And petrify a genius to a dunce."

In the usual commencement of mathematical studies, the learner is
required to admit that a point, of which he sees the prototype, a dot
before him, has neither length, breadth, nor thickness. This, surely,
is a degree of faith not absolutely necessary for the neophyte in
science. It is an absurdity which has, with much success, been
attacked in "Observations on the Nature of Demonstrative Evidence," by
Doctor Beddoes.

We agree with the doctor as to the impropriety of calling a visible
dot, a point without dimensions. But, notwithstanding the high respect
which the author commands by a steady pursuit of truth on all subjects
of human knowledge, we cannot avoid protesting against part of the
doctrine which he has endeavoured to inculcate. That the names point,
radius, &c. are derived from sensible objects, need not be disputed;
but surely the word centre can be understood by the human mind without
the presence of any visible or tangible substance.

Where two lines meet, their junction cannot have dimensions;
where two radii of a circle meet, they constitute the centre,
and the name centre may be used for ever without any relation
to a tangible or visible point. The word boundary, in like manner,
means the extreme limit we call a line; but to assert that it has
thickness, would, from the very terms which are used to describe it,
be a direct contradiction. Bishop Berkely, Mr. Walton, Philathetes
Cantabrigiensis, and Mr. Benjamin Robins, published several pamphlets
upon this subject about half a century ago. No man had a more
penetrating mind than Berkely; but we apprehend that Mr. Robins closed
the dispute against him. This is not meant as an appeal to authority,
but to apprize such of our readers as wish to consider the argument,
where they may meet an accurate investigation of the subject. It is
sufficient for our purpose, to warn preceptors not to insist upon
their pupils' acquiescence in the dogma, that a point, represented by
a dot, is without dimensions; and at the same time to profess, that we
understand distinctly what is meant by mathematicians when they speak
of length without breadth, and of a superfices without depth;
expressions which, to our minds, convey a meaning as distinct as the
name of any visible or tangible substance in nature, whose varieties
from shade, distance, colour, smoothness, heat, &c. are infinite, and
not to be comprehended in any definition.

In fa