Smith, David Eugene, 1860-1944 · Boston, New York [etc.] Ginn and Company · leaf 196
tempts to prove theproposition without the use of parallel lines. Of thesea German one, first given by Thibaut in the early partof the eighteenth century, is among the most interesting.This, in simplifiedform, is as follows: Suppose an indefi-nite line XY to lieon A B. Let it swingabout A,… … 180 THE TEACHING OF GEOMETRY but it is turned over, X being where Y was, and Y where .Ywas. In turning through A A, B, and C it has therefore turnedthrough two right angles. One trouble with the proof is that the rotation hasnot been about the same point, so that it has never beenlooked upon as…
Geometry
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