by Leonardo da Vinci
Available in 350 free installments
Owner:
The walls give way in cracks, some of which are more or less vertical and others are oblique. The cracks which are in a vertical direction are caused by the joining of new walls, with old walls, whether straight or with indentations fitting on to those of the old wall; for, as these indentations cannot bear the too great weight of the wall added on to them, it is inevitable that they should break, and give way to the settling of the new wall, which will shrink one braccia in every ten, more or less, according to the greater or smaller quantity of mortar used between the stones of the masonry, and whether this mortar is more or less liquid. And observe, that the walls should always be built first and then faced with the stones intended to face them. For, if you do not proceed thus, since the wall settles more than the stone facing, the projections left on the sides of the wall must inevitably give way; because the stones used for facing the wall being larger than those over which they are laid, they will necessarily have less mortar laid between the joints, and consequently they settle less; and this cannot happen if the facing is added after the wall is dry.
a b the new wall, c the old wall, which has already settled; and the part a b settles afterwards, although a, being founded on c, the old wall, cannot possibly break, having a stable foundation on the old wall. But only the remainder b of the new wall will break away, because it is built from top to bottom of the building; and the remainder of the new wall will overhang the gap above the wall that has sunk.
774.
A new tower founded partly on old masonry.
775.
Stones laid in regular courses from bottom to top and built up with an equal quantity of mortar settle equally throughout, when the moisture that made the mortar soft evaporates.
By what is said above it is proved that the small extent of the new wall between A and n will settle but little, in proportion to the extent of the same wall between c and d. The proportion will in fact be that of the thinness of the mortar in relation to the number of courses or to the quantity of mortar laid between the stones above the different levels of the old wall.
[Footnote: See Pl. CV, No. 1. The top of the tower is wanting in this reproduction, and with it the letter n which, in the original, stands above the letter A over the top of the tower, while c stands perpendicularly over d.]
776.
This wall will break under the arch e f, because the seven whole square bricks are not sufficient to sustain the spring of the arch placed on them. And these seven bricks will give way in their middle exactly as appears in a b. The reason is, that the brick a has above it only the weight a k, whilst the last brick under the arch has above it the weight c d x a.
c d seems to press on the arch towards the abutment at the point p but the weight p o opposes resistence to it, whence the whole pressure is transmitted to the root of the arch. Therefore the foot of the arch acts like 7 6, which is more than double of x z.
777.
An arch constructed on a semicircle and bearing weights on the two opposite thirds of its curve will give way at five points of the curve. To prove this let the weights be at n m which will break the arch a, b, f. I say that, by the foregoing, as the extremities c and a are equally pressed upon by the thrust n, it follows, by the 5th, that the arch will give way at the point which is furthest from the two forces acting on them and that is the middle e. The same is to be understood of the opposite curve, d g b; hence the weights n m must sink, but they cannot sink by the 7th, without coming closer together, and they cannot come together unless the extremities of the arch between them come closer, and if these draw together the crown of the arch must break; and thus the arch will give way in two places as was at first said &c.
I ask, given a weight at a what counteracts it in the direction n f and by what weight must the weight at f be counteracted.
778.
