VENI VIDI DA VINCI

Collections Newsletter Guild About Developers Patron Sign In

Library/Paris Manuscript E/144

Prev144 / 169Next

Paris Manuscript E — 144

100%

Reset zoom

Bibliothèque de l'Institut de France, Paris

Del grave.

Se l'angolo che si genera nel concorso delle due corde che sostengano un peso, sarà tagliato dalla linia intercentrica di tal peso, allora esso angolo fia diviso in due altri angoli; li quali essendo di nuovo tagliati dalla linia della equalità, allora fia[n] generati due triangoli, de' quali tal proporzione sarà da basa a basa, quale è da angolo a angolo; e tal proporzione fia da angolo a angolo, quale è da triangolo a triangolo; e la proporzione che è da triangolo a triangolo, è la medesima che è da gravità a gravità, nelle quali si divide il grave alle due dette corde, che 'l sospendano. Ma è proporzion conversa, imperò che il maggior peso si dà alla corda, che si fa lato estrinsico del minore triangolo.

Quanti sono li centri d'un corpo grave innuniforme.

Tre sono li centri d'una gravità uniformemente disforme, de' quali il primo è centro della gravità naturale, il secondo è il centro della gravità accidentale, il terzo è centro della magnitudine d'esso grave.

Ma il centro della gravità naturale non si dà in nella equilibra, se il corpo grave non è uniformemente di peso e figura conforme, come il corpo sperico o paralello e simili, ecc.

Of the heavy body. If the angle generated at the meeting of the two cords that support a weight is cut by the intercentric line of that weight, then that angle is divided into two other angles; and these, being cut again by the line of equality, generate two triangles, of which the proportion from base to base is as that from angle to angle; and the proportion from angle to angle is as that from triangle to triangle; and the proportion from triangle to triangle is the same as that from gravity to gravity, into which the heavy body is divided at the two said cords that suspend it. But it is inverse proportion, because the greater weight is given to the cord that becomes the outer side of the smaller triangle. How many are the centres of a non-uniform heavy body. Three are the centres of a uniformly disform gravity, of which the first is the centre of natural gravity, the second the centre of accidental gravity, the third the centre of the magnitude of that heavy body. But the centre of natural gravity is not found in equilibrium unless the heavy body is uniform in weight and of conforming figure, like a spherical or parallel body and the like, etc.

Inverse Proportion of Loads, and the Three Centres of a Body

Triangles from the cut angle give the loads inversely; a non-uniform body has three centres

Physics & Mechanics

Continuing 'of the heavy body,' Leonardo shows that when the intercentric line and the line of equality cut the angle of two supporting cords, the two triangles formed relate base to base as angle to angle and triangle to triangle, and this same ratio governs how the weight divides between the cords, though inversely, since the greater load falls on the cord forming the outer side of the smaller triangle. He then distinguishes three centres of a non-uniform heavy body: the centre of natural gravity, of accidental gravity, and of magnitude. He notes that the centre of natural gravity is found in equilibrium only when the body is uniform in weight and regular in figure, such as a sphere. The page is entirely text, with no diagram.

On this page

Triangles from the cut angle set the loads in inverse proportion

The intercentric line and the line of equality cut the cords' angle into two triangles, whose ratio (base to base, angle to angle, triangle to triangle) equals the ratio of the loads on the two cords. The proportion is inverse: the greater weight falls on the cord that forms the outer side of the smaller triangle.

The three centres of a non-uniform heavy body

A uniformly disform gravity has three centres: of natural gravity, of accidental gravity, and of magnitude. The centre of natural gravity is found in equilibrium only when the body is uniform in weight and regular in figure, such as a spherical or parallel body.

Reader's Edition — described with AI from the e-Leo transcription.