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But since every pair of contraries falls to be examined by one and
the same science, and in each pair one term is the privative of the
other though one might regarding some contraries raise the question,
how they can be privately related, viz. those which have an
intermediate, e.g. unjust and just-in all such cases one must maintain
that the privation is not of the whole definition, but of the infima
species. if the just man is 'by virtue of some permanent disposition
obedient to the laws', the unjust man will not in every case have
the whole definition denied of him, but may be merely 'in some respect
deficient in obedience to the laws', and in this respect the privation
will attach to him; and similarly in all other cases.
As the mathematician investigates abstractions (for before
beginning his investigation he strips off all the sensible
qualities, e.g. weight and lightness, hardness and its contrary, and
also heat and cold and the other sensible contrarieties, and leaves
only the quantitative and continuous, sometimes in one, sometimes in
two, sometimes in three dimensions, and the attributes of these qua
quantitative and continuous, and does not consider them in any other
respect, and examines the relative positions of some and the
attributes of these, and the commensurabilities and
incommensurabilities of others, and the ratios of others; but yet we
posit one and the same science of all these things--geometry)--the
same is true with regard to being
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