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

178

SUBJECT INDEX

Geometry, Absolute
Imaginary, 34.
Nominal, 157.
Non-Archimedean, 18.
Non-Euclidean, 1.
Parabolic, 39.
Semi-Euclidean, 18.
Geometry in the infinitesimal is
Euclidean, 111.
on the Limiting-Surface is
Euclidean, 29.
on the Sphere is independent of
the Parallel Postulate, 29.
Grenzkreis (see Limiting-Curve),
80.
Hilbert's Axiom of Parallels, 42.
Horocycle or horicycle (see Limiting-Curve), 80.
Infinite, contrasted with unbounded, 38, 39, 127.
Inversion in the Nominal Geometry corresponds to a reflection, 158, 166.
Legendre's Hypotheses of the
Acute Angle, Right Angle, and
Obtuse Angle, 15-17.
Length of a line in Elliptic Geometry, 129-131.
Limiting-Curve, or horocycle, 80.
Arc of, 119.
Area bounded by arc of, and
two of its axes, 120.
Axes of, 52.
Coordinates, 116.
Equation of, 97.
Theorems on, 81, 82, 95-97.
Limiting-Curves, Concentric, 82.
Area bounded by arcs of two
concentric, and two of their
axes, 120.
Theorems on Concentric, 91-95.
Limiting-Surface, 35.
Linea-L, 80.
Lines, Asymptotic, 15, 29, 56.
Divergent, 58.
Ideal, 68.
Nominal, 156, 161, 172.
Not-intersecting, 15, 34, 40, 54.
Parallel, 1, 28, 34, 40, 42.

Measure of area of triangles and
polygons, 88-90, 120, 124-126,
135.
Measurement of angles, 104, 105.
Napier's Rules, 102.
Not-intersecting lines, Two, in a
plane have a common perpendicular, 54.
diverge on either side of common
perpendicular, 58.
One-sided surface, 131.
Order, Axioms of, 157.
Pangmomtrie, 36.
Parallel constructions, 71-77.
Parallel lines, Euclid's treatment
of, 1, 2.
Bolyai's treatment of, 28, 29.
Hilbert's treatment of, 42, 43.
Lobatschewsky's treatment of,
33-35, 40-42.
Right-handed and left-handed,
43.
Theorems on, 43-50, 56.
Parallel Postulate, Euclid's, 2.
Impossibility of proving, 10,
29-32, 35-36, 170-171.
Two theorems independent of,
8-10.
Pasch's Axiom, 3.
Perpendicular bisectors of sides
of a triangle, 68-71, 84.
Points, at infinity, 47, 66.
Ideal, 67.
Nominal, 156, 160, 172.
Proper and improper, 66.
Points, Corresponding, 77.
Theorems on, on parallel lines,
78-80.
Pole of a line, 129.
Postulate of Archimedes, 5, 18.
of Dedekind, 4.
Principle of Continuity, 4.
Problems of construction, independent of Parallel Postulate
and Principle of Continuity,
5-8.
in Hyperbolic Geometry, 65.
Quadrilateral, Saccheri's, 51, 134.
with three right angles, 52, 134.