PLANE-POINT. 
118 
Plane Representation of Solids: vir, 26—30. 
Planes: diametral, of quadric surface, i, 255—8; point and line defined, n, 561—2; geometry of two 
dimensions, ii, 569—83; MacCullagh’s theorem of polar, iv, 12—20; lines and dots of cubic 
surfaces, vi, 365—6, 373—449; rational transformation, vn, 197—213, 216—9 ; quadric transformation, 
vn, 213—6; also lineo-linear, vn, 215—6; determined by point and three lines, vii, 571; fleflec- 
nodal, of a surface, x, 262—4; kinematics of, xi, 103—10, xm, 505—16; in Ency. Brit., xi, 571—2; 
osculating and normal, xi, 579—80; and surface, xi, 629 ; non-Euclidian geometry, xm, 481—504 ; 
and line distance, xm, 497. 
Planetary Theory: Desboves’, hi, 185, 203; development of disturbing function, in, 319—43, vn, 
511—27; variation in plane of orbit, III, 516—8, vii, 541—5; theorem of Jacobi, in, 519—21; 
Newcomb’s work, ix, 180—4. 
Planets: angular distance of two, vii, 377—9. 
Planet’s Orbit from Three Observations: vii, 384—6, 400—78; introductory, vii, 400—1; the general 
theory, vii, 401—6; determination of orbit from given trivector, vii, 406—12; time formulae, 
Lambert’s equation, vn, 412—5; formulae for transformation between two sets of rectangular axes, 
vii, 415—7; intersection of orbit plane by single ray, vii, 417—26; trivector and orbit, vii, 
426—8; special symmetrical system of three rays, vii, 428—9; Planogram No. 1, meridian 
90°—270°, vn, 429, 430—40; No. 2, meridian 0°—180°, vn, 429, 441—51; No. 3, orbit-pole at 
point A, vn, 429, 452—4; No. 4, orbit-pole in ecliptic, vn, 429, 455—9; No. 5, orbit-pole on 
a separator, vii, 429, 459—67; spherogram and isoparametric lines, vri, 467—8; ¿-spherogram and 
iseccentric lines, vn, 468—70; time-spherogram and isochronic lines, vn, 470—7. 
Planogram: the term, vn, 404 ; three plates, vn, to face 478 ; meridian 90°—270°, vn, 429, 430—40; 
0°—180°, vii, 429, 441—51; orbit-pole at point A, vn, 429, 452—4; in ecliptic, VII, 429, 455—9; 
on separator, vn, 429, 459—67. 
Plates {see Diagrams, also Tables). 
Plato: and geometry, xi, 446. 
Playfair, J.: on twelfth axiom of Euclid, xi, 435. 
Plerogram: the term, ix, 202. 
Plexus: the term, iv, 603, vi, 458; Sylvester’s term, xm, 46. 
Pliicker, J.: theory of algebraic curves, I, 53, 54 ; curves and developables, i, 207, 208, 210, 586—7 ; 
involution, i, 259, 261; elimination, and theory of curves, I, 344; geometry of position, I, 356, 
553—6; geometrical reciprocity, I, 380; reciprocal figures, I, 418; quadric surfaces, I, 421; cubic 
surfaces, I, 446 ; transformation of curves, I, 478; singularities of plane curves, I, 586, v, 520—2, 
619, xi, 450; cubic curves and cones, iv, 173—8; double tangents, iv, 186; points of six-pointic 
contact on cubic, iv, 207; cubic curves, iv, 495, 617, v, 402; line geometry, iv, 616—8; hyper 
boloid coordinates, v, 72; node-cusp, v, 265—6; curve classification, v, 354—400 ; numbers for 
singularities of plane curves, v, 424, 476, 517; higher singularities of plane curves, v, 426, 619 ; 
pencil intersections, v, 484; numbers of, vi, 68, vm, 41—5, xi, 469—73; species of cubical parabola, 
vi, 101 ; focus, vi, 515, xi, 481 ; six coordinates of a line, vn, 66; quartic surface models, vn, 
298—302 ; construction of a conic, vn, 592; hypergeometry, vm, xxxv; theory of curve and torse, 
vm, 74, 75—6, 80—1 ; theory of curves, xi, 467; envelopes, xi, 475—6; note on equations of, 
xm, 536. 
Pohlke, K.: theorem in axonometry, ix, 508. 
Poincar6, H.: lacunary functions, xm, 415. 
Poinsot, L.: polygons and polyhedra, iv, 81—5, 86—7, 609; inertia, iv, 563, 590—1; rotation of solid 
body, iv, 571—3, 577, 591 ; kinematics of solid body, iv, 580, 581, 591. 
Point: of cubic curve, ii, 382; satellite, n, 383; formulae, n, 405—9; theorems, n, 40.9—12; 
plane and line defined, n, 561—2; and ineunt of a curve, n, 574; lattice, m, 40; distances 
of, from triangle and formulae, iv, 510—2; tritom, v, 138; the term polar of, v, 570; and abstract