parallel to the perspective plane, find
its centre _O'_ by means of diagonals, and _O'_ will be the central
height of the pyramid and exactly over the centre of the base. From this
point _O'_ draw sloping lines _O'f_, _O'e_, _O'Y_, &c., and the figure
is complete.

Note the way in which we find the measurements on base of pyramid and on
line _MN_. By drawing _AS_ and _BS_ to point of sight we find _Te_,
which measures 100 feet at a distance of 1,600 feet. We mark off seven
of these lengths, and an additional 64 feet by the scale, and so obtain
the required length. The position of the third corner of the base is
found by dropping a perpendicular from _K_, till it meets the line _eS_.

Another thing to note is that the side of the pyramid that faces us,
although an equilateral triangle, does not appear so, as its top angle
is 382 feet farther off than its base owing to its leaning position.

CXXIII

THE PYRAMID IN ANGULAR PERSPECTIVE

In order to show the working of this proposition I have taken a much
higher horizon, which immediately detracts from the impression of the
bigness of the pyramid.

[Illustration: Fig. 225.]

We proceed to make our ground-plan _abcd_ high above the horizon instead
of below it, drawing first the parallel square and then the oblique one.
From all the principal points drop perpendiculars to the ground and thus
find the points through which to draw the base of the pyramid. Find
centres _OO'_ and decide upon the height _OP_. Draw the sloping lines
from _P_ to the corners of the base, and the figure is complete.

CXXIV

TO DIVIDE THE SIDES OF THE PYRAMID HORIZONTALLY

Having raised the pyramid on a given oblique square, divide the vertical
line OP into the required number of parts. From _A_ through _C_ draw
_AG_ to horizon, which gives us _G_, the vanishing point of all the
diagonals of squares parallel to and at the same angle as _ABCD_. From
_G_ draw lines through the divisions 2, 3, &c., on _OP_ cutting the
lines _PA_ and _PC_, thus dividing them into the required parts. Through
the points thus found draw from _V_ all those sides of the squares that
have _V_ for their vanishing point, as _ab_, _cd_, &c. Then join _bd_,
_ac_, and the rest, and thus make the horizontal divisions required.

[Illustration: Fig. 226.]

[Illustration: Fig. 227.]

The same method will apply to drawing steps, square blocks, &c., as
shown in Fig. 227, which is at the same angle as th