On the diminution of moist bodies of uneven thickness or width.

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 further 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 have not done. And the part b does not descend perpendicularly but is thrown outward obliquely, and it cannot, as the adversary would have it, be thrown inward, because that part detached 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 such a detached 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 detaches itself from the whole by throwing its lower part outward and not inward, as the adversary maintains, etc.

When whole or half tribunes are overcome from above by excessive weight, then their vaults will open with a crack that diminishes toward the top and is wide below, narrow on the inner side and wide on the outer, like the peel 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, above all because that which weighs more presses more upon 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 diminish more uniformly, cube a set upon the pavement, or cube b suspended in the air, both cubes being equal in weight and quantity and of earth mixed with equal moisture? The cube that rests upon the pavement diminishes more in its height than in its width, 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 ends of the two cylinders of fresh earth, that is a, b, will be the pyramidal figures c, d below. It is proved thus: the cylinder a set upon its pavement, being of earth well mixed with moisture, keeps sinking by means of its weight, which it gives to its base, and it will settle and thicken all the more the nearer its part is to its base, because there its whole weight is loaded, etc. The weight b will do the same, spreading the more the greater the weight it has beneath it, which greater amount is at the confines of its support.

The first most necessary part is their permanence. On the foundations that bear the composing members of temples and other public buildings. The proportion of depth to depth should be as that of weight to weight which is to 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 sinking deeper it is heavier. And this is proved because these layers are composed of the turbid matter of the waters discharged into the sea by the course of the rivers that pour into it. Of that turbid matter, the heavier part was that which first settled successively. And this the water does where it comes to rest, lifting first where it moves. And these layers of earth are revealed in the banks of the rivers which, with their continual courses, have cut and divided one mountain from another with great depth of cuts, where through the gravelly layers the waters have drained, and for this the material has dried and turned into hard stone, especially that of the finer mud. And this leads us to conclude that every part of the earth's surface was once the centre of the earth, and so conversely, etc.

On the fissures of walls that are wide at the foot and narrow at the head, 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 is built in contact with a damp hill and the rest remains in contact with the air; for then the rest shrinks in every direction, while the moist part keeps its first size. And then what dries in the air shrinks and diminishes, and what is kept damp does not dry, and the dry part readily breaks away from the damp, because that damp part has no tenacity to follow the motion of what is continually drying. On arched cracks, wide above and narrow below. Those arched cracks, wide above and narrow below, arise in walled-up doorways that settle more in their height than in their width, in proportion as the height is greater than the width, and in proportion as the mortar joints are more numerous in the height than in the width.

The crack diminishes as much less in r o than in m n as there is less material between r o than in 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 drawn at the side. 1st: whatever is moistened grows by as much as the moisture acquired. 2nd: and every moist thing shrinks in drying by as much as the moisture that separates from it.