If it be the office of comparison to reduce existing differences to Identity, the science, which most perfectly fulfils that end, is mathematics. The reason of that is, that quantitative difference is only the difference which is quite external. Thus, in geometry, a triangle and a quadrangle, figures qualitatively different, have this qualitative difference discounted by abstraction, and are equalised to one another in magnitude. It follows from what has been formerly said about the mere Identity of understanding that, as has also been pointed out (§ 99, note), neither philosophy nor the empirical sciences need envy this superiority of Mathematics. The story is told that, when Leibnitz propounded the maxim of Variety, the cavaliers and ladies of the court, as they walked round the garden, made efforts to discover two leaves indistinguishable from each other, in order to confute the law stated by the philosopher. Their device was unquestionably a convenient method of dealing with metaphysics,--one which has not ceased to be fashionable. All the same, as regards the principle of Leibnitz, difference must be understood to mean not an external and indifferent diversity merely, but difference essential. Hence the very nature of things implies that they must be different. 118.] Likeness is an Identity only of those things which are not the same, not identical with each other: and Unlikeness is a relation of things unlike. The two therefore do not fall on different aspects or points of view in the thing, without any mutual affinity: but one throws light into the other. Variety thus comes to be reflexive difference, or difference (distinction) implicit and essential, determinate or specific difference. * * * * * * While things merely various show themselves unaffected by each other, likeness and unlikeness on the contrary are a pair of characteristics which are in completely reciprocal relation. The one of them cannot be thought without the other. This advance from simple variety to opposition appears in our common acts of thought, when we allow that comparison has a meaning only upon the hypothesis of an existing difference, and that on the other hand we can distinguish only on the hypothesis of existing similarity.