Page:O. F. Owen's Organon of Aristotle Vol. 1 (1853).djvu/358

 until so many are first assumed, each of which is or wider extension, but all of them together are not of greater extent, for it is necessary that this should be the substance of a thing. For example, number, the odd is present with every triad, the first in both ways, both as not being measured by number and as not being composed of numbers. Now therefore the triad is this, viz. the first odd number, and the first in this way, for each of these is present, the one with all odd numbers, but the last also with the dual, yet all of them (together) with none (but the triad). Since however we have shown above, that those things which are predicated in respect of what a thing is are necessary, but universals are necessary, but what are thus assumed of a triangle, or any other thing, are assumed in respect to what a thing is, thus from necessity the triad will be these things. That this however is its essence appears from this, since it is necessary, unless the very nature of a triad were not this, that this should be a certain genus, either denominated or anonymous. It will be therefore of wider extension than to be with a triad alone, for let the genus be supposed of that kind as to be more widely extended according to power, if then it is present with nothing else than individual triads, this will be the essence of the triad. Let this also be supposed, that an ultimate predication like this of individuals is the essence of each thing, wherefore in like manner, when any thing is thus demonstrated, it will be the essence of that thing.

Nevertheless it is right when any one is conversant with a certain whole, to divide the genus into the individuals which are first in species,