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Codex Atlanticus — 0739 v

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© Veneranda Biblioteca Ambrosiana, Milan

Fa che questa figura ritorni nella sperienzia1, innanzi tu giudichi altro di lei.

Trave sostenuto da corde variamente angolate, con:

f-rStonmca

Tanto quanto li angoli fatti dalla linia d'un legato trave colle linie delle corde d'esso legatrice, sono minori l'uno che l'altro, tanto più peso d'esso trave sostiene la corda de l'uno angolo più che quella dell'altro. Diciamo l'angolo acuto a è per 2 volte l'angolo retto r2. Adunque se la corda f r sostiene 2 pesi del trave, la corda a f per nas[c]ere da la metà minore angolo che r, ne sostiene il doppio più peso, che saranno pesi 4.

Have this figure return to experiment before you judge anything else about it.

Beam held up by variously angled cords, with:

f r S t o n m c a. By as much as the angles made by the line of a bound beam with the lines of the cords that bind it are smaller one than another, by so much more of that beam's weight does the cord of the one angle bear than the other. Let us say the acute angle a goes twice into the right angle r. Therefore if the cord f r bears 2 weights of the beam, the cord a f, springing from the angle half as small as r, bears twice as much weight — which will be 4 weights.

Sharper cord angle bears double the beam's weight

A caution to test by experiment, and the angle-to-load proportion

Physics & Mechanics Arithmetic & Proportion Geometry

A large triangular figure fills the sheet: from a pulley at the top-left apex a family of curved and straight cords fans down to a horizontal beam, with a weight hanging at the corner. The text first warns that the figure must be checked against experiment before any judgement is drawn from it, then states the proportion: the more acute a cord's angle to the beam, the more of the beam's weight it bears. Worked out, if cord f r carries 2 of the beam's weights, cord a f, at half the angle, carries 4.

On this page

Test the figure by experiment before judging it

Before drawing any conclusion, Leonardo insists the figure be returned to experiment; only then may one judge anything further about it.

Half the angle, double the load: cords a f and f r

The rule is quantified with the cords' angles. As the angle a goes twice into the right angle r, cord a f bears twice what cord f r bears: if f r supports 2 of the beam's weights, a f supports 4.

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