Falling to the Centre of the World; Earth Moved by Water
Two motions of a falling body, the centre of gravity of a pyramid, and erosion by running water
On the left leaf (283v, written upside down beneath candelabra studies) Leonardo argues that any heavy body descending toward the centre of the world makes two motions whose lines of motion meet at a right angle, and locates the natural and accidental centres of gravity of a pyramid — the accidental centre a descending to the world-centre d — placing the natural centre one twenty-first of the pyramid's length from the accidental one and one fifth from the magnitude. Wedge ('cuniale') and equilateral pyramids are drawn as geometric solids. The right leaf (282r) turns to water moving earth ('Levare / Porre': running water strips earth from one place and deposits it in a hollow), to a balance in which 'when b e descends, a e f rises', and to a note that a blow is weaker the more unequal the angles into which it falls. The sheet also carries prominent untranscribed sketches — turned candlesticks or candelabra, geometric solids, a pulley pair, a waterbird, and a hand holding a pen; British Museum stamps appear on the leaves.
On this page
A falling body makes two motions meeting at a right angle
Every heavy body that could descend to the centre of the world would make two motions, the conjunction of whose lines would form a right angle; the motion from the centre of gravity to the conjunction with the centre of the world is always at a right angle.
Wedge and equilateral pyramids
Two solids are drawn and labelled 'wedge pyramid' (piramide cuniale) and 'equilateral pyramid' (piramide equilatera). Leonardo adds that no weight uniting with the centre of the world keeps its parts in proportion, and that a heavy body descending to that centre, having two centres, descends with two different motions.
The natural and accidental centres of gravity of a pyramid
If the accidental centre a descends to the world-centre d, representing the weight of the whole pyramid, then when that motion ends the motion of the natural centre c arises, meeting the first at a right angle. The natural centre of gravity lies 1/21 of the pyramid's length from the accidental centre, and 1/5 of the whole pyramid from the magnitude.
Running water strips earth from one place and deposits it in another
Two paired notes read 'To remove — I remove earth with running water and it settles below' and 'To deposit — deposit earth in this low place and it is carried by the water', describing how a current erodes and redeposits ground.
A balance: when b e descends, a e f rises
A lower figure labelled e c d f a b illustrates a balance or pulley in equilibrium: when the arm b e descends, the arm a e f mounts.
A blow is weaker at more unequal angles; centre of a hung weight
Whatever the blow, the more unequal the angles into which it falls, the weaker it is. The centre of any suspended weight lies on the straight line extending from the centre of the world to the centre of the cord that suspends it.