none but the Mathematicians only could finde any
demonstrations, that's to say, any certain and evident reasons. I
doubted not, but that it was by the same that they have examin'd;
although I did hope for no other profit, but only that they would
accustome my Minde to nourish it self with Truths, and not content it
self with false Reasons. But for all this, I never intended to endevour
to learn all those particular Sciences which we commonly call'd
Mathematicall; And perceiving, that although their objects were
different, yet did they nevertheless agree altogether, in that they
consider no other thing, but the divers relations or proportions which
are found therein; I thought it therefore better to examine those
proportions in generall, and without supporting them but in those
subjects, which might the more easily serve to bring me to the knowledg
of them. But withall, without any wayes limiting them, That I might
afterwards the better sit them to all others whereto they might be
applyed. Having also observ'd, That to know them, it would be sometimes
needfull for me to consider every one in particular, or sometimes only
to restrain them, or comprehend many together; I thought, that to
consider them the better in particular I ought to suppose them in
lines, for as much as I find nothing more simple, nor which I could more
distinctly represent to my imagination, and to my sences; But to hold or
comprehend many in one, I was oblig'd to explain them by certain Cyphers
the shortest I possibly could, and that I should thereby borrow the best
of the Geometricall Analysis, and of Algebra, & so correct all the
defects of the one by the other.

As in effect I dare say, That the exact observation of those few
precepts I had chosen, gave me such a facility to resolve all the
questions whereto these two sciences extend; That in two or three months
space which I employed in the examination of them, having begun by the
most simple and most generall, and every Truth which I found being a
rule which afterwards served me to discover others; I did not only
compasse divers truths which I had formerly judged most difficult, But
me thought also that towards the end I could determin even in those
which I was ignorant of, by what means and how farr it was possible to
resolve them. Wherein perhaps I shall not appear to be very vain if you
consider, That there being but one truth of every thing, who ever finds
it, knows as much of it as one can