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Library/Paris Manuscript B/46

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Paris Manuscript B — 46

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Bibliothèque de l'Institut de France, Paris

Arco visto di fronte e di fianco, con:

b c d - a f e - g M h; S - r t

Per che ragione questo arco è forte.

Dico che impossibile è che uno corpo maggiore possa entrare in uno minore. Essendo così, la linia g c h è molto maggiore che g h. Adunque il maggiore non enterrà nel minore g h, se quello non si rompe. E chiaro si po conoscere che a volere rompere una trave per tirare, questo essere poco fattibile. Adunque se confesserai per le dette ragioni g h non potersi rompere per tirare, l'angolo g f h e l'angolo g c h e 'l mezzo tondo di sopra non potrà mai passare per la corda, ovver basa g h.

Ancora similmente b d f e così a M e non possano avere mutazione, se 'l trave c M non si rompe. Essendo mal possibile, quasi impossibile è che l'arco si rompa, essendo a quello aggiunto la 'ncatenatura del rinterzare l'asse, che vanno nel tondo g a b c d e h, e d sarà interamente sicuro aggiugnendo a quello due sostegni traversi, come appare in nella figura r S t.

Edificio e giardino elevato adiacente, con:

orto

Il terreno che si cava della canove, si debbe elevare da canto tanto in alto che faccia un orto che sia alto quanto la sala. Ma fa che tra 'l terreno dell'orto e 'l muro della casa sia uno intervallo, a ciò che l'umido non guasti i muri maestri.

Arch seen from front and side, with:

b c d - a f e - g M h; S - r t

For what reason this arch is strong.

I say that it is impossible for a larger body to enter into a smaller one. This being so, the line g-c-h is much greater than g-h. Therefore the greater will not enter into the smaller g-h unless the latter breaks. And it can clearly be seen that to break a beam by pulling is scarcely feasible. Therefore, if by the said reasons you grant that g-h cannot be broken by pulling, the angle g-f-h and the angle g-c-h and the semicircle above will never be able to pass through the chord, or base, g-h. Likewise in the same way b-d-f and a-M-e cannot undergo change unless the beam c-M breaks. This being scarcely possible, it is almost impossible for the arch to break, given that to it is added the tie-work of trebling the boards that run in the circle g-a-b-c-d-e-h; and it will be entirely safe by adding to it two cross-supports, as appears in the figure r-S-t.

Building and adjacent raised garden, with:

garden

The earth that is dug from the cellars should be raised up at the side so high that it makes a garden as high as the hall. But see that between the garden's soil and the wall of the house there is an interval, so that the damp does not spoil the main walls.

Why an Arch Holds, and a Raised Garden

A geometric argument for the strength of a braced arch, plus advice on garden earthworks

Architecture Physics & Mechanics Civil Engineering

Leonardo analyses why a particular arch is strong, arguing geometrically that its chord g-h cannot be broken by pulling and that the springing angles and the semicircle above therefore cannot pass through the base, especially once tie-work and two cross-supports (r-S-t) are added. He draws the arch from front and side and labels it b-c-d, a-f-e, g-M-h. A separate note on building explains that earth dug from cellars should be banked up to form a garden (orto) as high as the hall, leaving a gap between the garden soil and the house wall so damp does not spoil the main walls.

On this page

Why the braced arch cannot break (g-h, r-S-t)

Leonardo reasons that a larger body cannot enter a smaller one, so the curved line g-c-h, being much greater than the chord g-h, cannot pass through it unless g-h breaks by pulling, which he holds scarcely feasible. Hence the angles g-f-h and g-c-h and the semicircle above cannot pass the base g-h; and with the boards trebled around the ring and two cross-supports added at r-S-t, the arch is made entirely safe.

A raised garden built from cellar spoil

The earth excavated from the cellars is to be banked up at the side high enough to form a garden level with the hall. Leonardo insists on leaving an interval between the garden soil and the house wall so that damp does not ruin the main load-bearing walls.

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