Friction, supports and where a loaded arch breaks
Why an arch loaded at mid-height fails at each quarter of its length
The right column shows a bracketed lintel on a wall, an upright frame, and arches loaded at their crowns, two of them labelled 'proposition' and 'definition' with weights S and N on cords. Leonardo notes that a support resists less the farther it sits from its fixed base, and that friction between equally heavy, equally rough bodies is harder the more horizontal, and easier the more oblique, their contact. He argues that an arch loaded at the middle of its height, if the weight exceeds its power, breaks at each quarter of its length, since a weight bears wholly on every part of its support. In the proposition and definition, the weight S carried on the arch b m tends to break it at d, which yields only after the part f o b breaks at its own middle o.
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Distance from the base and the ease of friction
That part of a support resists less which is set farther from its fixed base. Of frictions between bodies of equal weight and roughness, the more horizontal contact proves the more difficult, and conversely the more oblique the easier.
A loaded arch breaks at each quarter of its length
If an arch is loaded at the middle of its height and the weight exceeds the arch's power, it will break at each quarter of its length, between the power of the load and the resistance of the arch's feet. As much weight bears on the feet as on the middle, since every weight is wholly upon all its support and wholly in every part of it.
Where the weight S breaks the arch
The weight S, supported by the part of the arch b m, tends to break it at the middle point d. That point d will not yield until the part of the arch f o b first breaks at its middle o; but the load breaking at d is so powerful that it easily breaks at o as well, even though the weight of the arch f o b leans and presses upon b.