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 kwledge has been attained, because the true system must be based upon the essential laws of formation 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 igrance of aught beyond what it has seen, is naturally led to form artificial order. But when, through the use of the arbitrary classification, a fuller understanding of the subject is arrived at, then the objects are newly arranged according to what appears to us to have been the law in their creation. It has been thus in botany, zoology, sology, and other sciences, and will probably be thus in mathematics. The classification of curves, according to the degree of their equation in rectilinear and in polar co-ordinates, is natural to us, from our modes of inquiry and measurement; but it may t be natural to the curves; that is, it may t class them according to their laws of continuity and direction, which are the laws of their formation. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art techlogy to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.