Abstract
THE history of Analytical Geometry affords a curious subject of study to the thoughtful mathematician. It would seem that equations between coordinates were first used to express spatial relations discovered by intuitional processes, and the equations were combined algebraically to discover other implied spatial relations. For this purpose it was necessary to interpret in geometrical terms equations arrived at by algebraic processes from geometrical data, and the facility thus acquired led men to seek for similar interpretations of equations set down without reference to geometrical conditions. Hence it happens that modern developments of Analytical Geometry appear rather to present algebraic facts in geometrical language than to deduce results that can be apprehended by intuition from data of intuition. Such a notion as that of a cubic surface, for instance, would seem to be essentially analytical, and although it has been proved possible to arrange a geometrical construction for an algebraic curve whose equation is given, yet the construction arrived at is so artificial that intuition fails to grasp by its aid the necessary form of the curve. Looking at the subject in this way, it seems hardly too much to say that the algebra which was designed to be the servant of the geometer has become his master.
Die Grundgebilde der ebenen Geometrie.
By Dr. V. Eberhard, Professor at the University of Königsberg i.P. Bd. I. 8vo. xlviii. + 302 pp. Five plates. (Leipzig: Teubner, 1895.)
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References
Foster's "Physiology," 4th edition, p. 205.
Brunton and Tunnicliffe, Journal of Physiology, xvii. p. 272.
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L., A. Die Grundgebilde der ebenen Geometrie. Nature 52, 616 (1895). https://doi.org/10.1038/052616a0
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DOI: https://doi.org/10.1038/052616a0