Spherical trigonometry, geodetic reduction of a spherical angle A.51
Spherical trigonometry, Legendre's th. C.96 J.44 L.41 M.1 N.56 Z.20
Spherical trigonometry, Llhuillier's th. 905 A.20
Spherical trigonometry, Napier's eqs. 896 A.3 17 CM.3 LM.3 13
Spherical trigonometry, Napier's rules 881
Spherical trigonometry, supplement to, and geodesy A.36
Sphero-conics 5655a
Sphero-conics, homofocal C.50
Sphero-conics, mechanical cn LM.6
Sphero-conics, tg.c Q.8 9 Me.3 Z.6 23
Sphero-conjugate tangents An.55
Sphero-cyclides LM.16
Spheroidal trigonometry J.43 M.22
Spheroidic transformation f. of Bessel A.53
Spheroids 5604 6152
Spheroids, cubature 6158 A.2
Spieker's point A.58
Spiral A.28 L.69 N.79 Z.14
Spiral of Archimedes 5296 A.65 66
Spiral, conical N.45
Spiral, equiangular 5288
Spiral, hyperbolic 5302
Spiral, involute, of 4th order C.66
Spiral, involute, of circle 5306
squares J.22
Squares whose diagonals are chords of given circles A.64
Squares whose sides and diagonals are rational J.37
Squares whose sides pass through 4 points A.43
Squares, 64 transformed into 65, geo. Me.77
Squares, maximum in a triangle J.15
Squares, maximum with given sides J.25
Squares, sum of four L.57
Squares, sum of three G.15
Standards of length Pr.8 21
Statistics Z.26
Steiner's ths. and prs. A.53 J.13 14 16 18 23 25 36 71 73 N.48 56 59 62
Steiner's ths. and prs., Hexagon A.6
Steiner's ths. and prs., Ray-systems CD.6
Stereograms of surfaces LM.2
Stereographic projection A.39 JP.16 L.46
Stereometry JP.1 thsA.10 31 43 57 J.1 5
Stereometry, multiplication J.49
Stereometry, quadric and cubic eqs. and surfaces J.49
Sternpolygon and sternpolyhedron A.13
Stewart's geo.ths. CM.2 L.48 TE.2 15
Stigmatics see "Clinant"
Striction lines of conicoids Z.28
Strophoids AJ.7 N.75
Sturm's functions 506 A.62 C.36 62 68 G.1 20 J.48 L.46 48 67 Mo.58 78 N.43 46 52 54 66 67 81 Q.3
Sturm's functions and a quartic equation A.34
Sturm's functions and addition th. for elliptic functions of 1st kind Z.17
Sturm's functions and H. C. F. Pr.6
Sturm's functions and their reciprocal relations Mo.73
Sturm's functions, ap. to transcendental eqs. J.33
Sturm's functions, ap. to transf. of binomial eqs. L.42
Sturm's functions, ext. to simultaneous eqs. C.35
Sturm's functions, remainders J.43 48
Sturm's functions, tables P.57 Pr.8
Subdeterminants of a symm. system J.93 M.82
Subfactorial n Me.78
Subinvariants  seminvariants to binary qualities of unlimited order AJ.5
Subnormal 1160
Subsidiary angles 726 749
Substitutions A.62 C.ths66 67 74 76 79 G.9 10 11 14 19 L.65 72 M.13
Substitutions and conjugate substitutions C.21 22
Substitutions by approximation, of the ratio of the variables of a binary quantic to another function of the same degree C.80
Substitutions of equidistant numbers in an integral function of a variable N.51
Substitutions of n letters, geo. for n = 3, 4, 5, 6, and mystic hexagram An.83
Substitutions of six letters C.63
Substitutions of systems of equations N.81
Substitutions of the form  M.2
Substitutions which admit of a real inversion J.73
Substitutions which do not alter the value of the function C.21
Substitutions which lower the degree of an eq. in two variables and their use in Abelian integrals C.15
Substitutions, a th. of Sylvester AJ.1
Substitutions, ap. to functions of six or fewer variables C.21
Substitutions, ap. to linear d.e C.78
Substitutions, canonical forms of L.72
Substitutions, linear C.98 J.84 M.19 20
Substitutions, linear, and integral M.24
Substitutions, linear, for reduction of elliptic functions of 1st kind An.58
Substitutions, linear, of a determinant An.84
Substitutions, linear, powers and roots of C.94
Substitutions, linear, reduction of C.90 JP.29
Substitutions, linear, successive A.38
Substitutions, linear, which transform quadric functions into others which contain only the squares of the variables J.57
Substitutions, no. of in a given no. of cycles A.68
Substitutions, permutable amongst themselves C.21
Sum and difference calculus A.24
Sum of squares of lines drawn from a point to cut a curve in a given angle J.11
Summation of series 3781 A.10—13 26 30 55 62 No.84 C.87 88 J.10 31 33 LM.4 7 Mem.20 30 P.1782 1784—1787 1791 1798 1802 1806 1807 1811 1819 Pr.14 see
Summation of series by  2757
Summation of series by definite integrals A.4 6 38 J.17 38 42 46 74 Man.46 Mem.11
Summation of series by differences 264 Mem.30
Summation of series by differential formulae L.31 Mem.15
Summation of series of arcs A.63
Summation of series of derivatives and integrals C.44
Summation of series of sines and cosines J.4
Summation of series of terms of a high order C.32
Summation of series of transcendents in alg. differentials J.19
Summation of series, approximate 3820 J.5 I.24
Summation of series, Bernoulli's method J.31
Summation of series, C (n, r) products of a, a + b, ... a + (n — 1) b Q.18
Summation of series, Cauchy's th. M.4
Summation of series, formulae A.47 An.55 J.30
Summation of series, formulae,  Q.8
Summation of series, formulae, Lagrange's J.34 P.60
Summation of series, formulae, Maclaurin's C.86
Summation of series, formulae, Vandermonde's L.41
Summation of series, Kummer's method C.64
Summation of series, Lejeune Dirichlet's CD.9
Summation of series, periodic J.15
Summation of series, selected terms Me.75
Summation of series, theorem re  2708
Summation of series, trigonometrical and infinite Me.64
Superposition TE.21 23
Superposition of small quantities 1515
Supplement integrals J.98
Supplementary angles 620
Supplementary chords 1201
Supplementary cones thN.48
Supplementary curves 4917—4920 Man.54
Surds 108 N.47
Surds,  121 A.3 13 J.17 20 Mem.10 N.46 48
Surds,  ,  approximately J.13
Surds,  122
Surds,  124
Surds, quadratic see "Roots of numbers"
Surface curves A.39 60 An.54 C.21 80 L.66 G.19 J.2 N.54 84
Surface curves and osculating sphere C.73
Surface curves of intersection M.2 N.68
Surface curves of intersection of 2 quadrics A.16
Surface curves on a developable An.57
Surface curves on a developable, the osculating plane making a constant angle with it L.47
Surface curves on a one-fold hyperbola CD.4
Surface curves on an ellipsoid An.51 CD.3 geoL.50
Surface curves on cubic surfaces M.21
Surface curves on quadrics N.70
Surface curves on surfaces of revolution Z.18 28
Surface curves, an an alg. surface An.63
Surface curves, curvature of N.65
Surface curves, groups of rational M.3
Surface curves, multiple G.14
Surface curves, multiple, singularities of M.3
Surface curves, rectification of A.36
Surface curves, relation to their tangents C.82
Surface of centres 5774 A.68 An.57 C.70 71 E.30 L.41 58 LM.4 M.5 16
Surface of centres of a quadric Q.2
Surface of centres of a quadric, bitangents of Q.13
Surface of centres of a quadric, model of Mo.62
| Surface of centres of a quadric, principal axes of N.48
Surface of centres, curvatures of the two, relation C.74 79
Surface of centres, the two focal conics of a system of homofocal quadrics C.53
Surface or surfaces 5770 A.14 f32 41 59 60 62 An.51—53 55 60 61 65 71 At.57 C.17 33 37 49 ths58 61 64 67 69 80 86 99 G.3 21 J.9 ths13 58 63 64 85 98 JP.19 24 25 33 L.44 47 51 60 M.2 4 7 9 cn19 Mo.82 83 84 N.53 65 68 72 TI.14 Z.7 8 20
Surface or surfaces and p. d. e C.13 CD.2 Z.7
Surface or surfaces and plane curves J.54 72 M.7
Surface or surfaces and point at  on it J.65
Surface or surfaces and point moving on it L.76 77
Surface or surfaces and transversal, th. N.49
Surface or surfaces of corresponding points M.4
Surface or surfaces of elliptic cone An.51
Surface or surfaces of equal slope C.98 N.65
Surface or surfaces of even order A.70
Surface or surfaces of minimum area C.57 J.8 13 L.59 Q.14
Surface or surfaces of normals N.59
Surface or surfaces of nth order cnM.23
Surface or surfaces of nth order, 2nd, 3rd and 4th Mel.6
Surface or surfaces of revolution C.86 G.4
Surface or surfaces of revolution in perspective JP.20
Surface or surfaces of revolution of a conic about any axis in space JP.23 L.63
Surface or surfaces of revolution of constant mean curvature L.41
Surface or surfaces of revolution of reg. polygon about a side, vol. A.57
Surface or surfaces of revolution, areas and volumes 5877—5879 A.48
Surface or surfaces of revolution, meridian and contour curves of Z.21
Surface or surfaces of revolution, meridian of, a lemniscate G.21
Surface or surfaces of revolution, meridian of, generation of C.85
Surface or surfaces of revolution, oblique Q.6
Surface or surfaces of revolution, passing through a given line, tangent plane of N.84
Surface or surfaces of revolution, quadric A.55 L.60
Surface or surfaces of revolution, shortest line on A.38
Surface or surfaces of revolution, superposable C.80 N.81
Surface or surfaces which cuts the curve of intersection of two alg. surfaces in the point of contact of the stationary osculating planes L.63
Surface or surfaces whose coordinates are Abelian functions of two parameters C.92 M.19
Surface or surfaces whose normals all touch a sphere or conical surface JP.4
Surface or surfaces,  A.35
Surface or surfaces, , a = b = c = 1 A.21
Surface or surfaces, areas of G.22 N.52
Surface or surfaces, argument of points on LM.16
Surface or surfaces, complex M.5
Surface or surfaces, complex of 4th order and class M.2
Surface or surfaces, cut orthogonally by spheres 3393 C.36
Surface or surfaces, deficiency of M.3
Surface or surfaces, definitions 5770
Surface or surfaces, determined from two surfaces of centres A.68
Surface or surfaces, Dirichlet's problem An.71
Surface or surfaces, do. for surface of revolution JP.5
Surface or surfaces, doubly circumscribing an n-tic surface J.54
Surface or surfaces, Dupin's theorem C.74 CM.4 Q.12
Surface or surfaces, equation of gn5780 A.3
Surface or surfaces, equation of, for points near origin 5803
Surface or surfaces, families of C.70 Me.72
Surface or surfaces, flexure of J.18
Surface or surfaces, Gaussian theory of LM.12 N.52
Surface or surfaces, generation of C.94 97 G.9 J.49 L.56 83 M.18
Surface or surfaces, implexes of C.79 82
Surface or surfaces, number under 9 conditions C.62
Surface or surfaces, octic of zero kind G.12
Surface or surfaces, one-sided A.57
Surface or surfaces, order determined Me.83
Surface or surfaces, parabolic points of CD.2
Surface or surfaces, relation of in Riemann's sense M.7
Surface or surfaces, representation of J.83
Surface or surfaces, representation of, on a plane An.68 71 76
Surface or surfaces, representation of, one upon another An.77
Surface or surfaces, Riemann's symmetrical and periodicity modulus of the related Abelian integral of the 1st kind Z.28
Surface or surfaces, ruled octic with 5 quartic curves C.61
Surface or surfaces, ruled, with generators part of a linear complex C.84
Surface or surfaces, screw, parallel projection of cnZ.18
Surface or surfaces, section of, homogeneous eq. LM.15
Surface or surfaces, self-reciprocal LM.2
Surface or surfaces, self-reciprocal, quadric E.36
Surface or surfaces, sextic of first species M.21
Surface or surfaces, singularities of A.25 An.79 CD.7 CM.2 J.72 M.9 N.64 Q.9
Surface or surfaces, singularities of, 16 singular points C.92
Surface or surfaces, singularities of, cubics M.4
Surface or surfaces, singularities of, cubics and quadrics A.17
Surface or surfaces, solutions by infinites of 3rd order geoC.80
Surface or surfaces, Steiner's LM.5 14 M.5
Surface or surfaces, touching a fixed surface always G.20
Surface or surfaces, touching a plane along a curve CD.3 CM.2
Surface or surfaces, transformation of M.19
Surface or surfaces, trapezoidal problem Z.14
Surface or surfaces, two series of prsAn.73
Surface or surfaces, web-system J.82
surveying N.50
Surveying, geo. th. A.37
Symbolic geometry CD.1—4 see
Symbolical language E.28
Symmedian line E.42 N.83—85 Q.20
Symmedian point 4754c
Symmetrical conics of triangles A.59
Symmetrical connections by generating functions J.53
Symmetrical expressions 219
Symmetrical figures J.44
Symmetrical functions C.76 J.69 93 98 LM.13 Q.20 Z.4
Symmetrical functions of any number of variables C.82
Symmetrical functions of the common sol. of several eqs. An.58
Symmetrical functions, Brioschi's th. C.98
Symmetrical functions, multiplication of Me.85
Symmetrical functions, simple and complete M.18 20
Symmetrical functions, tables of AJ.5
Symmetrical functions, tables of, of 12-ic AJ.5
Symmetrical points of 1st order A.60 cnA.64
Symmetrical points of a triangle A.58
Symmetrical points of tetrahedrons A.60
Symmetrical products P.61 Pr.11
Symmetrical products with prime roots of unity Me.85
Symmetrical tetrahedral surfaces Z.11
Symmetry, plane and in space N.47
Synthesis C.18
Synthetic division 28
Synthetic division, evolution Me.68
Syntractrix 5282
Tables for empirical formulae AJ.5
Tables in theory of numbers Q.1
Tables of  ,  ,  ,  CP.13
Tables of Bernoulli's nos., logarithms, &c., calculation of J.2
Tables, mathematical xi
Tac-loci Me.83
Tamisage LM.14
tan nx, f. in N.53
tan x as a continued fraction Z.16
tan x as a continued fraction, do. tan nx Me.74
Tangencies (circles, points, and lines) 937 Pr.9 Q.2 8
Tangent cone at a singular point 5783
Tangent planes 5770—5782 p.c5790 CM.4 N.45
Tangent planes and surface, intersection of 5786—5789 L.58
Tangent planes to equidistant surfaces cnZ.28
Tangent planes, triple C.77
Tangential eq. with the intercept and angle of inclination for coordinates of the line P.77
tangents 1160 cnA.4 33 J.56 73 N.42 Z.23
Tangents and contact-point in loci and envelopes C.85 cnN.57
Tangents and normals 5100
Tangents and normals, relations A.51
Tangents at a multiple point, cn. JP.13
Tangents of a surface 5781
Tangents of a surface at singular points 5783 M.11 15
Tangents, conjugate (and Dupin's th.) An.60
Tangents, construction of M.22 N.80
Tangents, cut by lines at a constant angle A.43
Tangents, double Q.3
Tangents, eq. of, to find it 4120—4132 Me.66
Tangents, faisceaux of N.50
Tangents, locus of intersections of three LM.15
Tangents, parallel N.45
Tangents, segments of 4307
Tangents, segments of, equality of C.81
tanh S 2213
tantochrone L.44 An.53
Taylor's theorem 1500 1520 1523 A.8 13 AJ.4 ext1 C.58 CM.1 J.11 L.37 38 45 58 gz64 M.21 23 Me.72 73 75 Mem.20 N.52 63 70 74 79 TA.7 8 Z.gz 25
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