When he examines into the reason of this, he finds that in the two
sciences he has been dealing with systems of quantities, in which the
mathematical forms of the relations of the quantities are the same in
both systems, though the physical nature of the quantities may be
utterly different.
He is thus led to recognize a classification of quantities on a new
principle, according to which the physical nature of the quantity is
subordinated to its mathematical form. This is the point of view
which is characteristic of the mathematician; but it stands second to
the physical aspect in order of time, because the human mind, in order
to conceive of different kinds of quantities, must have them presented
to it by nature.
I do not here refer to the fact that all quantities, as such, are
subject to the rules of arithmetic and algebra, and are therefore
capable of being submitted to those dry calculations which represent,
to so many minds, their only idea of mathematics.
The human mind is seldom satisfied, and is certainly never exercising
its highest functions, when it is doing the work of a calculating
machine.
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