Motion and weight: natural versus accidental gravity
Spherical weights, a crossbow arrow, and the centres of natural and accidental gravity in flight
A page of the mechanics treatise setting out propositions under the headings Moto (motion) and Peso (weight). Leonardo argues that only spherical weights thrown straight up return along the same line they rose by, and that in a crossbow arrow the centre of flight sits above the centre of natural gravity. He adds that in long bodies the heavier part descends first, that non-spherical heavy bodies possess both natural and accidental gravity that contend with equal force, and concludes that in every motion the natural weight guides the accidental.
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Spherical weights thrown straight up
Only spherical weights driven upward along a perpendicular line are granted that their natural (falling) motion follows the very line first traced by the accidental (thrown) course. A non-spherical body cannot behave so simply.
Crossbow arrow and its centre of gravity
If an arrow shot from the crossbow rises along a perpendicular line, the centre of its flight is built above the centre of its natural gravity, so the centre of its natural motion must lie below the centre of the accidental weight.
Natural and accidental gravity of heavy bodies
All heavy bodies not of spherical shape possess within themselves both natural and accidental gravity, which contend with equal power when divided from the pole of the accidental heaviness. In every motion the natural weight makes itself the guide of the accidental.