THE ordinary theory of analytical geometry may be extended by analogy as follows: Let Xl, X2,... Xn be independent variables, each ranging over the complete real (or ordinary complex) continuum. Any particular set (Xl, X2,... Xn), in that order, is said to be a point, the co-ordinates of which are these Xi; and the aggregate of these points is said to form a point-space of n dimensions (Pn). Taking r<n, a set of r equations φ1=o, φ2=o,... φr=o, connecting the co-ordinates, will in general define a space Pn-r contained in Pn. Theorems about loci, contact, envelopes, and the principle of duality all hold good for this enlarged domain, and we also have a system of projective geometry analogous to the ordinary one.
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MATHEWS, G. Non-Euclidean Geometries. Nature 106, 790–791 (1921). https://doi.org/10.1038/106790a0