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 CUKVES OF THE HORIZONTAL LINES.

97

1st. Determine the angle B1, contained by the chords
B2BJ and BB1, from the form, log. tan. A = log.
31. r + log- a — log. b.; given a = B% and b =. h B1.

2nd. Bisect the chord B^1 in /, and trace the line
fgO at right angles to B2B\ and determine the
hypothenuse gBl of the triangle fBlg, from the
form, log. c = 10 + log. b — log. cos. A; given
/B1 = b, the angle fBlg = A, required c = ^B1;
Jig = KB1 — gB\ the angle hOg = angle B*B}h.

3rd. Determine the side hO, from the form, log. a -
log. b + log. tan. A — 10 ; given b = hg, angle A
= angle hgO = angle fgB1; required hO = a.

4th. The radius of the Upper Step = OB1 = fOh? + hB* = r, and the equation to the circle

when referred to the centre 0, is x = r r — y%. The vertical rise of the curve of the
Upper Step for any given point above the chord BB1 =x — Oh.

Given Bit «* 0'220 feet | angle B1
„ hBl = 50-668 „ j ^B1

hg
Angle hgO
Radius of Upper Step = OB1

x — Oh

Etc.

Example.—The Upper Step of the Parthenon.

0° 17' IF

21-809

28-859

89° 42; 49", angle hOg = 0° 17' ll/;, 7*0 = 5779'2 feet.

*/5779-22 + 50-6682 = 5779*422 feet = r.

5779-422 ft.-5779'2 ft. = 0*22 ft. = rise of Upper Step in

centre.
Etc.

Etc.

Fig. 4.—The Curved Lines in the Entablature and Pediment.

When the curve of the Architrave of the Parthenon is rectified, we find that it agrees
in all respects with the rise of the curve of the Upper Step, and that what Vitruvius has stated
is correct, namely, " that the Architrave will deviate from the straight line drawn from the
" extreme points, in proportion to the addition given to the centre of the Stylobate; " therefore
the columns are all executed of the same height, and the curve of the Architrave is identical
with the curve of the Upper Step, and the line of the Cornice naturally follows the curved line
of the Architrave.

The curved line of the Cornice being traced, this is found to regulate the lines in the
Cornice of the Pediment, for making in Fig. 4 the vertical lines a'b' = ab, c'cT = cd, e'f = ef,