Enneads VI.3: Plotino's Own Sense-Categories
Geometry Studies Quantities, Not Qualities
15. But how can you qualify the properties of quantity so as to call them equal or unequal? 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, does not conflict with similarity or dissimilarity in the genus of quantity. 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.