This section is from the book "The Building Trades Pocketbook", by International Correspondence Schools. Also available from Amazon: Building Trades Pocketbook: a Handy Manual of reference on Building Construction.
The outlines of the Greek moldings follow the curves of the conic sections - the parabola, hyperbola, and the ellipse - and but rarely the circle. The Roman moldings are nearly always formed of circular arcs, and for this reason lack the delicacy and refinement that characterize the details of the Grecian monuments.
Greek moldings may be divided into three classes, according to the number of curves composing their outlines. In the first class are the following:
The ovolo, echinus, or quarter-round is shown at (a) Fig. 4. The point b, direction of the axis ax, and the coordinates d a and a b, must be determined before the curve - which is part of a hyperbola - can be traced. Divide a b and b c into the same number of equal parts, and take the point x anywhere on the line a x - generally at a distance of from one to three times a d from d, according to the curve required. Draw lines as shown, and trace the curve through the intersections. It is well to assume a point o through which the curve must pass, and draw a line from 3 through o, thus fixing the point x.
The cavetto or cove (6) is one-quarter of an ellipse. Let a c and a b be the required height and depth for the cove b c. Draw the large semicircle ce with a radius equal to ac, and the small semicircle b g with a radius equal to a b. Draw any radius, as a, g, e. From g erect a perpendicular, and from e draw a horizontal line intersecting at d, a point on the ellipse. Other points may be similarly found.
The scotia (c) is also an elliptic curve, having axes inclined to the vertical; it may be drawn as shown for the cavetto.
The torus (d) is also part of an ellipse, in which two points d and c are given, throughwhich the ellipse must pass. Draw e h at any desired inclination through d. With any point as a as a center describe a semicircle passing through d. Draw cm perpendicular to eh: cn parallel to eh, and amn cutting
Fig 4 c n at n. Then the large circle must pass through n. With a as a center, and an as a radius, draw the outside circle, and complete the ellipse as before shown.
In the second class, composed of two curves, are the following:
The cyma recta, shown at (e), is often made up of two arcs of parabolas. Make a b equal to the required height, also a e and b c, each equal to one-half of the required depth. Divide ad,ae,bd, and 6 c into the same number of equal parts. Draw parallels to ab; also, the lines radiating from c and e, as shown. The curves may then be traced through the intersections. This molding, when more deeply cut, is sometimes made up of two reversed arcs of ellipses.
The cyma reversa (f) is often formed of reversed elliptic arcs. The inclination of the axis a b may be taken to suit the curve required. Through d draw d c perpendicular to a b; with d c as a semimajor axis, and any suitable length, as c h, as a semiminor axis, draw the quarter ellipse d h. Through e draw cf parallel to d c, giving f as the center of the second ellipse. With f as center, and fh and fe as radii, draw the inside and outside circles, and complete the curve with the quarter ellipse he.
The third class of moldings are those consisting of three curves, and are generally made up of arcs of circles combined with arcs of ellipses. The bird's-beak molding, shown at g, belongs to this class. The principal curve cad is an arc of a hyperbola. The arcs of the circles fk and ke have their centers on the line kg, and are tangent. The arc fm is a quarter ellipse.
Accessory moldings which may be used in connection with all the forms described are the fillet, which is the simple square band shown, crowning the cavetto in (6), and the bead, which is the small rope-like molding, rather more than a semicircle in section, shown at the base of the ovolo (a).