Of the stones that come apart from their mortar.

Stones of equal number in their height, walled with an equal quantity of mortar, make an equal settling in the departure of the moisture that softens that mortar.

The fissures of walls will never be parallel unless the part of the wall which separates from its remainder descends.

By the foregoing it is proved that the small quantity of new wall interposed between a and n will make little settling compared with the quantity of the same wall interposed between c and d, and such will be the proportion between the rarities of the said mortars as is the proportion of the numbers, or of the quantities, of the mortar interposed in the joints of the stones walled over the various heights of old walls.

What is the rule that makes buildings permanent.

The permanence of buildings is the rule contrary to the two preceding, that is, that the walls be raised aloft all equally, at equal grades, embracing the entire circuit of the building with the whole thicknesses of every sort of wall; and although the thin wall dries sooner than the thick, it will not have to break under the weight it may acquire from one day to another, because, if the sub-double dried in one day, the double would dry in two or thereabouts, and it will come to be balanced with little difference of weight in little difference of time.

Prognostics of the causes of the fissures of any wall.

That part of the wall which does not descend keeps in itself the obliquity of the corbel covering the obliquity of the wall descended from it.

Of the sites of foundations, and in what place they are the cause of ruins.

When the fissure of the wall is wider above than below, it is a manifest sign that the wall has the cause of its ruin remote from the perpendicular of that fissure.

The adversary says that it descends at the corbel.

And here the adversary says that r descends and not c.

Of the fractures of arches.

The arch made from the semicircle, which is loaded on the two opposite thirds of its curvature, will break in five places of its curvature. It is proved: let n, m be the weights which break the arch a b f; I say, by the foregoing, that since the ends c a are equally weighed down by the weight n, it will follow by the 5th that the arch will break in the part most remote from the two powers that press it, which is the middle e; and I mean to have said as much of the opposite arch d g b. Therefore the weights n, m come to descend, and cannot descend, by the 7th, without making themselves nearer; and they cannot draw nearer without the arch interposed between them drawing its ends nearer, which cannot come together without the breaking of its middle. Therefore the arch will break in five places, as was proposed, etc.

Question: of the weight given at a, what part of it answers in the line h f, and with what weight is the weight placed at f to be overcome.

Of the cause of the breaking of public and private buildings.

Walls break by fissures that run straight and some that run oblique. The fractures that run straight are generated by new walls built in junction with old walls, upright or toothed into the old walls, because such mortises, not being able to resist the insupportable weight of the wall joined to them, must break and give place to the descent of the said new wall, which settles a braccio for every ten braccia, more or less according to the greater or lesser amount of mortar interposed between the walled stones, and with mortar more or less liquid. And note that one ought always first to build the walls and then face them with the stones that are to face them, because, if it were not so done, the wall making a greater settling than the outer crust, it would be necessary that the mortises made in the sides of the walls should break, since the stones that face the walls, being of greater size than the stones they face, must receive a lesser quantity of mortar in their joints, and consequently make less settling, which cannot happen if such crusts are walled after the wall is dry.

a b is the new wall; c is the old wall which has already made its settling, and a b makes its settling afterwards; although a, being founded upon c, the old wall, cannot in any way break, having a stable foundation upon that old wall, but only the remainder of the new wall b will break, with what is walled above it from the summit of the building down to the base, the remainder of the new wall making a corbel over the wall that descends.