te and explain another. And at least that we take care that
the name of PRINCIPLES deceive us not, nor impose on us, by making us
receive that for an unquestionable truth, which is really at best but a
very doubtful conjecture; such as are most (I had almost said all) of
the hypotheses in natural philosophy.

14. Clear and distinct Ideas with settled Names, and the finding of
those intermediate ideas which show their Agreement or Disagreement, are
the Ways to enlarge our Knowledge.

But whether natural philosophy be capable of certainty or no, the ways
to enlarge our knowledge, as far as we are capable, seems to me, in
short, to be these two:--

First, The first is to get and settle in our minds [determined ideas of
those things whereof we have general or specific names; at least, so
many of them as we would consider and improve our knowledge in, or
reason about.] [And if they be specific ideas of substances, we should
endeavour also to make them as complete as we can, whereby I mean,
that we should put together as many simple ideas as, being constantly
observed to co-exist, may perfectly determine the species; and each of
those simple ideas which are the ingredients of our complex ones, should
be clear and distinct in our minds.] For it being evident that our
knowledge cannot exceed our ideas; [as far as] they are either
imperfect, confused, or obscure, we cannot expect to have certain,
perfect, or clear knowledge. Secondly, The other is the art of finding
out those intermediate ideas, which may show us the agreement or
repugnancy of other ideas, which cannot be immediately compared.

15. Mathematics an instance of this.

That these two (and not the relying on maxims, and drawing consequences
from some general propositions) are the right methods of improving our
knowledge in the ideas of other modes besides those of quantity, the
consideration of mathematical knowledge will easily inform us. Where
first we shall find that he that has not a perfect and clear idea of
those angles or figures of which he desires to know anything, is utterly
thereby incapable of any knowledge about them. Suppose but a man not to
have a perfect exact idea of a right angle, a scalenum, or trapezium,
and there is nothing more certain than that he will in vain seek any
demonstration about them. Further, it is evident, that it was not the
influence of those maxims which are taken for principles in mathematics,
that hath led the masters