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As a general rule, the corinthian column, with its base and capital, should be IX parts high. Its capital is to be as tall as the thickness of the column, in the lower part. However its base should be half that.
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The Corinthian capital was derived from a Corinthian maid. I am not going to expend any further effort telling teh story of the capital's origin because Vitruvius does it in the first chapter of his fourth book.
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the height of the Corinthian capital should be the same as the width of the column at the bottom, and the abacus is to be a seventh of the whole height. As for the remainder it should be divided up into three parts: one for the leaves at the bottom, the next given to the leaves in the middle, the third should be set out for the caulcoles (what we mean is the stalks). Between these stalks and the leaves in the middle a space should be left for the small leaves from which the caulcoles sprout. Having formed the bare capital marked B - which should be the same width at the bottom as the column is at the top - under the abacus is to be carved a collar, or rather a belt, which should be half the abacus in height. Once the abacus had then been divided up into three parts, one is to be for the cymatium with its collar and the other two should be for the abacus. Under the four corners of the abacus the large caulcoles are to be carved. In the centre of the abacus there should be a flower of the same height, under which are to be carved the small caulcoles. Under the large caulcoles - and also uner the small ones - the middle leaves should be carved. Between these should sprout the small leaves, and from the small leaves should sprout the caulcoles. The middle leaves should be viii in number - as should those below - arranged in the way shown in the figure C. The width of the abacus from corner to corner, by a diagonal line, should be two diameters of the column at the bottom. Having placed the bottom of the column insaide a square, draw a larger circle around it touching the four corners; having drawn outside that larger circle another square divided by diagonal lines, it will demonstrate that the said lines are two column width in length, as the text of Vitruvius says. However, drawing a perfect triangle on the line B,C, towards the corner X, will give the point for making the curve of the abacus, that is, for hollowing it out. Make the part which is between the larger circle and the smaller circle into fout parts. One is to remain above the letter A and three should be removed in this way: having placed the point of a pair of compasses on the point X and the other point above A, arc from B to C; where the curved line intersects with the two sides of the triangle are to be the edges of the horns of the capital. The example of this is in figure D. In this way the abacus turns out plumb with the socle of the base, with the result that there will be no line drawn without a purpose - on the contrary, all of the lines will be directed by geometrical theory and proven.Concerning the Corinthian architrave, frieze and cornice, Vitruvius gives no measurements whatsoever (as I said at the beginning of this chapter), although he mentions the origin of the modillons which can be used on every style of cornice, as can be seen from antiquity. However, in order to proceed modestly, not departing too much from the text of Vitruvius, I would place Ionic ornaments above the Corinthian capital, adding astragals to the architrave and an ovolo under the corona - which is what some modest Roman architects did.
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