responding to the thickness that has been determined for the
substructure, and then gradually diminish in extent so that at the
surface their projection is equal to the thickness of the wall of the
building.

[Illustration: RETAINING WALLS

(From the edition of Vitruvius by Fra Giocondo, Venice 1511)]

7. Furthermore, inside, to meet the mass of earth, there should be
saw-shaped constructions attached to the wall, the single teeth
extending from the wall for a distance equivalent to what is to be the
height of the substructure, and the teeth being constructed with the
same thickness as the wall. Then at the outermost angles take a distance
inwards, from the inside of the angle, equal to the height of the
substructure, and mark it off on each side; from these marks build up a
diagonal structure and from the middle of it a second, joined on to the
angle of the wall. With this arrangement, the teeth and diagonal
structures will not allow the filling to thrust with all its force
against the wall, but will check and distribute the pressure.

8. I have now shown how buildings can be constructed without defects,
and the way to take precautions against the occurrence of them. As for
replacing tiles, roof timbers, and rafters, we need not be so particular
about them as about the parts just mentioned, because they can easily be
replaced, however defective they may become. Hence, I have shown by what
methods the parts which are not considered solid can be rendered
durable, and how they are constructed.

9. As for the kind of material to be used, this does not depend upon the
architect, for the reason that all kinds of materials are not found in
all places alike, as has been shown in the first book. Besides, it
depends on the owner whether he desires to build in brick, or rubble
work, or dimension stone. Consequently the question of approving any
work may be considered under three heads: that is, delicacy of
workmanship, sumptuousness, and design. When it appears that a work has
been carried out sumptuously, the owner will be the person to be praised
for the great outlay which he has authorized; when delicately, the
master workman will be approved for his execution; but when proportions
and symmetry lend it an imposing effect, then the glory of it will
belong to the architect.

10. Such results, however, may very well be brought about when he allows
himself to take the advice both of workmen and of laymen. In fact, all
kinds