Science, Vol. 7: A Weekly Journal Devoted to the Advancement of Science; January-June, 1898 (Classic Reprint) - Softcover

Inhaltsangabe

Excerpt from Science, Vol. 7: A Weekly Journal Devoted to the Advancement of Science; January-June, 1898

Now consider the analogous case in space. Two pyramids upon congruent bases may be proved equal by bringing them into congruence with each other. But suppose that they differ only in that one is the obverse of the other, so that they could be brought into congruence only by looking at one of them in a mirror and then placing the other into congruence with the image of the first as seen in the mirror. Would we detract from the rigor of the demonstration by assuming the possibility of such an obversion without changing the volume of the pyramid? With a fourth dimension we should have no. Detraction from rigor. We would simply obvert the pyramid as we would turn over the triangle.

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