for instance, number into triad and dual, then to endeavour thus to assume the definitions of these, as of a straight line, of a circle, and of a right angle; afterwards assuming what the genus is, for instance, whether it is quantity or quality, he should investigate the peculiar passions through common first (principles.) For those which happen to the composites from individuals will be evident from the definitions, because definition and that which is simple are the principles of all things, and accidents are essentially present with simple things alone, but with others according to them. The divisions indeed by differences are useful for our progression in this way, but how indeed they demonstrate we have shown before, but they would thus be useful only for syllogizing what a thing is, and indeed they may appear to do nothing, but to assume every thing immediately, just as if any one assumed from the beginning without division. It makes some difference, however, whether what is predicated be so, prior or posterior, as for instance, whether we call animal, mild biped, or biped, animal mild, for if every thing consists of two, and one certain thing is animal mild, and again from this, and the difference, man or any thing else which is one, consists, we must necessarily make a postulate by division. Besides, thus only is it possible to leave out nothing in the definition, since when the first genus is assumed, if a person takes a certain inferior division, every thing will not fall into this; for instance, not every animal has entire or divided wings, but every animal which is winged, for this is the difference of it, but the first difference of animal is that into which every
