Vectors in four dimensions
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The interest attaching to n-dimensional geometry comes chiefly from two sources, first the light thrown upon analysis by a geometric interpretation of its results when more than three variables are involved, and second, the light thrown upon the geometries of a smaller number of dimensions by fitting them into their places in a more general theory, which brings out much more clearly than is otherwise possible their characteristic properties. The theory of vectors is a special aspect at geometry, and one which takes its inspiration from, and is highly useful to, the science of mechanics. Mr. Pemberton's work, therefore, is an attack upon a problem of considerable interest, yet one apparently only very little developed.