entagon. The angles at 1 2 will each be 72 deg, double that
at _A_, which is 36 deg.

[Illustration: Fig. 220.]

CXXI

THE PYRAMID

Nothing can be more simple than to put a pyramid into perspective. Given
the base (_abc_), raise from its centre a perpendicular (_OP_) of the
required height, then draw lines from the corners of that base to a
point _P_ on the vertical line, and the thing is done. These pyramids
can be used in drawing roofs, steeples, &c. The cone is drawn in the
same way, so also is any other figure, whether octagonal, hexangular,
triangular, &c.

[Illustration: Fig. 221.]

[Illustration: Fig. 222.]

[Illustration: Fig. 223.]

[Illustration: Fig. 224.]

CXXII

THE GREAT PYRAMID

This enormous structure stands on a square base of over thirteen acres,
each side of which measures, or did measure, 764 feet. Its original
height was 480 feet, each side being an equilateral triangle. Let us see
how we can draw this gigantic mass on our little sheet of paper.

In the first place, to take it all in at one view we must put it very
far back, and in the second the horizon must be so low down that we
cannot draw the square base of thirteen acres on the perspective plane,
that is on the ground, so we must draw it in the air, and also to a very
small scale.

Divide the base _AB_ into ten equal parts, and suppose each of these
parts to measure 10 feet, _S_, the point of sight, is placed on the left
of the picture near the side, in order that we may get a long line of
distance, _S 1/2 D_; but even this line is only half the distance we
require. Let us therefore take the 16th distance, as shown in our
previous illustration of the lighthouse (Fig. 92), which enables us to
measure sixteen times the length of base _AB_, or 1,600 feet. The base
_ef_ of the pyramid is 1,600 feet from the base line of the picture, and
is, according to our 10-foot scale, 764 feet long.

The next thing to consider is the height of the pyramid. We make a scale
to the right of the picture measuring 50 feet from _B_ to 50 at point
where _BP_ intersects base of pyramid, raise perpendicular _CG_ and
thereon measure 480 feet. As we cannot obtain a palpable square on the
ground, let us draw one 480 feet above the ground. From _e_ and _f_
raise verticals _eM_ and _fN_, making them equal to perpendicular _G_,
and draw line _MN_, which will be the same length as base, or 764 feet.
On this line form square _MNK_