実際，思いきって言うと，わたしが選んだこのわずかの規則を厳密に守ったことで，この二つの学科の及ぶどんな問題もきわめて容易に解けるようになり，二，三ヵ月かけてこれらの問題を検討するうちに，もっとも単純でもっとも一般的なものから始めて，発見したおのおのの真理をさらにほかの真理を見いだすのに役立つ規則としたので，以前たいへん難しいと思っていた多くの問題を解いてしまっただけでなく，しまいには，知らなかった問題さえも，どういうやり方でどこまで解けるかを決定できる，と思われたほどだ。この点で，次のことを考えていただければ，わたしがそれほど自惚れているとは映じないだろう。つまり，一つのことについては一つの真理しかないのだから，その真理を見つける人はだれでも，それについては人の知りうるかぎりのことを知っているわけである。たとえば，子供が算術を習って，その規則どおりにたし算すれば，その子供は計算している総和については，人間精神が見いだしうるすべてを見いだしたと確信してよい。というのも結局，真の順序に従い，かつ求めるもののあらゆる条件を正確に枚挙せよと教える方法は，算術の規則に確実性をあたえるすべてを含んでいるからである。
And, in point of fact, the accurate observance
of these few precepts gave me, I take the
liberty of saying, such ease in unravelling
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, all 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 sought includes all that gives certitude
to the rules of Arithmetic.