A sling and the changing power of its launch trajectories
Radiating lines a, e, f, g, h, i trace projectile paths from a whirling strap
Leonardo draws a sling — a handle labelled n ending in a hooked stop a b — charged with a round shot, with radiating lines a, e, f, g, h and i that trace the beginnings of possible launch trajectories. The note asks how the curved pivot a b must be altered to hurl the projectile along any chosen line, for instance at a right angle to the horizontal (the angle g b n). As the strap swings and a descends toward d, he reasons that the driving power falls off in a diminishing series of ratios — sesquialteral, then three-quarters, four-fifths, five-sixths and six-sevenths — continuing on to infinity.
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Adjusting the curved pivot a b to control the launch angle
Leonardo wants to know how the curved pivot a b ought to change if one wishes to launch along any variety of line. He instances launching along a right angle taken from the horizontal or from the perpendicular to the centre, that is the angle g b n.
Diminishing power ratios as a descends toward d
When a has descended to d, b will be at c and the power of d is no longer double that of c but sesquialteral. As a moves on to e, the power of d becomes three-quarters that of e, and then four-fifths, five-sixths and six-sevenths, proceeding on to infinity.
The sling: handle n and hooked stop a b holding a round shot
The drawing shows a sling whose handle, labelled n, ends in a curved hook labelled a and b that acts as a stop for the whirling strap. The strap is shown charged with a round projectile ready to be launched.