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. But this would violate one of the requisite
conditions, which are as follows. No ultimate group must be included
in more than a single division; different groups must not be
included in the same division; and every group must be found in some
division. It is plain then that we cannot get at the ultimate specific
forms of the animal, or any other, kingdom by bifurcate division. If
we could, the number of ultimate differentiae would equal the number
of ultimate animal forms. For assume an order of beings whose prime
differentiae are White and Black. Each of these branches will
bifurcate, and their branches again, and so on till we reach the
ultimate differentiae, whose number will be four or some other power
of two, and will also be the number of the ultimate species
comprehended in the order.
(A species is constituted by the combination differentia and matter.
For no part of an animal is purely material or purely immaterial;
nor can a body, independently of its condition, constitute an animal
or any of its parts, as has repeatedly been observed.)
Further, the differentiae must be elements of the essence, and not
merely essential attributes. Thus if Figure is the term to be divided,
it must not be divided into figures whose angles are equal to two
right angles, and figures whose angles are together greater than two
right angles. For it is only an attribute of a triangle and not part
of its essence that its angles are equal to two right angles
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