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But the more common term is hypergeometry, which, though belonging more especially to space of more than three dimensions, is also sometimes applied to any geometric system which transcends our ordinary ideas. In all geometric reasoning some propositions are necessarily taken for granted. These are called axioms, and are commonly regarded as self-evident.
To explain hypergeometry proper we must first set forth what a fourth dimension of space means, and show how natural the way is by which it may be approached. We continue our analogy from "flat-land" In this supposed land let us make a cross two straight lines intersecting at right angles. The inhabitants of this land understand the cross perfectly, and conceive of it just as we do.
There must be space outside as well as inside. Eternity of time and infinity of space are ideas that the intellect cannot fully grasp, but neither can it grasp the idea of a limitation to either space or time. The metaphysical conceptions of hypergeometry, or fourth-dimensional space, do not aid us.
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