Manning, Henry Parker, 1859- · Boston, U.S.A., Ginn & Company · leaf 40
called the Elliptic Geometry. THE THREE GEOMETRIES 29 The constructions would have been the same, and verynearly all the statements -would have been the same, if we hadtaken CD any arbitrary length on CF. The restriction which we have placed upon some ofthe propositions of this chapter is necessary… … side was produced so as to make AE = 2 AD. If AD weregreater than half the entire length of the straight line deter-mined by A and D, this would bring the point E past the pointA, and the angle CBE, which is equal to the angle C, insteadof being a part of the exterior angle CBF, becomes greaterthan…
Geometry, Non-Euclidean
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