139 
TRANSFORMATION—TWO-WAY. 
Transformation, Septic: of elliptic functions, x, 333—8, xn, 535—54. 
Transformation, Special Quartic: of elliptic functions, ix, 103—6. 
Transmutant : defined, n, 515. 
Transpose : the term, n, 493. 
Transvectant : form of covariants, vm, 404—8 ; (see also Derivatives). 
Trees: analytical forms called, in, 242—6, iv, 112—5, xi, 365—7; curves which satisfy given conditions, 
vi, 260 ; application to chemistry, ix, 202—4, 427—60, 544—5 ; problem and solution, x, 598—600 ; 
a theorem on, xm, 26—8. 
Triads: of seven and fifteen things, I, 481—4, 589; of fifteen things, v, 95—7. 
Triangle : harmonic relation of point and line, ii, 96—7 ; reciprocal triangles, in, 5—7 ; circumscribed 
about conic, properties of, in, 29—34 ; theorem of line and conic, v, 100—2 ; problems, v, 564, 566, 
593, vii, 581, 599, x, 575; locus in relation to, vi, 53—64; locus and envelope, vi, 72—82; solution 
of problem in Principia, Bk I. Sec. V. Lemma xxvn, vii, 30 ; potential of, ix, 270—1 ; non- 
Euclidian, xm, 482—3 ; nine-point circle of a plane, xm, 520—1. 
Triangle, In-and-circumscribed, the Problem of, Memoir: vm, 212'—57; introductory, vm, 212—3; 
tables, vm, 214—21 ; principle of correspondence, vm, 222—5 ; locus of a free angle, vm, 225—7 ; 
application of theory to locus, vm, 227—8 ; solutions for 52 cases, vm, 228—51 ; the case 52, 
vm, 251—57. 
Triangle, In-and-circumscribed : n, 87—90, 91—2, 138—44, 145—9, in, 67—75, 229—41, iv, 435—41, 
v, 489—92, 549—50, 553, vm, 565—6 ; a posteriori demonstration of porism, in, 80—5 ; (see also 
Porism). 
Triangle, Spherical: theorem of, iv, 80, xi, 97—9; nine-point circle of, xm, 548—51. 
Tricircular Sextic : ix, 562—70. 
Trident Curve : classification, v, 355—69, 395. 
Trigonometry : transformation of an expression, n, 45—6 ; multiple sines, x, 1—2 ; theorem in partitions 
and, x, 16; identities, xi, 38, xm, 538—40; formuke, xn, 108; an expansion, XII, 319—20. 
Trigonometry, Spherical : theorem, iv, 80, xi, 97—9 ; identity, vm, 525 ; foundation, xi, 570. 
Trigonometry, Spheroidal : ix, 197. 
Trihedral Pair: the term, vi, 374. 
Trinodal Quartic : x, 602 ; (see also Quartic Curves). 
Tripair: the term, x, 450—1. 
Tripartite : the term, vi, 464. 
Triple Tangent Planes : of cubic surfaces, i, 445—56, 589, vi, 372, 376. 
Triple Theta Functions : x, 432—6, xi, 47—9 ; algorithm for characteristics of, x, 441—5 ; and quartic 
curves, x, 446—54. 
Tris : the abbreviation in groups, xm, 119. 
Trisection : in theory of numbers, xi, 84—96. 
Tritom : and point, v, 138. 
Trivector : the term, vn, 400, 401 ; planet’s orbit from, vn, 406—12, 426—8. 
Trizomal (see Polyzomal Curves). 
Trope : the term, vi, 330, vm, 73, x, 54—5. 
Tropical Point : the term, xn, 433. 
Truel, H. D. : imaginaries, xn, 467. 
Tschirnhausen’s Transformation: vi, 165—9, xi, 3.96; for cubics, iv, 364—7, xm, 421; quartics, 
iv, 368—74, 375—82, v, 449—53 ; quintics, iv, 382—94 ; theory of equations, xi, 509. 
Tucker, R. : geometrical interpretation, x, 581. 
Twisted : the term, vi, 524—5. 
Two Centres Problem : iv, 524—32. 
Two-way Point : the term, xm, 507. 
18—2