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But as a man that walks alone, and in the dark, I resolv’d to goe so softly, and use so much circumspection in all things, that though I advanc’d little, I would yet save my self from falling. Neither would I begin quite to reject, some opinions, which formerly had crept into my belief, without the consent of my reason, before I had employed time enough to form the project of the work I undertook, and to seek the true Method to bring me to the knowledg of all those things, of which my understanding was capable.
I had a little studyed, being young, of the parts of Philosophy, Logick, and of the Mathematicks, the Analysis of the Geometricians, and Algebra: Three arts or sciences which seem’d to contribute somewhat conducing to my designe: But examining them, I observ’d, That as for Logick, its Sylogisms, and the greatest part of its other Rules, serve rather to expound to another the things they know, or even as Lullies art, to speak with judgment of the things we are ignorant of, then to learn them. And although in effect it contain divers most true and good precepts, yet there are so many others mixed amongst them, either hurtfull or superfluous, That it’s even as difficult to extract them, as ’tis to draw a Diana or a Mercury out of a lump of Marble, which is not yet rough—hewn; as for the Analysis of the Ancients, and the Algebra of the Moderns; besides that, they extend only to matters very abstract, and which seem to be of no use; The first being alwayes so tyed to the consideration of figures, That it cannot exercise the understanding, without very much tiring the imagination. And in the latter they have so subjected themselves to certain Rules and cyphers, that they have made a confus’d and obscure art which perplexeth the minde, in stead of a Science to instruct it. For this reason, I thought I ought to seek some other Method, which comprehending the advantages of these, they might be exempt from their defects. And as the multitude of Laws often furnisheth excuses for vice; so a State is fair better polic’d, when having but a few, they are very strictly observ’d therein: So, instead of the great many precepts whereof Logick is compos’d, I thought these four following would be sufficient for me, if I took but a firm and constant resolution not once to fail in the observation of them.
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.
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