First, we can have knowledge no further than we have IDEAS.
2. Secondly, It extends no further than we can perceive their Agreement or Disagreement.
Secondly, That we can have no knowledge further than we can have PERCEPTION of that agreement or disagreement. Which perception being: 1. Either by INTUITION, or the immediate comparing any two ideas; or, 2. By REASON, examining the agreement or disagreement of two ideas, by the intervention of some others; or, 3. By SENSATION, perceiving the existence of particular things: hence it also follows:
3. Thirdly, Intuitive Knowledge extends itself not to all the relation of all our Ideas.
Thirdly, That we cannot have an INTUITIVE KNOWLEDGE that shall extend itself to all our ideas, and all that we would know about them; because we cannot examine and perceive all the relations they have one to another, by juxta-position, or an immediate comparison one with another. Thus, having the ideas of an obtuse and an acute angled triangle, both drawn from equal bases, and between parallels, I can, by intuitive knowledge, perceive the one not to be the other, but cannot that way know whether they be equal or no; because their agreement or disagreement in equality can never be perceived by an immediate comparing them: the difference of figure makes their parts incapable of an exact immediate application; and therefore there is need of some intervening qualities to measure them by, which is demonstration, or rational knowledge.
4. Fourthly, Nor does Demonstrative Knowledge.
Fourthly, It follows, also, from what is above observed, that our RATIONAL KNOWLEDGE cannot reach to the whole extent of our ideas: because between two different ideas we would examine, we cannot always find such mediums as we can connect one to another with an intuitive knowledge in all the parts of the deduction; and wherever that fails, we come short of knowledge and demonstration.
5. Fifthly, Sensitive Knowledge narrower than either.
Fifthly, SENSITIVE KNOWLEDGE reaching no further than the existence of things actually present to our senses, is yet much narrower than either of the former.
6. Sixthly, Our Knowledge, therefore narrower than our Ideas.