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

608

INDEX

four points lie on a circle, 395, 398;
six points lie on a conic, 398;
two lines be parallel, 36, 45, 46,
402;
two lines be perpendicular, 37,
45, 46;
two lines be identical, 46, 402;
three lines be concurrent, 53, 189,
393; problems, 54-60, 62, 189,
394;
a line be orthogonal to a circle,
76;
two circles be orthogonal, 77;
a line be tangent to a conic, 183,
192, 403;
two diameters be conjugate, 291,
296;
a conic be degenerate, 257, 403;
a transformation be isogonal, 348.
Condition, in space, that
a point lie on a surface, 445;
a point lie on a curve, 471;
two points be collinear with the
origin, 441;
three points be collinear, 505;
four points be coplanar, 508;
five points lie on a sphere, 527;
two lines be perpendicular, 426,
435;
two lines be parallel, 420, 427,
430, 432, 436;
two lines intersect, 512;
three lines be parallel to a plane,
440;
the normals to four planes be
parallel to a plane, 508;
three lines be mutually perpendicular, 594;
a line lie in a plane, 506;
a line be tangent to a quadric,
567;
two planes be perpendicular, parallel, identical, 455;
three planes pass through a line,
504;
four planes pass through a point,
510;
a plane be orthogonal to a sphere,
545;
a line be orthogonal to a sphere,
546:
two spheres be orthogonal, 546;

a diameter and a diametral plane
be conjugate, 571;
three diameters be conjugate,
573;
three diametral planes be conjugate, 573;
three numbers be direction cosines,
422;
a directed trihedral be righthanded, 443.
Cones, 536.
Confocal conics, 145, 148.
Confocal parabolas, 95, 146.
Confocal paraboloids, 592.
Confocal quadrics, 590.
Conics as sections, of a circular
cone, 144;
- of a quadric cylinder, 534;
- of a quadric surface, 562.
Conies, definition of, 144;
equations of - in polar coirdinates, 202, 210, 211;
— as loci of equations of the
second degree, 257;
equation of - through five points,
395, 398;
six points on a -, 398, 399.
Conics, degenerate, definition of,
257;
equations of -, 191, 244, 253,
260, 402;
examples of -, 237, 246, 254, 259;
-through five points, 396, 397;
condition for -, 257, 402;
- as intersections with quadric
surfaces, 256, 257, 563, 569.
Conics, similar and similarly placed,
260;
- as sections of two quadric
surfaces, 535, 563, 580;
- - as parallel sections of a quadric surface, 550, 553, 555, 562 -564, 580.
Conjugate diameters and diametral
planes, 571-574, 579.
Conjugate diameters of a conic,
see Contents, Ch. XIV.
Conjugate diameters of a quadric
surface, 572-574, 579.
Conjugate diametral planes, 572 -574, 579.
Conjugate hyperbolas, 141, 296.