Pennethorne, John; Robinson, John [Ill.]: The geometry and optics of ancient architecture: illustrated by examples from Thebes, Athens, and Rome (London [u.a.], 1878)

THE COLUMNS, wi

the minor axis Bfr in 0, which becomes the centre of the ellipse, and through 0 trace the
major axis WV, and with these given elements construct the ellipse BW6V.

The second elliptical line, fr'V, is the arc of an ellipse, similar to the one already
described, varying only in the position of the centre Of and the axis major O'V.

PLATE VII.

THE VOLUTE OF THE CAPITAL OF THE IONIC COLUMN IN THE

VESTIBULE OF THE PROPYL^A.

The designing of the Ionic capitals is found to vary in every example in the adjustment
of the proportions and of the details, the same as in the capitals of the Doric order, for we
find that the Greek Architects never copied the designs of each other in the arrangement of
the details, but the leading principles, of laying down the masses of the capitals first in
aliquot parts, of designing the spiral lines within rectangular lines given in position and in
dimension, and of tracing all the curved lines of the capital as true mathematical curves, are
found to be the same in every example. Thus, in the Ionic capital of the Propylsea—

Fig. 1. Shows the first given proportions of the masses of the capital, figured in moduli
derived from the general proportions of the Column; also the proportions of the first
parallelogram, ABDC, within which the volute has to be designed, are also given in
position and in dimension. The given ratio of the sides of this first parallelogram,
BD : AB, is as 6 : 7.

Fig. 2. Shows the given proportions of the rectangular lines, forming the boundary of the
No. 1 guiding spiral line of the volute. The method by which they are proportioned
has been already explained. These rectangular lines fix, both in position and in
dimension, the three parallelograms, ABDC, AB'D'C, AWC", within which the
three revolutions of the No. 1 guiding spiral line of the volute are described,
according to the method already given. (See Plate VI.)

Fig. 3. Shows the volute drawn to one half of the real size. The No. 1 guiding spiral line
being given, there still remain the No. 2 and No. 3 spiral lines of the volute to be
described, and these appear in all cases to be regulated by the No. 1 spiral line;
thus the ratio of the sides of the first parallelogram, ABDC, BD : AB is as 6 : 7,
reducing this ratio to a smaller modulus; and, in the case of the volute of the
Propylaea, multiplying by 9 for laying down the details, then BD : AB is as 54 : 63
moduli.