Biquadratic equation and elliptic functions C.57 L.58
Biquadratic equation and sextic eqs.in the theory of conics and quadrics J.53
Biquadratic equation, cond. for two equal roots E.44
Biquadratic equation, reduction to a reciprocal equation L.63
Biquadratic equation, reduction to canonical form G.5
Biquadratic equation, solution of A.51 56 C.49 82 L.73 Q.19
Biquadratic equation, solution of, 4 variables J.27
Biquadratic equation, solution of, numerical C.61
Biquadratic equation, solution of, trigonometrical A.19 70
Biquadratic equation, solution of, without eliminating the 2nd term A.39
Biquadratic equation, values which make it a square 496 G.7 E.22
Biquadratic function with four variables An.59
Biquadratic involutions C.98
Biquaternions AJ.7 LM.4
Biternary forms with contragrcdient variables M.1
Bonnet, two formulae of G.4
Borchardt's functions J.82
Brachistochrone 3037 3044 L.48 Man.31 Me.80 Mem.22 N.77 80
Brahmins, trigonometrical tables of the TE.4
Brianchon's theorem 4783 A.53 C.82 CM.4 G.2 J.84 93 gzN.82 Z.6
Brianchon's theorem and analogues CD.7 Q.9
Brianchon's theorem and analogues on a quadric surface C.98 E.19
Brianchon's theorem and analogues on a sphere A.60
Brocard circle and Lemoine's point 4754c gzN.85
Burchardt's factor tables p.7
Burchardt's factor tables, erratum A.23
Burmann's theorem, d.c 1559
Calculating machine Pr.37
Calculus of chemical operations Pr.25
Calculus of direction and position AJ.6 M.pr6
Calculus of enlargement AJ.2
Calculus of equivalent statements see "Logic"
Calculus of forms (Invariant theory) CD.7 8 9
Calculus of infinitesimals, third branch of, viz., given y and  , to find x TE.24
Calculus of limits, ap. to a system of d.e C.15
Calculus of other subjects see "The subject"
Calculus of Victorius Z.16
Calculus, algebraic, which includes the calculus of imaginaries and quaternions C.91
calendar J.3 9 prs22
Calendar, Jewish J.f28
Canal surfaces A.1 10
Canon-arithmeticus of Jacobi C.39 63 L.54
Cantor's theorem M.22
Cardioid and ellipses Pr.6
Cardioid, b=a in 5328 Fig.129 A.59 63 68 LM.4 Me.64 N.81
Carnot's theorem 4778
Cartesian oval 5341—5358 A.69 C.97 LM.1 3 99 Me.75 Q.1 Me.74 Q.12 cn
Cartesian oval through 4 points on a circle LM.12
Cartesian oval with 2 imaginary axial foci LM.3
Cartesian oval, area of E.21
Cartesian oval, eq.with triple focus as origin E.9 23
Cartesian oval, foci E.7
Cartesian oval, functional images Q.18
Cartesian oval, mechanically drawn LM.5 6 Q.13
Cartesian oval, perimeter E.21
Cartesian oval, rectific. by ellip. functions C.80 87 LM.5
Cassinian oval 5313 Me.77 83 N.57
Cassinian oval, analogous surfaces An.61
Cassinian oval, radial of E.26
Cassinoid with n foci, rectif. of L.48
Catacaustic and diacaustic of a sphere JP.17
Catalecticant of a binary quantic E.37 38
Catenary 5273 Me.64 66 68
Catenary by parabolic trigonometry Pr.8
Catenary, revolving E.22
Cauchy's formula i.c 2712
Cauchy's formula i.c, closed curve theorem Mo.85
Cauchy's formula i.c, various formulae C.27
Caustics 5248—5249 Ac.4 L.46 P.57 67 Pr.8 14 15 Q.1 2 3 cn8 9 12
Caustics by successive reflexion from spheres J.13
Caustics of a cardioid Me.83
Caustics of a circle 5248 CD.2
Caustics of a cycloid A.30
Caustics of an ellipse, focus at centre J.44
Caustics of infinitely thin pencils J.98
Caustics of refraction at a plane surface N.47
Caustics, identity with pedals Z.14
Caustics, radii of curvature N.65
Caustics, surfaces and singularities J.76
Cell structure LM.16
Cells of bees N.56 Q.2
Centimetre-gramme-second system p.1
Centrals, theory of J.24
Centre of a circle touching two A.24
Centre of curves and surfaces L.46 Q.10
Centre of geometrical figures A.16
Centre of harmonic mean J.3
Centre of mean distance of curves and surfaces N.ths 85 Q.33
Centre of mean distance of points of contact of parallel tangents, ext. of th. L.44
Centre of similarity 947
Centre of similitude 1037
Centre of similitude of 2 quadrics each of which circumscribes the same quadric J.31
Centre of similitude of 3 circles 1046 4176
Centres, theory of J.24
Centro-baric methods in anal. geometry J.5
Centroid and its use in stereometre A.39
Centroid of a dice N.63
Centroid of a frustrum of a prism L.39
Centroid of a frustrum of a pyramid Me.79 N.76
Centroid of a gauche curve after development on a right line, locus of C.88
Centroid of a perimeter A.51
Centroid of a trapezium Q.9
Centroid of a triangle 951 A.52 58
Centroid of algebraic curves and surfaces An.68
Centroid of circular arc 6021 E.13
Centroid of common points of two conics A.3
Centroid of frustrums 6048 &c. A.33
Centroid of oblique frustrum of a cone E.33
Centroid of plane curves 5887 J.21 G.12
Centroid of spherical and other areas 5898 6051 J.50 L.39 42
Centroid of surface and solid of revolution 5896—5899 AJ.3 L.39
Centroid, formulae for 5884—5902 6015 JP.26 L.43
Change of independent variable 1760—1816 AJ.3 CM.1 G.2 L.40 58 Q.1 2 10 Z.17
Change of independent variable from x, y to r,  1768
Change of independent variable from x, y, z to r, ,  1783
Change of independent variable in a definite multiple integral 2774—2779 A.22 41
Change of independent variable in the theory of isotropic means C.34
Change of independent variable in transcendent definite integrals C.23
Characteristics E.5 J.71 M.6
Characteristics of conic A.1 C.67 72 76 83 JP.28 LM.9 M.15 N.66 71
Characteristics of conics of 5-point contact E.27
Characteristics of cubic systems C.74
Characteristics of curves and surfaces C.73
Characteristics of quadrics C.67 JP.28 N.68
Characteristics, relation between two characteristics in a system of curves of any degree C.62
Characteristics, surface groups defined by two C.79
Characteristics, surface groups defined by two,  C.78
Chart construction Mel.2 N.60 78
Chemico-algebraic theory AJ.1
Chemico-graphs AJ.1
Chess board, ths and prs A.56 E.34 42 44
Chessmen, relative value of E.39 Mel.3
Chinese arithmetic and algebra C.51 N.63
Chord joining two points on a circle 4157 A.43 44 E.22
Chord of contact for two circle 4172
Chronology J.26
circle 4136—4190 c.c A.1 3 th4 9 25 27 th47 C.94 J.14 17 Q.19 TE.th6
Circle and in-quadrilateral 733 CD.9
Circle and self-conj. triangle A.41
Circle and triangle, ths and prs A.30 57 LM.15 Q.4
Circle and two points; Alhazen's pr AJ.4
Circle of curvature 1254 5134 A.31 63 J.45 p.cN.84
Circle, and sphere, geo. Mo.82
Circle, approximate rectification and quadrature 6019 &c 6 geo13 14 43 J.32 Me.75 85 N.45 47 Q.4
Circle, arc of see "Circular arc"
Circle, area of segment 6035 A.27 39 44
Circle, chord of 4157 4158
Circle, chord of contact 1017 4138 4172
Circle, cn. from 3 conditions 937 JP.9
Circle, coaxal 1021—1036 A.23
| Circle, configuration of C.93
Circle, Cotes's properties 821 A.11
Circle, Cotes's properties, ext. to ellipse 30 P.13 TI.7
Circle, cutting three at given angles 4185 LM.3 5 N.83
Circle, Division of A.27 37 41 At.19 E.1 31 G.6 C.85 93 J.27 54 56 N.53 54
Circle, division of and theory of numbers J.30 84 87 N.56
Circle, division of, ths. on sum of sqs. of perpendiculars, &c. 1094—1098
Circle, eight circles touching three, cn 4189 Mel.3 Q.5
Circle, eight through 6 points of intersection of 3 conics Q.10
Circle, equation of 4136—4148 p.c Pr.27 TI.26
Circle, equation of, general eq. t.c 4691 4751
Circle, equation of, general eq. tg.c 4906
Circle, Euler's th. extended to ellips A.51
Circle, five-point th. E.5
Circle, four pairs of circles through 6 points common to 3 circle Q.9
Circle, four points concyclic, condition A.44 N.84
Circle, geometry of A.67 Z.24
Circle, groups of points on A.14
Circle, in tri-metric point-coordinates Z.27
Circle, lines of equi-different powers in two circles A.19
Circle, polar of x'y' 4138 4164
Circle, prs. 1049 At.19 L.46 see
Circle, rectangles of Z.14
Circle, ring of, touching two fixed J.39 Me.78
Circle, six points th. Q.8
Circle, system through a point on a plane or sphere G.16
Circle, tangents 4137—4143 4160 L.56 P.14
Circle, tangents, common to a circle and conic cnA.69
Circle, tangents, common to two circles 953 4171 cnA.34
Circle, tangents, locus of a point, the tangents from which to two circles have a given ratio geo.965 966
Circle, three 997—999 1036 1046—1051 4183—4187
Circle, through 3 points 4156 4738
Circle, through 3 points on a conic A.2 J.39
Circle, through mid-points of sides of a triangle see "Nine-point circle"
Circle, touching 3 circles, cn 946 1049 A.24 26 28 35 An.68 C.60 Me.62 N.63 65 66 84 Q.8
Circle, touching a conic twice J.56 N.65
Circle, touching the 4 circles which touch the sides of a spherical triangle A.4
Circle, two; eq. for angle of intersection 4180 4181
Circle, two; theorems 984—1045 Q.11 see "Coaxal
Circulants of odd order Q.18
Circulants, final expansion of Me.85
Circular and elliptic functions in continued fractions CD.4
Circular, arc, length centroid with real tangents Z.1
Circular, arc, length centroid, &c. 6019
Circular, arc, length centroid, graphic rectification and transposition of Z.2
Circular, cubics, involution of LM.1 7
Circular, cubics, involution of, chord of curvature of E.cn36
Circular, functions 606 A.17 J.16
Circular, points at infinity see "Imaginary ditto"
Circular, relation of Mobius LM.8 N.76 Q.2
Circular, segment: arc, chord and area 6035 N.63
Circulating functions P.18
Circum cubic of a complete quadrilateral G.10 Q.5
Circum-centre of a triangle 4642 tg.
Circum-circle of a polygon 746—748 A.19
Circum-circle of a quadrilateral 733 N.79
Circum-circle of a triangle 713 4738 tg. A.51 58
Circum-circle of a triangle and in conic N.79
Circum-circle of a triangle, coordinates of centre 4642
Circum-circle of a triangle, hypocycloidic envelope of Ferrers N.70
Circum-cone of a quadric, locus of vertex N.52
Circum-conic of a quadrilateral 4697 At.54
Circum-conic of a quadrilateral, locus of centre E.1
Circum-conic of a triangle 4724 tg. An.57
Circum-parallelogram of an ellipse 4367
Circum-pentagon of a conic M.5 N.67
Circum-polygon of a circle 746—748 CD.1 Me.80 N.66
Circum-polygon of a conic M.25
Circum-polygon of a cuspidal cubic LM.13
Circum-polygon of a cuspidal cubic, ditto quartic LM.14
Circum-polygon of a parabola CM.2
Circum-quadrilateral of a circle E.35 N.48
Circum-quadrilateral of two circle N.67
Circum-rhombus of an equil. triangle A.45
Circum-triangle of a conic N.70
Circum-triangle of a conic, locus of vertex 4800 E.35
Circum-triangle of a triangle J.30
Cissoid 5309—5312 A.62 69 N.43 85
Cissoid, tangents of LM.2
Cissoidal curves A.56
Clairaut's function and equations Pr.25
Clinant geometry Pr.10 11 12 15
Closed curves Me.77 geo
Closed curves and moving chord, Holditch's th 5244 gzMe.78 Q.2
Closed curves and moving chord, Holditch's th, ext. to surfaces Me.81
Closed curves,  being the tangents from xy LM.2
Closed curves, quadrature of A.61 N.43
Closed curves, quadrature, Crofton's ths A.55 C.65 68 E.36
Closed curves, rectification of 5204
Closed surfaces JP.21
Coaxal circle 1021—1036 4161—4170 Q.5
Coaxal circle, Poncelet's limiting points 4165 thJ.86
Coaxal circle, reciprocated 4558
Coaxal conics Q.10
Cochleoid,  A.70
Coefficients detached 28
Coefficients, differential 1402
Coefficients, indeterminate 232
Cogredients 1653
Collinear and concurrent systems of points and lines 967 A.69 G.21
Collineation and correlation M.22 prM.10
Collineation and correlation and reciprocity M.23
Collineation and correlation of plane figures, ground forms J.74
Collineation and correlation, "gleichstimmigkeit" of, in space Z.24 28
Collineation and correlation, multiple c. of two triangles A.2 70
Collineation and correlation, paradox Z.28
Combinations 94—107 trA.15 CP.8 G.18 J.5 13 21 34 38 th53 M.5 Z.2
Combinations of 1, 2, ...n, each c. having a sum  G.19 20
Combinations of dominoes An.73
Combinations of Euler and its use in an eq. L.39
Combinations of n dice each with p faces TE.21
Combinations of n points in space L.40
Combinations of observations L.50
Combinations of planes through a system of points N.57
Combinations,  L.42
Combinations, ap. to determinants JP.28
Combinations, C(n, r) = C(n-1, r-1)+C(n-1, r) 102
Combinations, C(n, r) an integer 366 L.42
Combinations, C(n, r) when n is fractional A.70
Combinations, complete, i.e., with repetitions C.92 N.42 74
Combinations, compound Man.79
Combinations, problem or theorem 105—107 A.21 C.97 CD.2 4 7 8 I.5 J.3 45 56 L.38 Mem.11 N.53 73 Z.15
Combinatorial products A.34
Combinatorial systems L.56
Combinatory analysis A.2 50 70 J.11 22 Mem.50 N.80
Commensurable quadratic divisors N.47
Commensurables TE.23
Commutative law 1489
Companion to the cycloid 5258
Complanation formula A.48
Complementary functions C.19 J.11
Complete functions C.86 J.48
Complete numbers Mo.62
Complete primitive 3163
Complex axes of a quadric Z.19
complex numbers A.28 C.90 99 G.11 J.22 35 67 93 L.54 75 80 M.22 Mo.70 Q.4
Complex numbers from the 31st roots of unity Mo.70
Complex numbers from the nth roots of unity J.40 Mo.70
Complex numbers from the roots of unity; class numbers J.65 Mo.61 63 70
Complex numbers in theory of residues of 5th, 8th and 12th powers L.43
Complex numbers, index and base of a power, geo Z.5
Complex numbers, prime and from roots of unity J.35 taMo.75
Complex numbers, prime and from the 5th roots of unity Mo.ta 59
Complex numbers, resolution of  , and when n=5 L.47
Complex roots of an algebraical eq M.1 N.44
Complex roots of an algebraical eq, of  Mo.57
Complex unities C.96 99 J.53
Complex unities, Klein's groups J.50
Complex variables, functions of An.59 68 71 82 83 G.3 6 J.54 73 83 M.19 Z.8 10
Complex variables, functions of, especially of integrals of d.e J.75 76
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