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Mathematical essays and recreations (1899)

Schubert, Hermann · Chicago: The Open Court publishing company; [etc., etc.] · leaf 97

An illustration from Mathematical essays and recreations, 1899, leaf 97
space which may bedenoted by the numbers 1, 2, 3, 4, 5 ; then imagine all the possibleten straight lines of junction drawn between each two of these points,namely, 1-2, 1-3 .. . . 4-5; and finally, also, all the ten planes ofjunction of every three points described, namely, the plane 1-2-3,1-2-4, •… … Fig. 36. THE FOURTH DIMENSION. 87 Thus, for example, on this plane the points 1-2, 1-3, and 2-3 will lie ina straight line, for through the three spatial points 1, 2, 3, a plane canbe drawn which will cut the plane of a drawing in a straight line.The reason, therefore, that the three points 3-4,…

Mathematics -- Philosophy · Magic squares · Hyperspace

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