VENI VIDI DA VINCI

Collections Newsletter Guild About Developers Patron Sign In

Library/Codex Atlanticus/0739 r

Prev1477 / 2238Next

Codex Atlanticus — 0739 r

100%

Reset zoom

© Veneranda Biblioteca Ambrosiana, Milan

Il peso, cioè il trave, dove la corda che lo sospende si partirà da esso trave infra angoli retti: mai esse corde aranno più peso che si sia quello del trave da loro sostenuto. E quando le corde si partiranno dal trave da loro sospeso infra angoli più acuti, sosterranno tanto più peso che quello del trave, quanto li angoli acuti fatti dalla linia del trave dove si congiugne colla linia della corda, fieno minori che li angoli retti.

Trave sospeso in varie posizioni, con:

1 r - 32 4 om-16 4ni-ha-8K4eb-c -4x4S df-y-g24 libbre t u d

Tal proporzione arà un peso in f che sostenga la testa del trave d g, con quello che sosterrà la testa del trave S X, che arà la punta S del triangolo c d S colla punta del rettangolo t, e similmente l'uno angolo dopo l'altro. Diciamo il trave d g sia 4 pesi. Chiaro è che 2 ne viene in d angolo retto e 2 ne starà nel contra peso f. Ora io vorrei dare tanto peso a f, che il detto trave s'alzassi insino in o l. Ora fa così: guarda quanto l'angolo o entra nell'angolo retto t, che v'entra 16 volte. Adunque 32 pesi in f starà pari con detta testa o.

The weight, that is the beam: where the cord that suspends it leaves the beam at right angles, those cords will never bear more weight than that of the beam they support. And when the cords leave the beam they suspend at more acute angles, they will bear as much more weight than that of the beam as the acute angles made by the line of the beam, where it joins the line of the cord, are smaller than right angles.

Beam suspended in various positions, with:

1 r – 32; 4 o m – 16; 4 n i – ha – 8; K 4 e b – c – 4 x 4 S; d f – y – g 24 pounds; t u d. Such a proportion will a weight at f have (the one that supports the head of the beam d g) with that which will support the head of the beam S X, which will have the point S of the triangle c d S together with the point of the rectangle t, and likewise one angle after another. Let us say the beam d g is 4 weights. It is clear that 2 come to d at the right angle and 2 will rest in the counterweight f. Now I should like to give so much weight to f that the said beam would rise as far as o l. Now do thus: look how many times the angle o enters the right angle t — it enters 16 times. Therefore 32 weights at f will stand level with the said head o.

Cords bear more weight as their angle to the beam sharpens

Statics of a suspended beam, with a worked counterweight of 32 at f

Physics & Mechanics Arithmetic & Proportion Geometry

A horizontal beam is drawn slung between two pulleys, with many cords fanning across it at different angles and hanging weights at each end. The surrounding text states the governing rule: cords leaving the beam at a right angle bear no more than the beam's own weight, while cords meeting it at ever more acute angles bear proportionally more. A worked example reasons that, since the angle o enters the right angle t sixteen times, a counterweight of 32 at f will hold the beam's head level at o.

On this page

Rule: right-angled cords bear only the beam's weight

Where the suspending cord leaves the beam at a right angle it never carries more than the beam's own weight; as the cords meet the beam at more acute angles they carry as much more weight as those angles fall short of a right angle.

Proportioning the counterweight at f

Leonardo reasons by number: the beam d g weighs 4, of which 2 come to the right angle d and 2 rest in the counterweight f. To raise the beam to o l he asks how many times the angle o enters the right angle t; it enters 16 times, so 32 weights at f will stand level with the head o.

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