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

INDEX

'609

Conjugate hyperbolic cylinders, 533.
Conjugate hyperboloids, 551;
- of revolution, 542;
sections of -, 563.
Construction, geometrical, of a parabola, 88;
-of an ellipse, 104, 114, 119;
-of a hyperbola, 124, 138, 143;
- of center, axes, foci, tangents
of a conic, 324, 325;
-of poles and polars, 319, 320,
325.
Constructions, mechanical, of a
parabola, 147;
- of an ellipse, 101, 147;
-of a hyperbola, 147.
Continued equality, cf. Equality.
Coordinate planes, 410.
Coordinates, rectangular, 7, 14; in
space, 409, 411, 589;
polar-, 193;
spherical -, 584, 590, 604;
cylindrical -, 587, 589, 604;
ellipsoidal -, 591.
Cramer's rule, 381, 464.
Cubic equations, graphs of, 85,
331, 353, 354.
Cubic, twisted, 492, 494.
Curves, in the plane, definition of,
19;
plotting of-, 19, 86, 331, 353;
in polar coordinates, 198;
symmetry of -, 84-87; in polar
coordinates, 201.
Curves, in space, definition of, 471;
parametric representation of -,
490;
Cylinders, equations of special, 444,
446;
definition and equations of general -, 532.
Cylindrical coordinates, 587, 589, 604.
Deformation of an elastic body, 357.
Degenerate conies, cf. Conics.
Descartes, 1.
Determinant of a transformation,
358.
Determinants, see Contents, Ch.
XVI;
applications of - to linear equations, 381-391, 401,403;

applications of - to plane analytic geometry, 391-399, 401 -403;
applications of - to solid analytic geometry, 438, 440, 443,
453, 463, 467, 477, 489, 496,
504, 507-511, 512-515, 517,
518, 526, 594, 599.
Diagonals of a determinant, 363.
Diameters of a conic, see Contents,
Ch. XIV.
Diameters of a quadric surface,
569-574,,579.
Diametral planes of a quadric surface, 570-574, 579.
Diodes, cissoid of, 214.
Directed line-segments, cf. Linesegments.
Directed trihedrals, 430-432;
right-handed and left-handed -,
443.
Direction angles of a directed line,
420.
Direction components, see Contents,
Ch. XVIII.
Direction cosines, see Contents, Ch.
XVIII;
- of three mutually perpendicular lines, 594.
Directrices of conics, 88, 116, 137.
Directrix of a cylinder, 532.
Discriminant, of a quadratic equation in x, 175, 402;
- of general equation of second
degree in x, y, 248, 402, 403.
Distance, between two points, 10;
in polar coordinates, 210; in
space, 414;
- of a point from a line, 41; in
space, 514;
- between two parallel lines, 51;
- of a point from a plane, 460;
- between two parallel planes,
466;
- between two lines in space,
515.
Division of a line-segment, 17, 416;
harmonic -, 309, 359, 575.
Eccentric angle, of an ellipse, 120,
306;
- of a hyperbola, 143.