but not always to internal. Whatever things then, being demonstrable, a man assumes without demonstration, these, if he assumes what appear probable to the learner, he supposes, and this is not an hypothesis simply, but with reference to the learner alone; but if, there being no inherent opinion, or when a contrary is inherent, the demonstrator assumes, he requires the same thing to be granted to him. And in this hypothesis and postulate differ, for postulate is any thing sub-contrary to the opinion of the learner, which though demonstrable a man assumes, and uses without demonstration.
Definitions then are not hypotheses, (for they are not asserted to be or not to be,) but hypotheses are in propositions. Now it is only necessary that definitions should be understood, but this is not hypothesis, except some one should say that the verb to hear is hypothesis. But they are hypotheses, from the existence of which, in that they are, the conclusion is produced. Neither does the geometrician suppose falsities, as some say, who assert, that it is not right to use a false (principle), but that the geometrician does so, when he calls a line a foot long when it is not so, or the line which he describes a straight line when it is not straight. The geometrician indeed concludes nothing from the lines being so and so, as he has said, but concludes those, which are manifested through these (symbols). Moreover postulate and every hypothesis are either as a whole or as in a part, but definitions are neither of these.
