Locke is very clear that knowledge consists in something radically different from belief: it is perception of the agreement or the disagreement between two ideas. On the basis of this knowledge we assent to various propositions that are proposed to the mind (and, indeed, cannot help but assent, any more than I could deny to myself that I am seeing the color white when it is taking up my field of vision; but Locke seems clearly enough to think that the knowledge itself is a perception, not a belief. (I think there is a good argument that this is actually the most common view of knowledge in the early modern period, on both the rationalist and empiricist sides; Locke is not being idiosyncratic here.) From Locke, Essay IV.1.2:
Knowledge then seems to me to be nothing but the perception of the connexion of and agreement, or disagreement and repugnancy of any of our ideas. In this alone it consists. Where this perception is, there is knowledge, and where it is not, there, though we may fancy, guess, or believe, yet we always come short of knowledge. For when we know that white is not black, what do we else but perceive, that these two ideas do not agree? When we possess ourselves with the utmost security of the demonstration, that the three angles of a triangle are equal to two right ones, what do we more but perceive, that equality to two right ones does necessarily agree to, and is inseparable from, the three angles of a triangle?
Indeed, Locke thinks that the sort of knowledge that most properly receives that name, the one that has "the utmost light and greatest certainty," is had simply by perceiving the agreement or disagreement between two ideas, and nothing else. This intuitive knowledge leaves no room for the intervention of a third idea, or anything else besides the perception itself of the two ideas, and is that by virtue of which everything else is known or understood.