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 of that science into those
wonderful discoveries they have made. Let a man of good parts know all
the maxims generally made use of in mathematics ever so perfectly, and
contemplate their extent and consequences as much as he pleases, he
will, by their assistance, I suppose, scarce ever come to know that
the square of the hypothenuse in a right-angled triangle is equal to
the squares of the two other sides. The knowledge that "the whole is
equal to all its parts," and "if you take equals from equals, the
remainder will be equal," &c., helped him not, I presume, to this
demonstration: and a man may, I think, pore long enough on those
axioms without ever seeing one jot the more of mathematical truths.
They have been discovered by the thoughts otherwise applied: the
mind had other objects, other views before it, far different from
those maxims, when it first got the knowledge of such truths in
mathematics, which men, well enough acquainted with those received
axioms, but ignorant of their method who first made these
demonstrations, can never sufficiently admire. And who knows what
methods to enlarge our knowledge in other parts of science may
hereafter be invented, answering that of algebra in mathematics, which
so readily finds out the ideas of quantities to measure others by;
whose equality or proportion we could otherwise very hardly, or,
perhaps, never come to know?
Chapter XIII
Some Further Considerations Concerning our Knowledge
1.
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