Of stones that detach from their mortar.

Stones equal in 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.

Never will the cracks of walls 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 the new wall interposed between a n will make little settling with respect to the quantity of the same wall interposed between c d; and such will be the proportion that the rarities of the said mortars have between them, as is the proportion of the numbers, or of the quantities, of the mortars interposed in the joints of the stones walled at the various heights of the 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 up all equally, at equal levels, embracing the whole circuit of the building with the whole thicknesses of every sort of wall; and further, although the thin wall dries sooner than the thick, it will not break under the weight it may gain from one day to the next, 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 cracks 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 the foundations and in what place they are cause of the ruins.

When the crack 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 crack.

The adversary says that the corbel a descends.

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

Of the breakings of arches.

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

Question: of the weight given at a, what part of it corresponds in the line h f, and with what weight must the weight placed at f be overcome?

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

Walls break by cracks that are straight, and some that are oblique. The cracks that are straight are generated by new walls built in conjunction with old walls, straight or with toothings joined to the old walls, because such toothings, not being able to resist the unbearable weight of the wall joined to them, must break and give place to the descent of the aforesaid new wall, which settles one braccio for every 10 braccia, more or less according to the greater or lesser amount of mortar interposed between the walled stones, and with more or less liquid mortar. And note that one should always first make the walls and then face them with the stones that are to face them, because, if it were not done so, the wall making a greater settling than the outer crust, it would be necessary for the toothings made on the sides of the walls to break, since the stones that face the walls, being of greater size than the stones faced by them, must receive a smaller quantity of mortar in their joints, and consequently make a smaller settling, which cannot happen, such crusts being walled after the wall is dry.

a b new wall, c is old wall which has already made its settling, and the a b makes the 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, together with what is walled above it, from the summit of the building down to the bottom, the remainder of the new wall making a corbel over the wall that descends.