This section is from the book "Cyclopedia Of Architecture, Carpentry, And Building", by James C. et al. Also available from Amazon: Cyclopedia Of Architecture, Carpentry And Building.
Of these two methods the lower is more appropriate to buildings of tremendous size, such as those erected by the Romans; while the Renaissance method of Serlio would be more appropriate for use on modern work. In this illustration it will be seen that the radius of the arc that determines the upper point of the pediment, and therefore its height, is found as indicated, by measuring down on the center line, from a point at the height of the top member of the cornice, a distance equal to one-half the pediment width, and then, with the point thus obtained as a center, striking a circle passing through the two ends of this same member. The intersection of this circle with the perpendicular center line of the pediment, gives the center for the arc that determines the pediment height.
In the method of Vitruvius, the entire width across the face of the pediment is divided into nine parts; and the distance of one of these parts is given to the plain face or tympanum of the pediment at the center. By dividing the width into eight instead of nine parts, a tympanum height on the center line would be obtained that would be approximately midway between those shown in these two methods.