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

48

THE APPABENT PROPORTIONS,

" parts of a building, and the pleasing effect of the same, keeping in view its appropriate
" character. It is divisible into three heads, which, considered together, constitute design;
" they are called Ichnography, Orthography, and Scenography.

" The first is the representation on a plane (XY, Fig. 1) of the ground plan of the work.

" The second is the elevation of the front and the return side (on the planes ZY, ZX).

" The third is the front and a receding side, the lines being drawn to their proper

vanishing points (namely, a perspective view showing the shadows and colours); these three

are the result of thought and invention. Thought is an effort of the mind ever incited by the

pleasure attendant on success in compassing an object. Invention is the effect of this effort,

which throws a new light on things the most recondite, and produces them to answer the

intended purpose." Book I., Chapter I.—" Arithmetic, assisted by the laws of Geometry,

determines those abstruse questions wherein the different proportions of some parts to others

" are involved."

The three heads into which Yitruvius divides this part of the Theory of Design may be

denned as follows:—

1st. Ichnography—the projection of the
plan upon the given horizontal plane XY,Fig. 1,
and the calculating and the drawing of all the
imaginary lines and angles that will be required
to be traced on this plane XY during the pro-
gress of the calculations for clearing the given
design of all apparent irregularities.

a

a

a

a

a

t(

PerpendzcuZccr
plasv&Y ■ Z -

ORTHORGRAPHY

p2

PerperujLicixLcw plane/X Z,

2nd. Orthography—the fixing of all the
points, as they are gradually determined by
calculation, upon the two given perpendicular
planes YZ and XZ, Fig. 1, so that when a
sufficient number of points composing the
figure in relief have been calculated, and the
projection of each point fixed upon the planes
XY, YZ, XZ, each point in space will be
determined by the intersection of two horizontal co-ordinates at right angles to each of the
planes YZ and XZ ; for example, the point M, the vertex of the Upper Step, is determined
in position by the intersection of the ordinates MM1 and MM2 and P by the intersection of the
ordinates PP1 and PP2.

Let XY always denote the horizontal plane passing through the point of sight 0. Let
XZ and YZ be two planes parallel to the front and to the return sides of the design, visible from
the point of sight 0. These two planes will be each of them perpendicular to the horizontal
plane XY, and will each of them pass through the point of sight 0; By means of these three