Plane and solid analytic geometry, by William F. Osgood and William C. Graustein.

INDEX

611

Hyperboloids of revolution, 541,
550, 551.
Identical transformation, 342.
Inequalities, loci of, 277, 279, 522.
Infinity, 13.
Initial ray, 193.
Intercepts, of a line, 33;
- of a plane, 450.
Intersection, of two lines, 22;
-of two curves, 23;
-of three planes, 463;
- of two planes, 470, 476;
- of a line and a plane, 488, 492;
-of a plane and a sphere,'529;
- of two spheres, 530;
— of a curve and a surface, 488,
492;
- of two surfaces, 472;
- of three surfaces, 463.
Invariants of general equation of
second degree, 257, 599.
Inverse of a transformation, 335.
Involutory transformations, 337.
Isogonal transformations, 336, 347,
359.
Kepler, 97.
Latus rectum, 94, 112, 135.
Lemniscate, 201, 207, 215, 286.
Limacon, 202, 215.
Line, equations of,
perpendicular to a given plane,
483;
parallel to two planes, 484;
parallel to a given line, 485;
perpendicular to two lines, 485.
Line, in plane, see Contents, Ch.
II;
equation of — in polar coordinates, 196, 210;
equatin of - in normal form,
28;
eqtions of - in determinant
form, 391, 393, 401;
three - through a point, 53,
189, 392;
problems in ttree - through a
point, 54-60, 62, 189, 394;
single equation for two -, 173,
190, 191.

Line, in space, see Contents, Chs.
XVIII, XX, XXI.
Line-segments, see Contents, Introduction, Chs. I, XVII.
Linear combination, of two lines,
165, 168, 169;
- of two curves, 167, 168, 170;
- of two planes, 498, 504, 506;
- of two surfaces, 520;
- of three planes, 521;
- of sets of numbers, 400.
Linear equation, in x, y, 31;
- in x, y, z, 448.
Linear equation, simultaneous, see
Contents, Ch. XVI, ~~ 8-10;
also 401, 403, 464, 510.
Loci of inequalities, 277, 279, 522.
Loci problems in plane, see Contents, Chs. V, XIII;
further exercises in -, 100, 123,
152, 214, 328;
- in polar coordinates, 214.
Loci problems in space, 497, 546,
582.
Locus of an equation, 19; in space,
445;
- of two simultaneous equations,
471.
Longitude, 584.
Mid-point of a line-segment, 16,
415.
Minimum ellipse of an unparted
hyperboloid, 550.
Minor of a determinant, 367;
use of - to evaluate a determinant, 367, 370, 380.
Nappe of a cone, 537.
Nicomedes, conchoid of, 215.
Nil-segment, 5.
Normal to an arbitrary curve, 158;
exercises in finding equations of
-, 160, 165.
Normal, to a parabola, 95;
- to an ellipse, 111, 112;
- to a hyperbola, 135.
Normal, to a plane, 447;
direction components of- -
449;
- to three planes parallel to a
plane, 463;