ation: Fig. 186.]

C

APPLICATION OF PREVIOUS PROBLEM

That is, to draw a circle above a circle. In Fig. 187 can be seen how by
means of the vanishing scale at the side we obtain the height of the
verticals 1, 2, 3, 4, &c., which determine the direction of the upper
circle; and in this second figure, how we resort to the same means to
draw circular steps.

[Illustration: Fig. 187.]

[Illustration: Fig. 188.]

CI

DORIC COLUMNS

It is as well for the art student to study the different orders of
architecture, whether architect or not, as he frequently has to
introduce them into his pictures, and at least must know their
proportions, and how columns diminish from base to capital, as shown in
this illustration.

[Illustration: Fig. 189.]

CII

TO DRAW SEMICIRCLES STANDING UPON A CIRCLE AT ANY ANGLE

[Illustration: Fig. 190.]

Given the circle _ACBH_, on diagonal _AB_ draw semicircle _AKB_, and on
the same line _AB_ draw rectangle _AEFB_, its height being determined by
radius _OK_ of semicircle. From centre _O_ draw _OF_ to corner of
rectangle. Through _f'_, where that line intersects the semicircle, draw
_mn_ parallel to _AB_. This will give intersection _O'_ on the vertical
_OK_, through which all such horizontals as _m'n'_, level with _mn_,
must pass. Now take any other diameter, such as _GH_, and thereon raise
rectangle _GghH_, the same height as the other. The manner of doing this
is to produce diameter _GH_ to the horizon till it finds its vanishing
point at _V_. From _V_ through _K_ draw _hg_, and through _O'_ draw
_n'm'_. From _O_ draw the two diagonals _og_ and _oh_, intersecting
_m'n'_ at _O_, _O_, and thus we have the five points _GOKOH_ through
which to draw the required semicircle.

CIII

A DOME STANDING ON A CYLINDER

[Illustration: Fig. 191.]

This figure is a combination of the two preceding it. A cylinder is
first raised on the circle, and on the top of that we draw semicircles
from the different divisions on the circumference of the upper circle.
This, however, only represents a small half-globular object. To draw the
dome of a cathedral, or other building high above us, is another matter.
From outside, where we can get to a distance, it is not difficult, but
from within it will tax all our knowledge of perspective to give it
effect.

We shall go more into this subject when we come to archways and vaulted
roofs, &c.

CIV

SECTION