Natural and accidental motion: pendulum and thrown stones
A weight swinging from a cord; the trajectories of stones cast into the air
The page is Leonardo's study of what he calls natural and accidental motion, illustrated by a round weight a hung by the cord f a from its attachment f. Falling to its lowest point n is 'natural' motion, seeking the centre of the world; the overswing from n to m, going against the weight's desire, is 'accidental' motion, always shorter and weaker. He extends the idea to stones thrown in an arc toward the sky, whose descending path curves more sharply and briefly than their rise, so that a stone cast straight up covers greater total length than one thrown low. Semicircular arc diagrams, projectile trajectories, a fan of paths, and marginal notes ('motion of equilibrium', 'bounce of a ball') accompany the text.
On this page
Natural versus accidental motion of a hanging weight
A round weight a hangs from the cord f a. Let fall, its descent from a to n is natural motion, seeking the point beneath its attachment f and the nearest point to the centre of the world; the overswing from n to m, against its desire, is accidental motion, always shorter and weaker than the natural. Natural motion grows swifter toward its end, accidental motion the opposite.
Trajectories of stones thrown into the air
Joining the accidental and natural motions of each course a stone makes through the air, one finds greater length of motion in a stone thrown straight toward the sky than in one thrown near the earth. The greater the arc of its highest summit, the smaller the natural descent; the smaller arc gives after it a greater natural motion.
The overswing in suspended gravity
That accidental motion will be more similar in length to its first natural motion — of which the natural is the shorter — when it is made in suspended gravity, as with the hanging weight.