hich is a very clumsy and
unscientific way of setting to work. The architects in such cases make
use of the centrolinead, a clever mechanical contrivance for getting
over the difficulty of the far-off vanishing point, but by the method
I have shown you, and shall further illustrate, you will find that you
can dispense with all this trouble, and do all your perspective either
inside the picture or on a very small margin outside it.

Perhaps another drawback to this method is that it is not self-evident,
as in the former one, and being rather difficult to explain, the student
is apt to take it on trust, and not to trouble about the reasons for its
construction: but to show that it is equally correct, I will draw the
two methods in one figure.

LXIII

TWO METHODS OF ANGULAR PERSPECTIVE IN ONE FIGURE

[Illustration: Fig. 125.]

It matters little whether the station-point is placed above or below the
horizon, as the result is the same. In Fig. 125 it is placed above, as
the lower part of the figure is occupied with the geometrical plan of
the other method.

In each case we make the square _K_ the same size and at the same angle,
its near corner being at _A_. It must be seen that by whichever method
we work out this perspective, the result is the same, so that both are
correct: the great advantage of the first or geometrical system being,
that we can place the square at any angle, as it is drawn without
reference to vanishing points.

We will, however, work out a few figures by the second method.

LXIV

TO DRAW A CUBE, THE POINTS BEING GIVEN

As in a previous figure (124) we found the various working points of
angular perspective, we need now merely transfer them to the horizontal
line in this figure, as in this case they will answer our purpose
perfectly well.

[Illustration: Fig. 126.]

Let _A_ be the nearest angle touching the base. Draw AV1, AV2. From
_A_, raise vertical _Ae_, the height of the cube. From _e_ draw eV1,
eV2, from the other angles raise verticals _bf_, _dh_, _cg_, to meet
eV1, eV2, fV2, &c., and the cube is complete.

LXV

AMPLIFICATION OF THE CUBE APPLIED TO DRAWING A COTTAGE

[Illustration: Fig. 127.]

Note that we have started this figure with the cube _Adhefb_. We have
taken three times _AB_, its width, for the front of our house, and twice
_AB_ for the side, and have made it two cubes high, not counting the
roof. Note also the use of the measuring-poi