what is not proportionate, or what is to be broken, or to incline; but that they are, they demonstrate through things common, and from those which have been demonstrated. So also astronomy, for all demonstrative science is conversant with three things, those which are laid down as existing, and these are the genus, (the essential properties of which the science considers,) and common things called axioms, from which as primaries they demonstrate; and thirdly, the affections, the signification of each of which the demonstrator assumes. There is nothing however to prevent certain sciences overlooking some of these, as if the genus is not supposed to be, if it be manifest that it exists, (for it is not similarly manifest that number is, as that the cold and hot are,) and if (the science) does not assume what the affections signify, if they are evident, as neither does it assume what things common signify, (as what it is) to take away equals from equals, because it is known; nevertheless these things are naturally three, viz. that about which demonstration is employed, the things demonstrated, and the principles from which they are.
Neither however hypothesis nor postulate is that which it is necessary should exist per se, and be necessarily seen, for demonstration does not belong to external speech, but to what is in the soul, since neither does syllogism. For it is always possible to object to external discourse,
