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

CONTENTS xi
PAGE
~ 58. The hyperbolic functions of complementary segments - 98
~ 59. The equations connecting the sides and angles of a rightangled triangle - - - 100
~ 60. Corresponding equations for an oblique-angled triangle - 103
~ 61. The measurement of angles - 104
~ 62. The trigonometrical functions, and the fundamental equation
of hyperbolic trigonometry - - 105
~ 63. The relations connecting the sides and angles of a triangle
(cont.) - - -- 108
~ 64. The angle of parallelism 109
~ 65. The Euclidean formulae hold true in infinitesimal geometry
on the hyperbolic plane - -109
CHAPTER V.
MEASUREMENTS OF LENGTH AND AREA, WITH THE
AID OF THE INFINITESIMAL CALCULUS.
~ 66. The element of arc in Cartesian coordinates - - 112
~ 67. The element of arc in polar coordinates - -114
~ 68. The element of arc in limiting-curve coordinates - 116
~ 69. Applications of these formulae - - 118
~ 70. The element of area in limiting-curve coordinates - - 119
~ 71. The element of area in Cartesian coordinates - - - 122
~ 72. The element of area in polar coordinates - - - 123
~ 73. The area of a triangle and of a quadrilateral with three
right angles -- -. -124
CHAPTER VI.
THE ELLIPTIC PLANE GEOMETRY.
~ 74. Plane geometry when the straight line is not infinite - - 127
~ 75. The pole of a line -12'
~ 76. All lines have the same length- - - - 129
~ 77. The two elliptic geometries - -131
~ 78. The sum of the angles of a triangle 132
~ 79. Saccheri's quadrilateral, and the quadrilateral with three
right angles - - -. 134