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| Sondheimer E., Rogerson A. — Numbers and Infinity: A Historical Account of Mathematical Concepts |
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| Предметный указатель |
 12 35 65 67 97
continued fraction for 65
infinite product for 119
abacus 6, 13
Abel, Abel-Ruffini theorem 63
Abel, N.H. 63
Accademia dei Lincei 118
Achilles paradox see Zeno of Elea
Adams, J.F. 78
Addition 27
addition commutative law 27
Al-Khowarizmi 6
Al-Khowarizmi Al-jabr wa’l-muqabalah 6
Aleph zero 149
Alexandria 5
Algebra division 74 78
Analytical Society 125
Angle, trisection of 64 89
Antiphon 92
Apollonius of Perga 5 112
Arab mathematics 6
Archimedes of Syracuse 5 45 95
Archimedes of Syracuse estimate of 97
Archimedes of Syracuse Method 102
Archimedes of Syracuse quadrature of parabola see area of parabola
Archimedes of Syracuse Sand-Reckoner 96
Area of circle 86 92
area of parabola 98
area under hyperbola 109
Argand, J.R. 48
Argand, J.R., Argand diagram see complex plane
Aristotle 33 147
Astronomy 4
Atomism 87
axiom of Archimedes of Syracuse see axiom of continuity
Axiom of continuity 93 95
Axioms 30
Babbage, Charles 14
Babbage, Charles, Analytical Engine 14
Babylonian mathematics 3 42
Babylonian number system 3 86
Barrow, Isaac 117 119 121
Barrow, Isaac, Geometrical Lectures 119
Base 1 2 3 4 7 10
Berkeley, George 124
Berkeley, George, Analyst 124
Bernoulli, Daniel 132
Bernoulli, Jakob 124
Bernoulli, Johann 46 124
Bhaskara 45
Binary number system see base 2
Biquadratic equation see quartic equation
Bolzano, Bernhard 140
Bombelli, R. 55
Bombelli, R., Algebra 55
Boole, George 75
Boole, George, Investigation of the Laws of Thought 75
Boole, George, The Mathematical Analysis of Logic 75
Boolean algebra 75
Brahe, Tycho 105
branching networks 144
Briggs, Henry 13
Brownian motion 142
Buergi, Jobst 12
Calculating machine 13
Calculus, integral 87 105 123
Cantor, Georg 147
Cardan, Jerome 46 52
Cardan, Jerome, Ars Magna 52
Cardan, Jerome, Cardan’s solution of the cubic equation 51
Carpenter’s rule 32
Cauchy, A.L. 63 135 137 138 148
Cavalieri, B. 105
Cavalieri, B., Geometria Indivisibilibus 105
Cayley, Arthur 78 80
Cayleynumbers , see octonions complex 22 38 69
Clifford algebra 79
Clifford, W.K. 79
Cohen, P.J. 158
Complex plane 39
Computers 7 14
Continuity 88
Continuum Hypothesis 158
Convergence 128
Convergence uniform 136
Conway, J.H. 154
Copernicus, N. 105
Cube, duplication of 64 89
Cubic equation 49
Cubic equation, irreducible case 54
cuneiform number symbols 3
de Fermat, Pierre 19 34 108 112 115
de Fermat, Pierre, Fermat’s last theorem 23
De La Vallee-Poussin, C.J. 21
de L’Hospital, G.F.A. 124
de L’Hospital, G.F.A., Analyse des infiniment petits 124
de L’Hospital, G.F.A., L’Hospital’s rule 124
de Morgan, Augustus 48
Decimal system 1
Dedekind, J.W.R. 38 148 150
del Ferro, Scipione 51
Delian problem see cube duplication
demotic script 2
Derivative 111 138
Descartes, Rene 46 112 117
Descartes, Rene, La Geometrie 46
Differential calculus 87 111 123
Differential equations 124 126
Differentials 139
DIMENSION 143 156
Diophantos 23 45
Diophantos, Arithmetica 23
Diophantos, Diophantine equations 24
Dirac, P.A.M. 85
Dirichlet, P.G.L. 17 136 137
Distributive law 28
Divisibility 15
Division 31
D’Alembert, J.L. 130
e 35 65 67
e, irrationality proof 65
Egypt 2
Einstein, A. 83
Eleatics 88
Eratosthenes of Cyrene 103
Erdoes, P. 21
Euclid of Alexandria 5 16 21 115
Euclid of Alexandria, Elements 45
Euclid of Alexandria, Euclidean algorithm 25
Eudoxus of Cnidus 38
Eudoxus of Cnidus, method of exhaustion 90 92
Eudoxus of Cnidus, theory of proportions 44
Euler, Leonhard 19 26 47 55 65 126
Exhaustion, method of see Eudoxus of Cnidus
Ferrari, L. 56
fibonacci see Leonardo of Pisa
Field 31 80
field non-Archimedean 93
Field of complex numbers 39
Field of real numbers 38
Field skew 74
Fluxions, method of 121
Fourier, J.B.J. 63 133
Fourier, J.B.J., Fourier series 133
Fourier, J.B.J., Theorie analytique de la chaleur 133
Fractals 142
Fractions see also numbers rational
fractions continued 65
fractions decimal 9
fractions unit 10
| Function 126
Function continuous 138
function continuous and non-differentiable 140
function Dirichlet’s discontinuous 137
Function discontinuous 135
Function multivalued 47
Function periodic 131
function stationary value 116
function, function space 83
Fundamental Theorem of Arithmetic see unique factorisation
Fundamental theorem of calculus 115
Galileo Galilei 105 116 148
Galois, Evariste 63
Galois, Evariste, Galois group 64
Galois, Evariste, Galois theory 64
Gauss, C.F. 15 20 48 60 63
Gelfond, A.O. 68
Gematria 15
Gibbs, J.W. 82
Goedel, Kurt 158
Goldbach conjecture 18
Golden Age of Greece 5 90
Grassmann, H. 75
Grassmann, H., Lineale Ausdehnungslehre 75
Graves, J.T. 78
Greatest common divisor 24
Greek number system 4
Gregory of Saint-Vincent 109
Gregory, James 119
Gregory, James, Gregory’s series 119
Group theory 63 80
group theory, group of rotations 41
Hadamard, J. 21
Hamilton, W.R. 70 81
Hardy, G.H. 26
Harmonic series 128
Hausdorff, F. 143
Heaviside, O. 82
Heiberg, J.L. 102
Hermite, Charles 67 141
Hieratic script 2
hieroglyphic numbers 2
Hilbert, David 68
Hindu-Arab numbers 1 6
Hippasus of Metapontum 43
Hippocrates of Chios 90
Hippocrates of Chios, areas of lunes 90
Huygens, Christiaan 118
Huygens, Christiaan, Horologium Oscillatorum 118
Hyperreal numbers 140
Ideals 24
incommensurability 33
Indivisibles 105
Infinite descent 34
Infinite series 127
Integers 15 29
integers definite 114 137
integers indefinite 113
integers Lebesgue 138
Integers negative 28
Integers positive see numbers natural
integers Riemann 137
Irrational numbers 33 44 153
Jacobi, C.G.J. 63
Kepler, Johann 105 116
Kepler, Johann, Stereometria Doliorum 116
Kinematics 116
Kuhn, T.S. viii
Kummer, E.E. 23 24
Lagrange, J.L. 63 64 133
Lakatos, I. viii
Lambert, J.H. 66
Least upper bound 37
Lebesgue, H. 138
Legendre, A.M. 20
Leibniz, G.W. 7 14 46 47 53 110 114 123
Leonardo of Pisa 6 11
Leonardo of Pisa, Liber Abaci 6 11
Levi-Civita, T. 83
LIMIT 9 122 138 139
Lindemann, C.L.F. 67
Linear associative algebra 79
Liouville, J. 67 154
Logarithms 12 110
Logarithms of negative numbers 46
Lorentz transformations 85
Maclaurin, Colin 119
Maclaurin, Colin, Maclaurin’s series 119
Matrices 80
matrices, Pauli spin matrices 81
Maxima and minima 115
Maxwell, J.Clerk 81
Measure 138
Measure theory 138
measure, measure zero 153
Mercator, N. 120
Mercator, N., Mercator’s series 120
Mersenne numbers 19
Multiplication 27
multiplication commutative law 27
Napier, John 12
Napier, John, Mirifici Logarithmorum Canonis Descriptio 12
Napier’s bones, Napier’s rods 13
Natural numbers 15 27
Newton, Isaac 46 114 120 121
Newton, Isaac, Newton’s algorithm 3
Newton, Isaac, Principia 121
Nicolo of Brescia see Tartaglia
Non-commutative algebra 74
Non-Euclidean geometry 30 48 79
Non-standard analysis 139
numbers algebraic 22 65 67 154
Numbers Fermat 19 21
Octonions 78
Ordering of integers 29
ordering ordered field 31 38
Oresme, Nicole 128
OUGHTRED, W. 13
PACIOLI, L. 49
Pacioli, L., Summa di Arithmetica 49
Pascal, Blaise 13 112 117
Peacock, George 74
Peano, Giuseppe 143
Peano, Giuseppe, space-filling curve 143
Peirce, Benjamin 79
Peirce, Charles 79
pentagon, subdivision of regular 34
Perspective 49
place values 1
Plato 5 34 90 92
Plutarch 96
Poisson, S.-D. 63
polynomials, factorisation of 59
Popper, Sir Karl viii
Prime number theorem 21
Prime numbers 15
Principle of continuity 72
Probability, theory of 112 138 142
Ptolemy 5
Ptolemy, Almagest 5
Public-key cryptography 19
Pythagoras, Theorem of 33 84 91
Pythagorean triples 23
Pythagoreans 32 42 88 132
Quadratic equations 39
Quadrature of the circle see circle squaring
quadrature of the parabola see area of parabola
Quartic equation 56
Quaternions 72 82
quaternions and rotations 75 79
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