The centre of gravity and the balance of the water-screw
Euclid's law of the suspended centre applied to a screw poised on its pole
Citing 'the ninth of the second of the Elements,' Leonardo argues that the centre of any suspended weight comes to rest beneath the centre of its support, and he defines the 'central line' as the straight line imagined from a body to the centre of the world. He states that a suspended weight standing farther from that line gains force upon its natural weight, then concludes that the water of a screw, having its centre of gravity on the central line of its pole, is set in motion by any small weight added to one side. The upper diagram shows a beam suspended from a stand through pulleys, and three circular figures below show weights hung to test this displacement.
On this page
Euclid's rule: the suspended centre rests beneath its support
Citing 'the ninth of the second of the Elements,' Leonardo states that the centre of every suspended weight comes to rest beneath the centre of its support. He defines the 'central line' as the straight line imagined from a body to the centre of the world, and says a suspended centre of gravity desires to unite itself with the central line of its support.
An eccentric weight gains force
A suspended weight that by chance stands farther from the central line of its support acquires more force upon its natural weight. The three circular figures drawn across the middle of the sheet show weights hung so as to test this displacement.
The water of the screw poised on its pole
Leonardo concludes that the water of the screw has the centre of its gravity on the central line of its pole, so that any small weight added on one side becomes the cause of its motion. Because it bears its weight upon its poles and always touches only at a point, it will be of easier motion than c.
A balance beam carried on pulleys
At the top of the sheet a horizontal beam is suspended from an upright stand by pulleys, a device for studying where a hanging load comes to rest relative to the centre of its support.