Projective geometry, by Oswald Veblen and John Wesley Young.

INDEX
The numbers refer to pages

Abelian group, 67
Abscissa, 170
Abstract science, 2
Addition, of points, 142, 231; theorems
on, 142-144; other definitions of, 167,
Exs. 3, 4
Adjacent sides or vertices of simple
n-line, 37
Algebraic curve, 259
Algebraic problem, 238
Algebraic surface, 259
Alimlllenlt, assumptions of, 16; consistency of assumptions of, 17; theorems
of, for the plane, 17-20; theorems of,
for 3-space, 20-24; theorems of, for
4-space, 25, Ex. 4; theorems of, for
n-space, 29-33
Amodeo, F., 120, 294
Anharmonic ratio, 159
Apollonius, 286
Associative law, for correspondences,
66; for addition of points, 143; for
multiplication of points, 146
Assumption, Ho, 45; Ho, role of, 81,
261; of projectivity, 95; of projectivity, alternative forms of, 105, 106,
Exs. 10-12; 298
Assumptions, are necessary, 2; examples of, for a mathematical science,
2; consistency of, 3; independence
of, 6; categoricalness of, 6; of alignment, 16; of alignment, consistency
of, 17; of extension, 18, 24; of closure, 24; for an n-space, 33
Axial pencil, 55
Axial perspectivity, 57
Axis, of perspectivity, 36; of pencil,
55; of perspective collineation, 72; of
homnology, 104; of coordinates, 169,
191; of projectivity on conic, 218
Base, of plane of points or lines, 55; of
pencil of cnmplexes, 332
Bilinear equation, binary, represents
projectivity on a line, 156; ternary,
represents correlation in a plane, 267
Binary form, 251, 252, 254
BOcher, M., 156, 272, 289, 330
Braikenridge, 119
Brianllon point, 111
Brianchon's theorem, 111

Bundle, of planes or lines, 27, 55; of
conics, 297, Exs. 9-12; of quadrics,
311; of complexes, 334, Ex. 7
Burnside, W., 150
Bussey, W. H., 202
Canonical forms, of collineations in
plane, 274-276; of correlations in a
plane, 281; of pencils of conics, 287 -293
Castelnuovo, G., 139, 140, 237, 297
Categorical set of assumptions, 6
Cayley, A., 52, 140
Center, of perspectivity, 36; of flat pencil, 55; of bundle, 55; of perspective
collineation in plane, 72; of perspective collineation in space, 75; of
homology, 104; of coordinates, 170;
of projectivity on conic, 218
Central perspectivity, 57
Characteristic constant of parabolic
projectivity, 207
Characteristic equation of matrix, 165
Characteristic throw and cross ratio, of
one-dimensional projectivity, 205, 211,
Exs. 2, 3, 4; 212, Exs. 5, 7; of involution, 206; of parabolic projectivity,
206
Chasles, 125
Class, notion of, 2; elements of, 2; relation of belonging to a, 2; subclass of
a, 2; undefined, 15; notation for, 57
Clebsch, A., 289
Cogredient n-line, 84, Ex. 13
Cogredient triangle, 84, Exs. 7, 10
Collineation, defined, 71; perspective, in
plane, 72; perspective, in space, 75;
transforming a quadrangle into a
quadrangle, 74; transforming a fivepoint into a five-point, 77; transforming a conic into a conic, 132; in plane,
analytic form of, 189, 190, 268; between two planes, analytic form of,
190; in space, analytic form of, 200;
leaving conic invariant, 214, 220, 235,
Ex. 2; is the product of two polarities, 265; which is the product of
two reflections, 282, Ex. 5; double elements of, in plane, 271; characteristic equation of, 272; invariant figure
of, is self-dual, 272

335