Excerpt from An Elementary Treatise on Curvature: Also, a Fragmentary Essay on Curves A true system of classification is attainable only When a high degree of knowled ge has been attained, because the true system must be based upon the essential laws of forma tion in the objects classified. Convenience demands some classification, Which at first is necessarily arbitrary and this arbitrary system may, in one sense, be called natural, since the mind, in its craving for order, and its ignorance of aught beyond What it has seen, is naturally led to form artificial order. But When, through the use of the arbitrary classifi cation, a fuller understanding of the subject is arrived at, then the objects are newly arranged according to What ap pears to us to have been the law in their creation. It has been thus in botany, zoology, nosology, and other sciences, and Will probably be thus in mathematics. The classification of curves, according to the degree of their equation in recti linear and in polar co-ordinates, is natural to as, from our modes of inquiry and measurement; but it may not be natu ral to the curves; that is, it may not class them according to their laws of continuity and direction, Which are the laws of their formation.

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