the star would, so that saying is false.
An arrow's transverse motion is never straight
Transverse motion drawn from the mover's power is never straight; though the arrow seems for a space to go in a straight line, this cannot be, only an imperceptible deviation invisible to the eye. Leonardo proves the arrow, launched with a power of a thousand while pulled by one degree of natural weight toward the center of the world, descends a tiny fraction as it flies.
A 500-braccia shot divided; the doubling series to 4096
Dividing a 500-braccia crossbow shot into a thousand degrees makes each degree half a braccio, and the thousandth of a half-braccio is nearly imperceptible, like a hair. Were the degrees 4096 instead, the number could be halved down to unity without any fractions, illustrated by the series 1, 2, 4, 8 ... up to 4096.
