perceives that the lines he makes hide,
or coincide with, the outlines of the object. And then by putting a
sheet of paper on the other side of the glass, it is made manifest to
him that the lines he has thus drawn represent the object as he saw it.
They not only look like it, but he perceives that they must be like it,
because he made them agree with its outlines; and by removing the paper
he can convince himself that they do agree with its outlines. The fact
is new and striking; and serves him as an experimental demonstration,
that lines of certain lengths, placed in certain directions on a plane,
can represent lines of other lengths, and having other directions, in
space. By gradually changing the position of the object, he may be led
to observe how some lines shorten and disappear, while others come into
sight and lengthen. The convergence of parallel lines, and, indeed, all
the leading facts of perspective, may, from time to time, be similarly
illustrated to him. If he has been duly accustomed to self-help, he will
gladly, when it is suggested, attempt to draw one of these outlines on
paper, by the eye only; and it may soon be made an exciting aim to
produce, unassisted, a representation as like as he can to one
subsequently sketched on the glass. Thus, without the unintelligent,
mechanical practice of copying other drawings, but by a method at once
simple and attractive--rational, yet not abstract--a familiarity with
the linear appearances of things, and a faculty of rendering them, may
be step by step acquired. To which advantages add these:--that even thus
early the pupil learns, almost unconsciously, the true theory of a
picture (namely, that it is a delineation of objects as they appear when
projected on a plane placed between them and the eye); and that when he
reaches a fit age for commencing scientific perspective, he is already
thoroughly acquainted with the facts which form its logical basis.

As exhibiting a rational mode of conveying primary conceptions in
geometry, we cannot do better than quote the following passage from Mr.
Wyse:--

"A child has been in the habit of using cubes for arithmetic; let
him use them also for the elements of geometry. I would begin with
solids, the reverse of the usual plan. It saves all the difficulty
of absurd definitions, and bad explanations on points, lines, and
surfaces, which are nothing but abstractions.... A cube presents
many of the