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| Lectures on Elementary Mathematics |
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| Предметный указатель |
Academies, rise of 62 63
Ahmes 151
Algebra among the Arabs 59 152
Algebra in Europe 60
Algebra in India 152
Algebra in Italy 64
Algebra, application of geometry to 100 127
Algebra, definition of 2
Algebra, essence of 55
Algebra, hand-writing of 69
Algebra, history of 54 151
Algebra, the generality of 69
Algebra, the name of 59
Algebraical resolution of equations, limits of the 96
Alligation, alternate 47
Alligation, generally 44
Analysis, indeterminate 47 55
Angle, trisection of an 62 81
Angular sections, theory of 80
annuities 16
Apollonius 54 59
Arabs, Algebra among the 59 152
Archimedes 54 58 151
Arithmetic, operations of 24
Arithmetic, universal 2
Arithmetical progression revealing the roots 112 120
Arithmetical proportion 12
Astronomy, mechanics, and physics, curves of errors in 136
Average life 45
Bachet de Meziriac 58
Ball 152
Binomial theorem 115
Binomials, extraction of the square roots of two imaginary 77
Biquadratic Equations 63 88 94 133
Bombelli 63 64
Bret, M. 93
Briggs 20
Buteo 61
Cantor 54 60 152
Cardan 60 61 68 82 90
Checks on multiplication and division 39
circle 144
Circle and inscribed polygon, problem of the 138
Circle, squaring of the 62
Clairaut 69 90
Coefficients, greatest negative 107 117
Coefficients, indeterminate 89
Common divisor of two equations 121
Complements, subtraction by 26
Constantinople 58
Continued fractions, solution of alligation by 50
Convergents 7
Cube roots of a quantity, the three 70
Cube, duplication of the 62
Cubic radicals 75
Curves, advantages of the method of 135 144
Curves, employment of in the solution of problems 127—149
Curves, method of, submitted to analysis 143
Curves, representation of equations by 101
de Meziriac, Bachet 58
Decimal fractions 9
decimal numbers 27
Decimals, division of 31
Decimals, multiplication of 30
DeMorgan 5
Descartes viii 8 60 65 89 93 127
Differences, the equation of 114 123
Differential calculus 131
Diophantine problems 55
Diophantus 54 151
Division of decimals 31
Division, by eight 34
Division, by nine 34
Division, by seven 34
Divisor, greatest common 2
Duebring, E. 5
Duehring, E. v
Duodecimal system 32
Ecole Normale v xi 5 11 12
Economy of thought vii
Efflux, law of 42
Eleven, the number, test of divisibility by 37
Elimination, general formulae for 122
Elimination, method of 121
Equations of an even degree, roots of 106
Equations of an odd degree, roots of 105
Equations of the fifth degree 64 96
Equations of the fourth degree 63 87 133
Equations of the mth degree 96
Equations of the second degree 56
Equations of the third degree 60 66 80
Equations, a machine for solving 126
Equations, biquadratic 88
Equations, common divisor of two 121
Equations, constructions for solving 100 124
Equations, general remarks upon the roots of 102
Equations, graphic resolution of 102
Equations, limits of the algebraical resolution of 96
Equations, real roots of, limits of the 107
Equations, theory of 65 84
Equi-different numbers 13
Errors, curve of 136
Euclid 2 57
Euler viii x 93
Europe, algebra in 60
Evolution 11 40
Experiments, an expedient for supplying lacunae in a series of 148
Experiments, average of 46
Falling stone, spaces traversed by a 42
False, rule of 137
Fermat 58
Ferrari, Louis 64
Ferreus, Scipio 60
Fifth degree, equations of the 96
Fink 152
Fourth degree, equations of the 133
Fractional expressions in equations 134
Fractions 2
Fractions, continued 3
Fractions, converging 6
Fractions, decimal 9
Fractions, origin of continued 10
France 58 61
Galieo ix
Geometers, ancient 54 58 59
Geometrical, calculus 24
Geometrical, proportion 13
Geometry 24 60
Geometry, application of to algebra 100 127
Germany 61
Girard, Albert 62
Grain of different prices 44
Greeks, mathematics of the vii 54 151
Hand-writing of algebra 69
Harriot 65
Hero 59 151
Horses 43
Hudde 65 82
Huygens 9 10
Hypsicles 151
Imaginary binomials, square roots of 77
Imaginary expressions 79 83
| Imaginary quantities, office of the 87
Imaginary roots, occur in pairs 99
Inderminate analysis 47 55
Inderminate coefficients 89
Inderminates, the method of 83
Ingredients 48
Interest 15
Intersections, with the axis give roots 102 113
Inventors, great 22
Involution and evolution 11
Irreducible case 61 65 69 73 82
Italy, cradle of algebra in Europe 61 64
Laborers, work of 41
Lagrange, J.L. v vii
Laplace v xi
Lavoisier xii
Leibnitz viii
Life insurance 45
Life, probability of 46
Light, law of the intensity of 129
Lights, problem of the two 129
Limits of roots 107—120
Logarithms 16 40
Logarithms, advantages in calculating by 28
Logarithms, origin of 19
Logarithms, tables of 20
Machine for solving equations 124—126
Mathematics, evolution of vii
Mathematics, exactness of 43
Mathematics, wings of 24
Mean values 45
Mechanics, astronomy, and physics, curves of errors in 136
Metals, mingling of, by fusion 44
Minimal values 132
Mixtures, rule of 44 49
Monge v xi
Mortality, tables of 45
Moving bodies, two 98
Multiple roots 105
Multiplication of decimals 30
Multiplication, abridged methods of 26
Multiplication, approximate 29
Multiplication, inverted 28
MUSIC 22
Napier 17
Napoleon xii
Negative roots 60
Newton, his problem viii 145
Nine, property of the number 31
Nine, property of the number generalised 33
Nizze 58
Numeration, systems of 1
Numerical equations, conditions of the resolution of 97
Numerical equations, position of the roots of 98 see
Numerical equations, resolution of 96—126
Observations, expedient for supplying lacunae in series of 148
Observer, problem of the, and three objects 140
Oughtred 30
Paciolus, Lucas 59 60
Pappus 59
Parabolic curves 144
Peletier 61
Peyrard 58
Physics, astronomy, and mechanics, curves of errors in 136
Planetarium 9
Point in space, position of a 139
Polygon, problem of the circle and inscribed 138
Polytechnic School v xi
Positive roots, superior and inferior limits of the 109
Powers 10
Practice, theory and 43
Present value 15
Printing, invention of 59
Probabilities, calculus of 45
Problems 110
Problems for solution 62
Problems, employment of curves in the solution of 127—149
Proclus 59
Progressions, theory of 12 14
Proportion 11
Ptolemy 59
Radical expressions in equations 134
Radicals, cubic 75
Ratios, constant 2 11 42
Reality of roots 76 83 85 93
Regulafalsi 137 148
Remainders, negative 35
Remainders, theory of 34 38
Romans, mathematics of the 54
Roots of a biquadratic equation 94
Roots of equations of the third degree 71
Roots, limits of the positive and negative 119
Roots, method for finding the limits of 110
Roots, multiple 105
Roots, negative 60
Roots, quantity less than the difference between any two 113
Roots, separation of the 112
Roots, smallest 116
Roots, superior and inferior limits of the positive 109
Roots, the arithmetical progression revealing the 112 120
Roots, the reality of the 74 76 79 83 85 93
Rule of false 137
Rule of mixtures 44
rule of three 11 40
Rule, Cardan's 68
Science, development of vii
Science, history of 22
Seven, tests of divisibility by 35
Signs + and - 57
Squaring of the circle 62
Stenophrenic symbols 7
Straight line 144
Substitutions 111 123
Subtraction, new method of 25
Sum and difference, of two numbers 56
Supposition, rule of 137 148
symbols vii
Tables 137
Tables, expedient for supplying lacunae in 148
Tannery, M. Paul 58 151
Tartaglla 60 61
Temperament, theory of 23
Theon 59
Theory and practice 43
Theory of remainders, utility of the 38
Third degree, equations of the 71 82
Three roots, reality of the 93
Trial and error, rule of 137 148
Trisection of an angle 62 81
Turks 58
Undertemined quantities 82
Unity, three cubic roots of 72
Unknown quantity 55
Values, mean 45
Values, minimal 132
Variations, calculus of x
Vatican library 58
Vieta viii 62 65
Vlacq 20
Wallis viii
Wertheim, G. 58
Woodhouse x
Xylander 58
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