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

SUBJECT INDEX.

Numbers refer to pages.

Absolute Science of Space, 27-29.
Absolute unit of length, 17, 25.
Absolute units as compared with
relative, 17, 90.
Angle of parallelism, 41, 50, 109.
Associated Right-angled Triang] es
63-66.
Circle, Arc of, 118.
Area of, 124.
of infinite radius (see LimitingCurve), 80.
Three kinds of, in Hyperbolic
Geometry, 83, 170.
One kind of, in Elliptic Geometry, 135.
Complementary segments, 51.
Hyperbolic functions of, 98-99.
Congruence, Axioms of, 2, 5.
of infinite areas, 17.
Consistency of the Non-Euclidean
Geometries, Ch. VIIT.
Correspondence between rightangled triangle and quadrilateral with three right angles,
59-63.
Courbe-limits (see Limiting-Curve),
80.
Defect of triangle, 54.
of polygon, 89.
Direction of parallelism, 45.
Direction-theory of parallels, 11.
Displacement equivalent to two
reflections or inversions in the
nominal geometry, 158, 159,
166.

Element of arc, in Elliptic Geometry, 152.
in Hyperbolic Geometry, Cartesian Coordinates, 112-114.
in Limiting-Curve Coordinates,
117-118.
in Polar Coordinates, 114-116.
Element of area, in Elliptic Geometry, 152.
in Hyperbolic Geometry, in Cartesian Coordinates, 122-123.
in Limiting-Curve Coordinates, 119-121.
in Polar Coordinates, 123-124.
Equidistant-Curve, 82.
Base-line of, 83.
Concave to base-line, 83.
Arc of, 118.
Equivalent polygons, 84.
Equivalent triangles, 85.
Theorems on, 85-88.
Euclid's unexpressed axioms, 3, 4.
Parallel Postulate or Parallel
Hypothesis, 2.
Postulates I.-II., 3.
Postulate III., 5, 74.
Excess of a triangle, 134.
Exterior angle, Theorem of (I. 16),
3, 130, 131.
in triangle with one angular
point at infinity, 48.
Geometry, Absolute, 29.
Astral, 22.
Elliptic, 39, 131.
Euclidean, 2.
Hyperbolic, 39.