DISCOURSE ON THE METHOD

15

proportions

all the others to which they would apply. Then, having noticed that, in order to know them, I would sometimes need to consider each one in particular and sometimes only to remember them or to understand several together, I thought that, to consider them better in particular, I ought to represent them as lines, because I found nothing simpler or that I could more distinctly represent to my imagination and my senses; but that, to remember them or to understand several together, I needed to express them by the briefest possible symbols original: "chiffres." Descartes is referring to the mathematical notation used in algebra to simplify complex relationships.; and that, by this means, I would borrow all that is best in geometrical analysis and algebra, and correct all the defects of the one by the other.

Indeed, I dare say that the exact observation of these few precepts I had chosen gave me such ease in disentangling all the questions to which these two sciences extend, that in the two or three months I spent examining them—having begun with the simplest and most general, and each truth I found being a rule that served me afterward to find others—not only did I succeed in solving several that I had formerly judged very difficult, but it also seemed to me toward the end that I could determine, even in those areas I was ignorant of, by what means and to what extent it was possible to resolve them. In this, I will perhaps not appear too vain to you if you consider that, there being only one truth for each thing, whoever finds it knows as much about it as can be known; and that, for example, a child instructed in arithmetic, having performed an addition according to its rules, can be certain of having found, regarding the sum he was examining, all that the human mind could find. For, after all, the method that teaches one to follow the true order and to enumerate exactly all the circumstances of what one seeks, contains everything that gives certainty to the rules of arithmetic.

But what satisfied me most about this method was that through it I was assured of using my reason in everything, if not perfectly, at least as best as was in my power; moreover, I felt that by practicing it, my mind was gradually becoming accustomed to conceiving its objects more clearly and more distinctly; and that, not having restricted the method to any particular subject matter, I promised myself to apply it as usefully to the difficulties of other sciences as I had done to those of algebra. Not that I would therefore dare to undertake at once to examine all those that might present themselves, for that itself would have been contrary to the order it prescribes;
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but, having noticed that their principles must all be borrowed from philosophy, in which I found none—