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Mathematical essays and recreations (1899)

Schubert, Hermann · Chicago: The Open Court publishing company; [etc., etc.] · leaf 91

An illustration from Mathematical essays and recreations, 1899, leaf 91
The percep-tion that the eleventh axiom does not admit of demonstration with-out the employment of one of the foregoing substitutes may bestbe gained from the consideration of congruent figures. Everyreader will remember from his first instruction in geometry that thecongruence of two triangles is… … In the case of triangles which are congruent, as are I and II inthe preceding cut, this coincidence may be effected by the simpledisplacement of one of the triangles ; so that even a two-dimensionalbeing, supposed to be endowed with powers of reasoning, but onlycapable of picturing to itself…

Mathematics -- Philosophy · Magic squares · Hyperspace

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