On the shrinkage of moist bodies of uneven thickness or breadth.

The window a is the cause of the rupture of b, and this rupture is increased by the weight n m, which drives, or penetrates, more into the earth that receives its foundation than the lightness of b does; and moreover the old foundation beneath b has settled, which the pillars n m had not done, and the part b does not descend perpendicularly but rather throws itself outward, obliquely, and cannot, as the adversary claims, throw itself inward, because that part, disunited from the whole, is wider on the outside than on the inside, and the lips of the remainder are of the same shape; and if that disunited part had to go inward, the greater would have to enter into the lesser, which would be impossible. Therefore it is concluded that of necessity the part of such a semicircle separates itself from the whole by throwing its lower part outward and not inward, as the adversary would have it, etc.

When whole or half tribunes are overcome above by excessive weight, then their vaults will open with an opening diminishing on the upper side and wide below, narrow on the inner side and wide on the outer, like the skin of an apple or orange divided into many parts along its length; for the more it is pressed by the opposite parts of its length, the more that part of the joints will open which is farthest from the cause that presses it. And for this reason one must never load the arches of the vaults of any semicircle with the arches of its building, especially because what weighs more presses more on what is beneath it and descends more upon its foundations, which cannot happen to lighter things, such as the aforesaid semicircles.

Which of these two cubes will shrink more uniformly, the cube a resting on the floor, or the cube b suspended in the air, both cubes being equal in weight and quantity and of earth mixed with equal moisture?

That cube which rests on the floor shrinks more in its height than in its breadth, which the cube suspended above in the air cannot do. It is proved thus: the cube resting upon ... This same matter stands better here below.

The final form of the two cylinders of fresh earth, that is a, b, will be the pyramidal figures below, c, d. It is proved thus: the cylinder a, resting on its floor, being of earth much mixed with moisture, goes settling by means of its own weight which it gives of itself to its base, and it will settle and thicken the more the nearer its part is to its base, because there its whole weight is loaded, etc. The weight b will do the like, spreading the more the greater the weight it has beneath it, that greater amount lying at the confines of its support.

The first and most necessary quality is their permanence.

Of the foundations that the composing members of temples and other public buildings have. Such proportion must there be from depth to depth as there is from weight to weight that must be discharged upon those members.

Every part of the depth that the earth has for some space is made in layers, and every layer is composed of parts heavier and lighter one than another; in going deeper it is heavier. And this is proved because these layers are composed from the turbid matter of the waters discharged into the sea by the course of the rivers that pour into it. Of which turbid matter the heavier part was that which was discharged first, successively. And this the water does where it comes to rest, lifting up first where it moves. And these layers of earth are made manifest at the sides of rivers which, with their continual courses, have cut and divided with great depth of cuts one mountain from another, where the waters have drained through the gravelly layers, and for this reason the material has dried and turned into hard stone, and especially that of the finer mud. And this makes us conclude that every part of the earth's surface was once the centre of the earth, and so, conversely, etc.

Of the fissures in walls, which are wide at the foot and narrow at the top, and their cause.

That wall always cracks which does not dry uniformly, in equal time.

And a wall of uniform thickness does not dry in equal time when it is not in contact with an equal medium, as when one part of a wall were built in contact with a moist mountain and the rest remained in contact with the air; for then the rest contracts in every direction, while the moist part keeps its first size. And then what dries in the air contracts and diminishes, and what is moistened does not dry, and the dry part readily breaks away from the moist, because that moist part has no tenacity to follow the motion of what is continually drying.

Of arched fissures, wide above and narrow below.

Those arched fissures, wide above and narrow below, arise in walled-up doorways that settle more in their height than in their breadth, in proportion as the height is greater than the breadth, and in proportion as the joints of the mortar are more numerous in the height than in the breadth.

The fissure diminishes as much less at r o than at m n as there is less material between r o than at m n.

Every fissure made in a concave place is wide below and narrow above, and this arises as b c d shows in the figure at the side.

1st: Whatever is moistened grows by as much as is the moisture acquired.

2nd: And every moist thing contracts in drying by as much as is the moisture that divides from it.