Three Absurdities of Certain Modern Theories of Education [pp. 265-292]

The Old Greeck Geometry.,
logical and metaphysical, as well as mathematical, than were
called out in the construction of that most splendid synthesis of
the human intellect. How much may even the sublime structure
of the modern mathematics, ever rising higher and higher into
the illimitable relations of space and quantity, be indebted for
its security and fair proportions to the strength of the founda tion, which was so rapidly laid by the Grecian mind. Archi medes is mainly known from the semi-fabulous stories of Plutarch
respecting his machines; to the scholar and the historian of
science, the chief interest respecting him will ever come from
the deep mason-work of his conical and spherical geometry.
Among the changes in modern education, there is no one, we
think, more questionable than the substitution of Legendre for
Euclid. One great end of mathematical, and especially of geo metrical study, is almost wholly lost by it. The logic, which led
to that most perfect idea of synthetical truth, seems to have
formed no part of the Frenchman's plan. Should it, however,
be thought to betray a want of modesty for one who is not a
mathematician to make some of these declarations, we can only
plead the relations of the subject to other departments of educa tion. There is much more than a mathematical interest
involved. It reaches to all the other provinces of the mind's
culture. In respect to the higher and more analytical
branches of mathematical science, all deference would be shown
to those whose peculiar department of knowledge it may be said
to be; yet even here, the opinion may be modestly hazarded,
that something of a more synthetical nature, consisting of texts,
and propositions, and formal rules in place of mere symbolical
formulas, and also, to some extent, geometrical illustrations,
might be of service to the student in some parts of these
difficult branches, especially at the commencement. They
might give him clearness and solidity when he comes afterwards, in the more intricate winding of the labyrinth, to turn
himself through necessity to the tort and firm, yet slender
thread of analysis. The old geometry, and indeed all synthetical science, as we have defined it, may be said to have length,
breadth, and depth. The analytical mathematics may be compared to an endless line of truth stretching on to infinity, taxing by its exceeding subtlety the highest powers of the human
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