GEOMETRY STUDIES QUANTITIES, NOT QUALITIES.
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).