re _HS_ and _DC_, however far they may be produced
and however close they may appear to get, can never meet.

[Illustration: Fig. 41.]

Fig. 41 is a perspective view of the same figure--but more extended. It
will be seen that a line drawn from the tenth upright _K_ to _S_ cuts
off a tenth of _AB_. We look then upon these two lines _SP_, _OP_, as
the sides of a long parallelogram of which _SK_ is the diagonal, as
_cefd_, the figure on the ground, is also a parallelogram.

The student can obtain for himself a further illustration of this rule
by placing a looking-glass on one of the walls of his studio and then
sketching himself and his surroundings as seen therein. He will find
that all the horizontals at right angles to the glass will converge to
his own eye. This rule applies equally to lines which are at an angle to
the picture plane as to those that are at right angles or perpendicular
to it, as in Rule 7. It also applies to those on an inclined plane, as
in Rule 8.

[Illustration: Fig. 42. Sketch of artist in studio.]

With the above rules and a clear notion of the definitions and
conditions of perspective, we should be able to work out any proposition
or any new figure that may present itself. At any rate, a thorough
understanding of these few pages will make the labour now before us
simple and easy. I hope, too, it may be found interesting. There is
always a certain pleasure in deceiving and being deceived by the senses,
and in optical and other illusions, such as making things appear far off
that are quite near, in making a picture of an object on a flat surface
to look as if it stood out and in relief by a kind of magic. But there
is, I think, a still greater pleasure than this, namely, in invention
and in overcoming difficulties--in finding out how to do things for
ourselves by our reasoning faculties, in originating or being original,
as it were. Let us now see how far we can go in this respect.

VIII

A TABLE OR INDEX OF THE RULES OF PERSPECTIVE

The rules here set down have been fully explained in the previous pages,
and this table is simply for the student's ready reference.

RULE 1

All straight lines remain straight in their perspective appearance.

RULE 2

Vertical lines remain vertical in perspective.

RULE 3

Horizontals parallel to the base of the picture are also parallel to
that base in the picture.

RULE 4

All lines situated in a plane that is parallel to the pic