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. Our Knowledge partly necessary partly voluntary.

Our knowledge, as in other things, so in this, has so great a conformity
with our sight, that it is neither wholly necessary, nor wholly
voluntary. If our knowledge were altogether necessary, all men's
knowledge would not only be alike, but every man would know all that is
knowable; and if it were wholly voluntary, some men so little regard or
value it, that they would have extreme little, or none at all. Men that
have senses cannot choose but receive some ideas by them; and if they
have memory, they cannot but retain some of them; and if they have
any distinguishing faculty, cannot but perceive the agreement or
disagreement of some of them one with another; as he that has eyes, if
he will open them by day, cannot but see some objects, and perceive a
difference in them. But though a man with his eyes open in the light,
cannot but see, yet there be certain objects which he may choose whether
he will turn his eyes to; there m