regular solids; they should also be accustomed to the
figures in mathematical diagrams. To these should be added their
respective names, and the whole language of the science should be
rendered as familiar as possible.

Mr. Donne, an ingenious mathematician of Bristol, has published a
prospectus of an Essay on Mechanical Geometry: he has executed, and
employed with success, models in wood and metal for demonstrating
propositions in geometry in a _palpable_ manner. We have endeavoured,
in vain, to procure a set of these models for our own pupils, but we
have no doubt of their entire utility.

What has been acquired in childhood, should not be suffered to escape
the memory. Dionysius[19] had mathematical diagrams described upon
the floors of his apartments, and thus recalled their demonstrations
to his memory. The slightest addition that can be conceived, if it be
continued daily, will imperceptibly, not only preserve what has been
already acquired, but will, in a few years, amount to as large a stock
of mathematical knowledge as we could wish. It is not our object to
make mathematicians, but to make it easy to our pupil to become a
mathematician, if his interest, or his ambition, make it desirable;
and, above all, to habituate him to clear reasoning, and close
attention. And we may here remark, that an early acquaintance with the
accuracy of mathematical demonstration, does not, within our
experience, contract the powers of the imagination. On the contrary,
we think that a young lady of twelve years old, who is now no more,
and who had an uncommon propensity to mathematical reasoning, had an
imagination remarkably vivid and inventive.[20]

We have accustomed our pupils to form in their minds the conception of
figures generated from points and lines, and surfaces supposed to move
in different directions, and with different velocities. It may be
thought, that this would be a difficult occupation for young minds;
but, upon trial, it will be found not only easy to them, but
entertaining. In their subsequent studies, it will be of material
advantage; it will facilitate their progress not only in pure
mathematics, but in mechanics and astronomy, and in every operation of
the mind which requires exact reflection.

To demand steady thought from a person who has not been trained to it,
is one of the most unprofitable and dangerous requisitions that can be
made in education.

"Full in the midst of Euclid dip at once,