arallel to base _AB_. Then through the points thus obtained draw the
circle as shown in this figure, which also shows us how the
circumference of a circle in perspective may be divided into any
number of equal parts.

[Illustration: Fig. 175.]

XCIV

HOW TO DIVIDE A PERSPECTIVE CIRCLE INTO ANY NUMBER OF EQUAL PARTS

This is simply a repetition of the previous figure as far as its
construction is concerned, only in this case we have divided the
semicircle into twelve parts and the perspective into twenty-four.

[Illustration: Fig. 176.]

[Illustration: Fig. 177.] We have raised perpendiculars from the
divisions on the semicircle, and proceeded as before to draw lines to
the point of sight, and have thus by their intersections with the
circumference already drawn in perspective divided it into the required
number of equal parts, to which from the centre we have drawn the radii.
This will show us how to draw traceries in Gothic windows, columns in a
circle, cart-wheels, &c.

The geometrical figure (177) will explain the construction of the
perspective one by showing how the divisions are obtained on the line
_AB_, which represents base of square, from the divisions on the
semicircle _AKB_.

XCV

HOW TO DRAW CONCENTRIC CIRCLES

[Illustration: Fig. 178.]

First draw a square with its diagonals (Fig. 178), and from its centre
_O_ inscribe a circle; in this circle inscribe a square, and in this
again inscribe a second circle, and so on. Through their intersections
with the diagonals draw lines to base, and number them 1, 2, 3, 4, &c.;
transfer these measurements to the base of the perspective square (Fig.
179), and proceed to construct the circles as before, drawing lines from
each point on the base to the point of sight, and drawing the curves
through the inter-sections of these lines with the diagonals.

[Illustration: Fig. 179.]

Should it be required to make the circles at equal distances, as for
steps for instance, then the geometrical plan should be made
accordingly.

Or we may adopt the method shown at Fig. 180, by taking quarter base of
both outer and inner square, and finding the measurement _mn_ on each
side of _C_, &c.

[Illustration: Fig. 180.]

XCVI

THE ANGLE OF THE DIAMETER OF THE CIRCLE IN ANGULAR
AND PARALLEL PERSPECTIVE

The circle, whether in angular or parallel perspective, is always an
ellipse. In angular perspective the angle of the circle's di