Let the cornice at Fig. 244 be the given cornice. Upon any point in the lowest line of the lowest member, as at a, with the height of the required cornice for radius, describe an intersecting arc across the uppermost line, as at b; join a and b; then b 1 will be the perpendicular height of the upper fillet for the proposed cornice, 1 2 the height of the crown moulding - and so of all the members requiring to be enlarged to the sizes indicated on this line. For the projection of the proposed cornice, draw a d at right angles to a b, and c d at right angles to b c; parallel with c d draw lines from each projection of the given cornice to the line ad; then ed will be the required projection for the proposed cornice, and the perpendicular lines falling upon c d will indicate the proper projection for the members.
To proportion a cornice according to a larger given cornice, let A (Fig. 245) be the given cornice. Extend a o to b, and draw c d at right angles to a b; extend the horizontal lines of the cornice, A, until they touch o d; place the height of the proposed cornice from o to e, and join f and e; upon o, with the projection of the given cornice, o a, for radius, describe the quadrant ad; from d draw db parallel to fe; upon o, with o b for radius, describe the quadrant b c; then o c will be the proper projection for the proposed cornice. Join a and c; draw lines from the projection of the different members of the given cornice to ao parallel to od; from these divisions on the line a o draw lines to the line o c parallel to a c; from the divisions on the line of draw lines to the line oe parallel to the line fe; then the divisions on the lines o e and o c will indicate the proper height and projection for the different members of the proposed cornice. In this process, we have assumed the height, o e, of the proposed cornice to be given; but if the projection, o c, alone be given, we can obtain the same result by a different process. Thus: upon o, with oc for radius, describe the quadrant c b; upon o, with o a for radius, describe the quadrant ad; join d and b; from f draw fe parallel to db: then oe will be the proper height for the proposed cornice, and the height and projection of the different members can be obtained by the above directions. By this problem, a cornice can be proportioned according to a smaller given one as well as to a larger; but the method described in the previous article is much more simple for that purpose.