The elements of non-Euclidean plane geometry and trigonometry, by H. S. Carslaw.

SUBJECT INDEX

179

Ray, Definition of, 5.
Relativity, Theory of, 175.
Representation of Non-Euclidean
Geometry in Euclidean, 154 -156.
Rotation-method of proof for
sum of angles of a triangle, 25.
Saccheri's Hypotheses of Acute
Angle, Right Angle, and
Obtuse Angle, 13-15.
Similar triangles impossible in
Non-Euclidean Geometry, 54,
135.
Sphere of infinite radius (see Limiting-Surface), 29.
Squaring of the circle, 29.
Sum of the angles of a triangle,
and the hypotheses of
Saccheri and Legendre, 12 -18.
and the Postulate of Archimedes, 18.
in Elliptic Geometry, 132-134.
in Hyperbolic Geometry, 53.
System of circles, cutting a fixed
circle diametrally, 171-174.
Extension to Solid Geometry
174.
orthogonal to a fixed circle,
160-170.

System of circles
Extension to Solid Geometry,
170.
passing through a fixed point
156-159.
Extension to Solid Geometry,
159-160.
Trigonometrical Functions, 105,
140.
Trigonometry, of right-angled triangle, in Elliptic Plane,
136-152.
in Hyperbolic Plane, 100-102,
108-110.
The Cosine Rule, 1.04, 109.
The Sine Rule, 103, 109.
Truth of the Euclidean Geometry,
174, 175.
Work of Bolyai, 27-32.
Gauss, 19-26.
Lambert, 17.
Legendre, 15-19.
Lobatschewsky, 32-38.
Riemann, 38-41.
Saccheri, 12, 15.
Schumacher, 25.
Schweikart, 21.
Taurinus, 23.
Wachter, 21.

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