In this way I believed that I could borrow all that was best
both in geometrical analysis and in algebra, and correct all the defects
of the one by help of the other.
And, in point of fact, the accurate observance of these few precepts gave me,
I take the liberty of saying, such ease in unraveling all the questions
embraced in these two sciences, that in the two or three months
I devoted to their examination, not only did I reach solutions of
questions I had formerly deemed exceedingly difficult but even as regards
questions of the solution of which I continued ignorant, I was enabled, as
it appeared to me, to determine the means whereby, and the extent to which
a solution was possible; results attributable to the circumstance that I
commenced with the simplest and most general truths, and that thus each
truth discovered was a rule available in the discovery of subsequent ones
Nor in this perhaps shall I appear too vain, if it be considered that, as
the truth on any particular point is one whoever apprehends the truth,
knows all that on that point can be known. The child, for example, who
has been instructed in the elements of arithmetic, and has made a
particular addition, according to rule, may be assured that he has found,
with respect to the sum of the numbers before him, and that in this
instance is within the reach of human genius. Now, in conclusion, the
method which teaches adherence to the true order, and an exact enumeration
of all the conditions of the thing .
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