is but the reviving of some past knowledge) that he was once certain of the truth of this proposition, that the three angles of a triangle are equal to two right ones.  The immutability of the same relations between the same immutable things is now the idea that shows him, that if the three angles of a triangle were once equal to two right ones, they will always be equal to two right ones.  And hence he comes to be certain, that what was once true in the case, is always true; what ideas once agreed will always agree; and consequently what he once knew to be true, he will always know to be true; as long as he can remember that he once knew it.  Upon this ground it is, that particular demonstrations in mathematics afford general knowledge.  If then the perception, that the same ideas will eternally have the same habitudes and relations, be not a sufficient ground of knowledge, there could be no knowledge of general propositions in mathematics; for no mathematical demonstration would be any other than particular:  and when a man had demonstrated any proposition concerning one triangle or circle, his knowledge would not reach beyond that particular diagram.  If he would extend it further, he must renew his demonstration in another instance, before he could know it to be true in another like triangle, and so on:  by which means one could never come to the knowledge of any general propositions.  Nobody, I think, can deny, that Mr. Newton certainly knows any proposition that he now at any time reads in his book to be true; though he has not in actual view that admirable chain of intermediate ideas whereby he at first discovered it to be true.  Such a memory as that, able to retain such a train of particulars, may be well thought beyond the reach of human faculties, when the very discovery, perception, and laying together that wonderful connexion of ideas, is found to surpass most readers’ comprehension.  But yet it is evident the author himself knows the proposition to be true, remembering he once saw the connexion of those ideas; as certainly as he knows such a man wounded another, remembering that he saw him run him through.  But because the memory is not always so clear as actual perception, and does in all men more or less decay in length of time, this, amongst other differences, is one which shows that demonstrative knowledge is much more imperfect than intuitive, as we shall see in the following chapter.

CHAPTER II.

Of the degrees of our knowledge.

1.  Of the degrees, or differences in clearness, of our Knowledge:  I. Intuitive