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"The lower ones," says Vitruvius (book 5, ch. 1). A remarkable precept, in my opinion, and so remarkable that perhaps it would be more consistent, according to his own principles, to make them a fourth part larger. For in book 3, chapter 2, where the master deals with the tapering of columns, we have an optical rule: the higher they are, the lesser their upper tapering ought to be, because the eye itself naturally contracts objects, more or less, in proportion to the distance; which consideration might appear to be neglected in the caution we have just given. But Vitruvius (the best interpreter of himself), in the aforementioned place in the fifth book, well resolves his intent with these words: The upper columns are to be made a fourth part smaller than the lower ones, because those which are lower ought to be firmer for supporting the load: preferring, as a wise mechanic, natural reason to mathematical and subtle concepts abstracted [from nature]. And yet, in book 4, chapter 4, he again seems to affect subtlety, conceding that columns, the more they are fluted, can be the more slender: because the eye, he says, by touching more numerous and frequent signs, wanders through a greater circuit of vision. The whole object appears larger, and thus, as much as those cavities take away, so much is supplied by the deception of vision. But here, too, I think the master ought to have considered natural inconvenience more; for although columns may appear to us to be made thicker by the duct of the flutings, yet in reality they are weaker in themselves, and therefore, perhaps, if you weigh the matter well, it would have been fitting for them not to be more slender, but more corpulent; unless appearance outweighs truth. But one must not dispute with the Master.
The third caution is that the projecturae (as they are called) should be very moderate, especially the cornices of the lower orders. For while some think they are giving them a beautiful and regal appearance through amplitude, they sometimes impede the interior light (of which I shall say more in its proper place), and also detract from the appearance of the exterior facade; as appears in one of the principal structures in Venice, namely, the Palace Grimani on the Grand Canal, which is somewhat disfigured by this magnificent error. There is no need now to say more about columns and their adjuncts, concerning which architects are so prolix in their writings, as if the very terms of epistylia, zophori, cornices, and the like were sufficient for graduating the masters of this art. But allow me, before I proceed to another subject, to head off a familiar objection. It will perhaps be said that all this doctrine regarding the five orders better suits the stone quarries of Asia, which provided 127 columns, 60 feet high, for the Ephesian temple; or those of Numidia, where marbles abound; rather than English wits, who are forced to be content with less noble materials. To which I reply that this ought not to deter our own people: for I have often contemplated with the greatest pleasure in Venice the Atrium Graecum (we may interpret it as an anti-portico in the Greek manner) constructed by Andrea Palladio above eight columns of the composite order; the bases are of stone without stylobates, the shafts or bodies are of mere bricks, three and a half feet in the lower diameter, and consequently thirty feet high, as he himself described in his second book. I have never seen such magnificent columns of stone or marble: for the bricks were first formed circularly, and then, before they were burned, cut into four or more parts; the sides of which are afterwards joined so tightly, and the wedges meet so exactly in one center, that the columns appear to be made from a single stone. This brief description I did not wish to pass over, so that it might appear that we are lacking in art rather than material to satisfy our desires.
Following the columns in my distribution are the Antae (commonly pilasters), of which Vitruvius makes mention in book 5, chapter 1, and scarcely anywhere else, under the name parastadae, as Philander opines; which grammatical argument (though perhaps not sufficiently clear) I do not wish to examine at length. What thing is being designated is plain from the idiom.