Now
commensurately universal demonstration is of the latter kind: if we
engage in it we find ourselves reasoning after a fashion well
illustrated by the argument that the proportionate is what answers
to the definition of some entity which is neither line, number, solid,
nor plane, but a proportionate apart from all these. Since, then, such
a proof is characteristically commensurate and universal, and less
touches reality than does particular demonstration, and creates a
false opinion, it will follow that commensurate and universal is
inferior to particular demonstration.
We may retort thus. (1) The first argument applies no more to
commensurate and universal than to particular demonstration. If
equality to two right angles is attributable to its subject not qua
isosceles but qua triangle, he who knows that isosceles possesses that
attribute knows the subject as qua itself possessing the attribute, to
a less degree than he who knows that triangle has that attribute. To
sum up the whole matter: if a subject is proved to possess qua
triangle an attribute which it does not in fact possess qua
triangle, that is not demonstration: but if it does possess it qua
triangle the rule applies that the greater knowledge is his who
knows the subject as possessing its attribute qua that in virtue of
which it actually does possess it.
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