The first was, never to receive any thing for true, but what I evidently knew to be so; that's to say, Carefully to avoid Precipitation and Prevention, and to admit nothing more into my judgment, but what should so clearly and distinctly present it self to my minde, that I could have no reason to doubt of it.
The second, to divide every One of these difficulties, which I was to examine into as many parcels as could be, and, as was requisite the better to resolve them.
The third, to lead my thoughts in order, beginning by the most simple objects, and the easiest to be known; to rise by little and little, as by steps, even to the knowledg of the most mixt; and even supposing an Order among those which naturally doe not precede one the other.
And the last, to make every where such exact calculations, and such generall reviews, That I might be confident to have omitted Nothing.
Those long chains of reasons, (though simple and easie) which the Geometricians commonly use to lead us to their most difficult demonstrations, gave me occasion to imagine, That all things which may fall under the knowledg of Men, follow one the other in the same manner, and so we doe only abstain from receiving any one for true, which is not so, and observe alwayes the right order of deducing them one from the other, there can be none so remote, to which at last we shall not attain; nor so hid, which we shall not discover. Neither was I much troubled to seek by which it behooved me to begin, for I already knew, that it was by the most simple, and the easiest to be discern'd. But considering, that amongst all those who formerly have sought the Truth in Learning, 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.