PONCELET—POTENZKREIS.
120
ideal factor of branch or branches, vi, 481—5 ; the trizomal and tetrazomal, vi, 485; intersection
of two v zomals having same zomal curve, vi, 486—7; theorem of decomposition of tetrazomal,
vi, 487—9; application to trizomal, vi, 489—94; tetrazomal curve, vi, 494; variable zomal of
trizomal curve, resumed, vi, 494—7; Part II, subsidiary investigations, vi, 497—515; preliminary
remarks, vi, 497—8 ; circular points at infinity; rectangular and circular coordinates, vi, 498—9 ;
antipoints; definition and fundamental properties, vi, 499—500; antipoints of circle, vi, 500;
antipoints and pair of orthotomic circles, vi, 500; forms of equation of circle, vi, 501 ; system
of 16 points, vi, 501—3; property in regard to four confocal conics, vi, 503—4; system of sixteen
points, the axial case, vi, 504—5; involution of four circles, vi, 505—8; locus connected with
foregoing, vi, 508—9; formulae of two sets each of four concyclic points, vi, 509—11; ditto
further properties, vi, 512—5; Part III, theory of foci, vi, 515—34; the general theory, vi, 515—7;
foci of conics, vi, 517—9; variable zomal applied to conic, vi, 519—21; foci of circular cubic
and bicircular quartic, vi, 521—2; centre of circular cubic, and nodo-foci, etc., of bicircular quartic,
vi, 522—3; circular cubic and bicircular quartic; symmetrical case, vi, 523; ditto, singular forms,
vi, 523—6 ; analytical theory for circular cubic, vi, 526—8; ditto, for bicircular quartic, vi, 528—30;
property that points of contact of tangents from pair of concyclic foci lie in a circle, vi, 530—34;
Part IV, trizomal and tetrazomal curves where the zomals are circles, vi, 534—66; the trizomal
curve-tangents at /, J, etc., vi, 534—7; foci of conic represented by equation in areal coordinates,
vi, 537; theorem of variable zomal, vi, 539—41; relation between conic and circle, vi, 541—2;
case of double contact, Casey’s equation in problem of tactions, vi, 543; intersections of conic
and orthotomic circle on set of four concyclic foci, vi, 543—4; construction of symmetrical curve,
vi, 544—6; focal formulae for general curve, vi, 547; circular cubic, vi, 548—9; focal formulae
for symmetrical curve, vi, 549 ; symmetrical circular cubic, vi, 549—50; general ditto, vi, 550—3;
transformation to new set of concyclic foci, vi, 553; tetrazomal curve, decomposable or indecomposable,
vi, 553—4; cases of indecomposable, vi, 554—5; ditto, centres being in line, vi, 555—6; the
decomposable curve, vi, 556—7 ; ditto, centres not in a line, vi, 557—61 ; ditto, centres in a line,
vi, 561—5; ditto, transformation to a different set of concyclic foci, vi, 565—6; theory of Jacobian,
vi, 566—8; Casey’s theorem for circle touching three given circles, vi, 568—73; a norm when
the centres are in line, vi, 573—5; trizomal curves with cusp or two nodes, vi, 575—6.
Poncelet, J. V.: harmonic relations, n, 96; porism of in-and-circumscribed triangle, hi, SO—5;
rectangular hyperbola, in, 254; in-and-circumscribed polygon, v, 21—2; reciprocal polars, xi, 466.
Pont6coulant, G. de: Systeme du Monde, in, 309—10; Lunar Theory, in, 521, vn, 357.
Porism: homographic, defined, in, 74, 84; allographic defined, in, 75, 85; of polygon and correspondence,
ix, 94.
Porism of in-and-circumscribed Polygon: ii, 87—9, 91—2,97, 138—44, 145—9, iv, 292—308, vm,
14—21, 212.
Porism of in-and-circumscribed Triangle: n, 56, 87—90, 91, in, 67—75, 80—5, 229—41. v, 549—50,
579, VIII, 212—57.
Portraits of Cayley: frontispiece to vols. vi, vn, xi.
Pos: the abbreviation in groups, xm, 119.
Positive: the rule of signs, iv, 595—6, xi, 492.
Postulandum of Curve: the term, i, 583, vn, 140, xu, 501; and capacity, xm, 115.
Postulation: the term, i, 583, vn, 140, 225, vm, 394; of curve, xu, 501.
Potential: and attractions, i, 195.
Potentials: of polygons and polyhedra, ix, 266—80; of ellipse and circle, ix, 2S1—301 ; Smith’s Prize
question on, xi, 261—4.
Potential-solid : prepotential, ix, 346—7.
Potential-surface : prepotential, ix, 343—6.
Potenzkreis of Steiner: in, 113.
