principal elements of geometry; it at once exhibits
points, straight lines, parallel lines, angles, parallelograms,
etc., etc. These cubes are divisible into various parts. The pupil
has already been familiarised with such divisions in numeration,
and he now proceeds to a comparison of their several parts, and of
the relation of these parts to each other.... From thence he
advances to globes, which furnish him with elementary notions of
the circle, of curves generally, etc., etc.

"Being tolerably familiar with solids, he may now substitute
planes. The transition may be made very easy. Let the cube, for
instance, be cut into thin divisions, and placed on paper; he will
then see as many plane rectangles as he has divisions; so with all
the others. Globes may be treated in the same manner; he will thus
see how surfaces really are generated, and be enabled to abstract
them with facility in every solid.

"He has thus acquired the alphabet and reading of geometry. He now
proceeds to write it.

"The simplest operation, and therefore the first, is merely to
place these planes on a piece of paper, and pass the pencil round
them. When this has been frequently done, the plane may be put at a
little distance, and the child required to copy it, and so on."

A stock of geometrical conceptions having been obtained, in some such
manner as this recommended by Mr. Wyse, a further step may be taken, by
introducing the practice of testing the correctness of figures drawn by
eye: thus both exciting an ambition to make them exact, and continually
illustrating the difficulty of fulfilling that ambition. There can be
little doubt that geometry had its origin (as, indeed, the word implies)
in the methods discovered by artizans and others, of making accurate
measurements for the foundations of buildings, areas of inclosures, and
the like; and that its truths came to be treasured up, merely with a
view to their immediate utility. They would be introduced to the pupil
under analogous relationships. In cutting out pieces for his
card-houses, in drawing ornamental diagrams for colouring, and in those
various instructive occupations which an inventive teacher will lead him
into, he may for a length of time be advantageously left, like the
primitive builder, to tentative processes; and so will learn through
experience the difficulty of achieving his