OSCN ODE—PEDAL. 
116 
Oscnode: defined, и, 28—32. 
Oscular: the term, vi, 334, 361, 362. 
Ostrogradsky, M. A.: dynamic equations, hi, 186, 203; transformation of differential equations, iv, 514; 
virtual velocities, ix, 207. 
Outcrops : the term, viii, 326, 351. 
Oval Chuck for Quartic Curves : viii, 151—5. 
Ovals: of Descartes, i, 479, n, 118, 336, ш, 66; and quartic curves, v, 468—70; twice-indented, x, 
318; and functions, xi, 540; in Ency. Brit., xi, 549—51; roots of algebraic equations, xiii, 37; 
Sylvester’s work at, xiii, 47 ; orthomorphosis, хш, 185—6, 202. 
Oxygen : trees of, ix, 427—60. 
П: Wallis’s investigation for, xiii, 22—5. 
Pagani, Gr. M. : central forces problem, iv, 520, 590 ; motion of solid body, iv, 583, 590. 
Painvin, L. : last multiplier, iv, 551, 590. 
Parabola: inflexions of cubical divergent, v, 284—8, vi, 101—4; classification, v, 356, 395, vi, 101; 
line and circle, problem, v, 607 ; polyzomal curves, vi, 542 ; cubic curves, xi, 478 ; in Ency. Brit., 
xi, 548—51, 561—4; orthomorphosis of circle into, xn, 328—36; and epitrochoid, xiii, 86—7; 
orthomorphosis into circle, xiii, 421—2. 
Parabolic Cyelide : ix, 73—8. 
Paraboloids: in Ency. Brit., xi, 576—9. 
Paradox : the d’Alembert-Carnot geometrical, xn, 305—6. 
Paraffins : trees of, ix, 427—60. 
Parallel Curves: envelopes and surfaces, iv, 123—33, 152—7, 158—65; and evolutes, viii, 31—5; theory 
of, x, 260; the critic in solar eclipses, x, 311—5. 
Parallels : and non-Euclidian geometry, xiii, 480—1, 481—9 ; the terms right and left, xiii, 488, 
502. 
Parallel Surfaces : of paraboloid, viii, 7 ; of ellipsoid, viii, 9, ix, 591 ; in Ency. Brit., x, 637—8. 
Parametric Class and Order : of systems of cones, v, 552. 
Parametric Latitude: vu, 16, ix, 238. 
Parametric Relation: vi, 463—4; of triple orthogonal system, viii, 292—315. 
Parazome : the word, vi, 477. 
Partial Differential Equations: integral of, hi, 166; system of, viii, 517—8; Jacobi’s, in transform 
ation of elliptic functions, xn, 530—3; on a, xiii, 358—61. 
Particle : under central forces, x, 575 ; {see also Dynamics). 
Partition of Numbers : и, 218, 235—49, v, 48 ; and quantics, n, 265 ; supplementary researches, 
ii, 506—12 ; a problem in, in, 247—9 ; tactical, v, 294, xi, 443. 
Partitions: conjugate, due to Ferrers, n, 419; formulae in, iii, 36—7; problem of double, iv, 
166—70; of a close, v, 62—5, 617; problems, vn, 575, x, 611, xi, 61—2; tables, ix, 480—3, 
xi, 357—64; theorems in trigonometry and, x, 16; in Ency. Brit., xi, 589—91 ; note on a partition- 
series, xn, 217—9 ; non-unitary partition, xn, 273—4 ; Sylvester’s constructive theory of, xiii, 47 ; 
of a polygon, xiii, 93—113; and seminvariants, xiii, 269. 
Pascal, B. : hexagram of, i, 356 ; limaçon of, i, 480 ; some theorems of geometry of position, i, 
550—6 ; lines of, i, 551, 588 ; curves, xi, 447 ; inscribed hexagon, xi, 556. 
Pascal’s Theorem : intersection of curves, i, 25—7 ; demonstration, i, 43—5 ; Chasles’ form of, i, 45 ; 
on, i, 322—8, 414, vi, 129—34, 594 ; generalized, v, 4; notation of points and lines, vi, 116—22, 594. 
Peacock, G. : multiple algebra, xn, 460, 467, 469, 470—1. 
Peaucellier, A. : mechanical construction of Cartesian by his cell, ix, 317 ; cell of, and scalene trans 
formation, ix, 527—34 ; Sylvester on his discoveries, хш, 44. 
Pedal Curves : Maclaurin on, v, 113—4.