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

INDEX

Abridged notation, 171;
problems in -, 189, 287.
Absolute value, 4;
use of -, 11, 41, 42, 51, 466.
Acoustical property of conics, cf.
Focal property.
Affine transformations, 342;
homogeneous -, 348, 355;
singular -, 358.
Anchor ring, 544.
Angle, in the plane, positive sense
for measurement of, 13;
slope -, 13;
- between two lines, 38.
Angle, in space, between two lines,
407, 425, 435, 442;
direction - of a directed line, 420;
- between two planes, 455;
- between a line and a plane, 487.
Asymptotes, 129, 259.
Asymptotic cone, 543, 552, 557.
Asymptotic planes of a hyperbolic
cylinder, 533.
Axes of a conic, 88, 102, 125, 127;
equations of -, 260;
construction of -, 324.
Axes of a quadric surface, 533, 549,
551, 555.
Axes of coordinates, 7, 410.
Auxiliary circle of an ellipse, 120;
- of a hyperbola, 143.

Central conics, 299, 313.
Central line of a strain, 304.
Central quadrics, 575, 601.
Circle, see Contents, Ch. IV;
null -, 67;
equation of - in determinant
form, 394, 398;
nine-point -, 78;
- as limit of ellipses, 103, 140;
parametric representation of -,
119;
common chords of three -, 170;
equations of - in polar coordinates, 194, 211;
- inscribed in a triangle, 283;
four points on a -, 395, 398.
Circle in space, 529;
tangent line to -, 545;
as section of a quadric surface,
564.
Cissoid, 214.
Coefficient of a strain, 309.
Colatitude, 584.
Columns and rows of a determinant,
363;
interchanges of -, 376, 380.
Compatibility of n+1 equations in
n unknowns, 384, 401, 403,
510.
Compression, simple, cf. Strain,
one-dimensional.
Conchoid, 215.
Condition that
the roots of a quadratic equation
be equal, 175;
two sets of numbers be proportional, 385;
an equation be homogeneous, 538.
Condition, in the plane, that
a point lie on a curve, 19;
two points be collinear with the
origin, 25, 402;
three points be collinear, 54,
392; problems, 60-63, 394:

Bisectors of angles, between
lines, 281, 287;
- between two planes, 522.
Brennpunkt, 97.

two

Cardioid, 201, 209, 215, 286.
Cassini, ovals of, 215.
Center of a conic, 102, 125, 247,
259;
construction of -, 324.
Center of a quadric surface, 543,
549, 551.

607