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

INI

Projecting planes of a line, 501,
503.
Projection, of a point on a line, 5,
405;
- of a directed line-segment on a
line, 5, 405, 408, 441;
- of a broken line on a line, 5,
406;
- of a directed line-segment on
the axes, 9, 413;
- of a point on a plane, 406;
- of a line on a plane, 406, 501 -503;
- of an area on a plane, 516,
517;
- of a plane curve on a plane,
534.
Quadrants, 8.
Quadratic equation, discriminant of,
175, 402;
sum of roots of -, 274.
Quadric cones, 539;
sections of -, 144, 539, 561-563,
565.
Quadric cylinders, 532;
sections of —, 533;
degenerate -, 602.
Quadric surfaces, see Contents, Ch.
XXIII;
confocal -, 590, 592;
- of revolution, 540;
similar —, 581.
Radical plane of two spheres, 530.
Radius vector, 193, 584.
Ray, equation of, in polar coordinates, 196.
Rectangular hyperbola, 132;
problems concerning -, 151, 152,
157;
equation of - in polar coordinates,
207;
equation of - in form 2 xy = a2,
221;
more general equations of
239, 258, 259.
Reflection in the origin, 342.
Reflections in the axes, 336.
Rigid motion of the plane, 358.
Rotation of axes, 219, 239, 241;
in space, 593.

Rotations of the plane, 332.
Rows and columns of a determinant,!
36;
interchanges of -, 376, 380.
Rulings, of a cylinder, 532;
- of a cone, 536;
- of an unparted hyperboloid,
555-559, 568, 581-583;
- of a hyperbolic paraboloid,
559-561, 568, 582, 583.
Sections, of quadric cylinders, 533;
of quadric cones, 144, 539,
561-563,565;
of a quadric surface, defined,
549;
parallel -, 549, 561;
circular - -, 564;
cf. also Ellipsoid, etc.
Shears, simple, 351;
factorization of -, 355, 359.
Shrinkings of the plane, 334, 337.
Similar and similarly placed conics,
cf. Conics.
Similarity, of two parabolas, 89;
- of two ellipses, 103, 121;
- of two hyperbolas, 128, 149;
- of two quadric surfaces, 581.
Similitude, transformations of, 334,
358.
Slope angle, 13.
Slope of a curve, definition. of,
154;
general method of finding 154 -158,160-163;
exercises in -, 159, 164, 188.
Slope, of a line, 12;
- of a circle, 72;
- of a parabola, 94, 161;
- of an ellipse, 162;
- of a hyperbola, 163;
- of a general conic, 188.
Sphere, see Contents, Ch. XXIL
~~ 1-5;
null -, 524;
further problems concerning
544-546;
- transformed by one-dimensional strains, 578, 579.
Spherical coordinates, 584, 590, 604.
Spiral, of Archimedes, 202;
-, hyperbolic, 202.

)EX 613
Rotations of the plane, 332.
Rows and columns of a determinant,
36};
interchanges of -, 376, 380.
Rulings, of a cylinder, 532;
- of a cone, 536;
of an unparted hyperboloid,
555-559, 568, 581-583;
- of a hyperbolic paraboloid,
559-561, 568, 582, 583.
Sections, of quadric cylinders, 533;
of quadric cones, 144, 539,
561-563, 565;
-- of a quadric surface, defined,
549;
parallel -, 549, 561;
circular - -, 564;
cf. also Ellipsoid, etc.
Shears, simple, 351;
factorization of -, 355, 359.
Shrinkings of the plane, 334, 337.
Similar and similarly placed conics,
cf. Conics.
Similarity, of two parabolas, 89;
- of two ellipses, 103, 121;
-of two hyperbolas, 128, 149;
- of two quadric surfaces, 581.
Similitude, transformations of, 334,
358.
Slope angle, 13.
Slope of a curve, definition, of,
154;
general method of finding -, 154 -158, 160-163;
exercises in -, 159, 164, 188.
Slope, of a line, 12;
- of a circle, 72;
- of a parabola, 94, 161;
- of an ellipse, 162;
- of a hyperbola, 163;
- of a general conic, 188.
Sphere, see Contents, Ch. XXII,
~~ 1-5;
null -, 524;
further problems concerning -,
544-546;
transformed by one-dimensional strains, 578, 579.
Spherical coordinates, 584, 590, 604.
Spiral, of Archimedes, 202;
-, hyperbolic, 202.