15. But how can you qualify the properties of quantity so as to call
them equal or unequal?[392] Is it not usual to say of two triangles
that they are similar? Could we not also predicate similarity of
two magnitudes? Doubtless, for what is called similarity,[393]
does not conflict with similarity or dissimilarity in the genus of
quantity.[394] Here, indeed, the word "similarity" is applied to
magnitudes in a sense other than to quality. Besides, if (Aristotle)
said that the property characteristic of quantities is to enable them
to be called equal or unequal, this does not conflict with predicating
similarity of some of them. But as it has been said that the special
characteristic of qualities is to admit of being called similar
or dissimilar, we must, as has already been explained, understand
similarity in a sense other than when it is applied to magnitudes.
If similar magnitudes be identical, we must then consider the other
properties of quantity and quality which might be present in them
(so as clearly to contrast their differences). It may also be said
that the term "similarity" applies to the genus of quantity so far as
this contains differences (which distinguish from each other similar
magnitudes).
DIFFERENCES WHICH COMPLETE THE BEING MUST BE PREFIXED TO THAT TO WHICH
THEY REFER.
In general, the differences which complete a being should be classified
along with that of which they are the differences, especially when a
difference belongs to a single subject. If a difference complete the
being of a subject, and do not complete the being of another, this
difference should be classified along with the subject whose being it
completes, leaving that whose being it does not complete for separate
consideration. By this we do not mean completing the Being in general,
but completing some particular being, so that the subject spoken of as
a particular one admits no further essential addition. We therefore
have the right to say that triangles, or that quadrilaterals, as
well as surfaces and solids, are equal, and to predicate equality or
inequality of quantitative entities. But we yet have to study whether
quality only can be said to be similar or dissimilar.[395]