Elements of the philosophy of the human mind. By Dugald Stewart. Rev. and abridged, with critical and explanatory notes, for the use of colleges and schools. By Francis Bowen ...

186 INVENTION.
and habit, even in those sciences in which it is generally supposed that every thing depends on natural genius.
When we consider the geometrical discoveries of the ancients,
in the form in which they are exhibited in the greater part of
the works which have survived to our times, it is seldom possible for us to trace the steps by which they were led to their
conclusions; and, indeed, the objects of this science are so
unlike those of all others, that it is not unnatural for a person,
when he enters on the study, to be dazzled by its novelty, and
to forml an exaggerated conception of the genius of those men
who first brought to light such a variety of truths, so profound
and so remote from the ordinary course of our speculations.
We find, however, that, even at the time when the ancient
analysis was unknown to the moderns, such mathematicians as
had attended to the progress of the mind in the discovery of
truth, concluded a priori, that the discoveries of the Greek
geometers did not, at first, occur to them in the order in which
they are stated in their writings. The prevailing opinion was,
that they had possessed some secret method of investigation,
which they carefully concealed from the world; and that they
published the result of their labors in such a form, as they
thought would be most likely to excite the admiration of their
readers. The revival of the ancient analysis, by some late mathematicians ill this country, has, in part, justified these remarks, by
showring to how great a degree the inventive powers of th(
Greek geometers were aided by that method of investigation;
and by exhibiting some striking specimens of address in the
practical application of it.
The solution of problems, indeed, it may be said, is but one
mode in which mathematical invention may be displayed. The
discovery of new truths is what we chiefly admire in an original
genius; and the method of analysis gives us no satisfaction with
respect to the process by which they are obtained.
Rtow new theorems are discovered. - To remove this difficulty
completely, by explaining all the various ways in which new
theorems may be brought to light, would lead to inquiries foreign
to this work. In order, however, to render the process of the