 -function 68 70
-polynomial 63
Abscissa 1
Absolute value 24
Amplitude 24
Argument 24
axes 1
Bend point 3 9 11
Bezout determinant 162
Bezout on elimination 160
Binomial equation 84
Borchardt's theorem 174
Budan's theorem 103 175
Cardan's formulae 32
Cauchy: symmetric functions 78
Columns of determinant 128
Columns of determinant, alike 130 138
Common divisor 8 95 164
Complementary minors 141
Complex number 21 47
Complex number, geometrical representation 24
Conjugate imaginary 22 29
Continued fraction 125
Continuity 12 51
coordinates 1
Cube roots 26 35
Cube roots, of unity 23 24
Cubic equation 10 11 16 17 31 40 75 80 90 99 119 122 167—168
De Moivre's quintic 76
De Moivre's theorem 25
Decagon 88
Derivative 5 69 93 96 103 106 110 158
Descartes on the quartic 42
Descartes rule of signs 105 168 175
Determinant 127 134 154—175
Diagonal term 134
Discriminant 33 41 157
Discriminant of cubic 33 78 99 158—159 162
Discriminant of quartic 41 45 100
Divisor 58 164
Double root 8 (see “Discriminant”)
Duplication of cube 90
Element of determinant 128
Eliminant 150
Elimination 152—160
Equal roots 8 11 33 34 45
Equation of squared differences 78 125 171
Euler on elimination 159
Euler on elimination, quartic 44
Expansion of determinant 130 133 138
Factor of determinant 131
Factor Theorem 8
Ferrari on the quartic 38
fold 8
Fourier on roots 106
Fundamental theorem of algebra 47
Geometrical see “Complex”
Geometrical construction 16 87 90 92
Graffe on finding roots 121
Graph 2 14
Graphical solution 2 15—17 110
Homogeneous equations 148
Horner's method 115
Imaginary number 21
Imaginary roots 28 102 107 120 124 174-175
Inflexion point 9 44
Inflexion tangent 10
Integral root 59
Interchange in determinants 132—134 137—138
Interpolation 111
interval 97
Invariant 42
Irrational 30
| Irreducibility of resultants 152
Irreducible case 34 35
Isolated 95
Lagrange on the quartic 40
Lagrange, solution of equations 125
Laplace's development 141—143
Linear equations 127—129 144—149
Lower limit to roots 58
Minor 129
Modulus 24 25
Moivre see “De”
Multiple root 8 (see “Discriminant”)
Newton's formula 70 169 170
Newton's method for integral roots 59
Newton's method of solution 109—115
Ordinate 1
Pentagon 88
periods 85
plotting 2
Polar coordinates 19
Polynomial 3 6
Polynomial, sign of 14
Primitive root 28
Product of determinants 143
Quadratic equation 15
Quartic 16 38 42 80 99 120 173
Quintie 76 80 83
Radian 27
Rank of determinant 145
Rational integral function 3
Rational root 61
Reciprocal equation 81
Reduced cubic 10 31
Reduced quartic 42
Regula Falsi 111
Regular polygon 27 87—90
Relations between roots and coefficients 32 39 55 Ch. 169 170
Relatively prime 28
Remainder theorem 8
Resolvent cubic 38 39
Resultant 150
Rolle's theorem 93
Roots of unity 27
Roots, nth 26
Roots, theorems on 13 15 30 34 39 45 47 55 59 61 64 69 76 90 93 96 100 103 105 112 174-176
Rows of determinant 128
Rows of determinant, alike 138
slope 3 6
Solution of numerical equations 109
Solvable by radicals 75 84
Square root 23
Sturm's functions 98
Sturm's functions, generalized 176
Sturm's theorem 95—102
Sum of roots 39 56
Sum of roots, powers of roots 69 72 169
Sylvester on elimination 154
Symmetric function 63 121
Symmetric in all roots but one 76
Synthetic division 116
Taylor's theorem 6 113
Transformed equation 10 115 119
Trigonometric form 24
Trigonometric solution of cubic 34 36
Trinomial equation 11
Triple root 8
Trisection of angle 90
Tschirnhausen 79 164
Upper limit to roots 57 175
Variation in signs 95
Vector 18
Vieta on the cubic 31
Waring's formula 72
|
|
|
О проекте