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There is no need to speak of mixed figures, partly circular and partly angular, because having already dealt with the simple ones, the mixed ones, according to their composition, share the same relationships. There is only one objection against them, namely that they offend uniformity; concerning which, therefore, something must be said regarding the external aspect, with which we are now concerned. In architecture, two contrary tendencies might be seen—uniformity and variety—which, however, can be reconciled with one another, as can be seen in the great exemplar of Nature, to which I must often return. For no structure can be more uniform than that of our own body in its entire configuration, with both sides corresponding as much in number as in quality and measure of parts; and yet some parts are round, like the arms, others flat, like the hands, some convex, and some concave, so that we see that diversity does not destroy uniformity; and the members of a noble structure can correspond quite well, even though they are varied, provided we do not proceed to certain extravagant inventions, of which I shall speak more broadly when I come to the division of the whole work. One must also beware of enormous heights of six or seven stories, just as one must beware of irregular figures; and, conversely, one must beware of low, wide facades, which are unattractive; and again, that the face of the structure should not be narrow and the belly deep. Certain nations or cities are addicted to these extremes, whose names may civilly be passed over in silence. And this is sufficient concerning the general configuration or aspect of the work.
Now concerning the individual parts. All the parts of a structure can be reduced to five heads, which division I have accepted from Baptista Alberti, so that I may attribute to him what is his own. These are: Foundation, Walls, Openings or apertures, Compartition, Roof. Regarding these, I have proposed to gather the principal cautions and, in passing, to touch upon the reasons of natural Art, so that my discourse may appear less mechanical.
First, therefore, regarding the foundation, it requires the most exact care; for if it happens to sink, it will disturb all the pleasure of the house. Therefore, so that we may well lay the foundation of our habitation, we must first consider the bed (so to speak) of the soil upon which we intend to build, and then the substructure, as the Ancients call it. Regarding the first, we have a general precept in Vitruvius, repeated twice by him as a matter of great importance: first in book I, chapter 5, and again more aptly in book III, chapter 3, in these words, as Philander well corrected the common texts: Let the foundations of the substructure be dug, if they can be found, to the solid and into the solid. By these words, I judge him to recommend not only a diligent but also a zealous examination of what the soil can bear, warning us that we should not acquiesce to an apparent solidity unless the entire earth that we dig is similarly solid. But how deeply one should proceed in this investigation, he nowhere determined, if I remember correctly, because perhaps this depends more upon prudence than upon a certain rule, according to the weight of the structure. Andrea Palladio, however, has beautifully attempted to reduce it to rules, allowing for this digging (which he calls Cavazione) the sixth part of the height of the entire structure; except if there are cellars under the ground, for then (as it seems) he would wish us to dig a little deeper. Some Italians prescribe: after we have chosen the area and extended the limits of the work, first to dig wells and cisterns and other subterranean conduits, and sewers for discharging the filth of the house, with a double benefit; for both the nature of the soil is safely detected, and the openings serve to evacuate such vapors which, having no other exit, could perhaps shake the structure. And this is sufficient concerning the Foundation, which, although it is not a part of the solid fabric, was nevertheless an opportune place here to treat of it.
There follows the Substructure, or foundation of the entire building, which supports the walls; and it is an artificial foundation, just as the former was natural. In which these things are chiefly to be noted: first, that the ground be exactly leveled; whence the Italians for the most part...