A Source Book in Mathematics, 1200-1800

Front Cover
D. J. Struik
Harvard University Press - Mathematics - 446 pages
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Contents

ARITHMETIC Introduction
1
Leonardo of Pisa The rabbit problem
2
Recorde Elementary arithmetic
4
Stevin Decimal fractions
7
Napier Logarithms
11
Pascal The Pascal triangle
21
Fermat Two Fermat theorems and Fermat numbers
26
Fermat The Pell equation
29
Kepler Integration methods
192
Galilei On infinites and infinitesimals
198
Galilei Accelerated motion
208
Cavalieri Principle of Cavalieri
209
Cavalieri Integration
214
Fermat Integration
219
Fermat Maxima and minima
222
Torricelli Volume of an infinite solid
227

Euler Power residues
31
Euler Fermats theorem for n 3 4
36
Euler Quadratic residues and the reciprocity theorem
40
Goldbach The Goldbach theorem
47
Legendre The reciprocity theorem
49
CHAPTER H ALGEBRA Introduction
55
Chuquet The triparty
60
Cardan On cubic equations
62
Ferrari The biquadratic equation
69
Viete The new algebra
74
Girard The fundamental theorem of algebra
81
Descartes The new method
87
Descartes Theory of equations
89
Newton The roots of an equation
93
Euler The fundamental theorem of algebra
99
Lagrange On the general theory of equations
102
Lagrange Continued fractions
111
Gauss The fundamental theorem of algebra
115
Leibniz Mathematical logic
123
Introduction
133
Oresme The latitude of forms
134
Regiomontanus Trigonometry
138
Fermat Coordinate geometry
143
Descartes The principle of nonhomogeneity
150
Descartes The equation of a curve
155
Desargues Involution and perspective triangles
157
Pascal Theorem on conics
163
Newton Cubic curves
168
Agnesi The versiera
178
Cramer and Euler Cramers paradox
180
Euler The Bridges of Konigsberg
183
ANALYSIS BEFORE NEWTON AND LEIBNIZ Introduction
188
Stevin Centers of gravity
189
Roberval The cycloid
232
Pascal The integration of sines
238
Pascal Partial integration
241
Wallis Computation of TT by successive interpolations
244
Barrow The fundamental theorem of the calculus
253
Huygens Evolutes and involutes
263
NEWTON LEIBNIZ AND THEIR SCHOOL Introduction
270
Leibniz The first publication of his differential calculus
271
Leibniz The first publication of his integral calculus
281
Leibniz The fundamental theorem of the calculus
282
Newton and Gregory Binomial series
284
Newton Prime and ultimate ratios
291
Newton Genita and moments
300
Newton Quadrature of curves
303
LHdpital The analysis of the infinitesimally small
312
Jakob Bernoulli Sequences and series
316
Johann Bernoulli Integration
324
Taylor The Taylor series
328
Berkeley The Analyst
333
Maclaurin On series and extremes
338
DAlembert On limits
341
Euler Trigonometry
345
DAlembert Euler Daniel Bernoulli The vibrating string and its partial differential equation
351
Lambert Irrationality of TT
369
Fagnano and Euler Addition theorem of elliptic integrals
374
Euler Landen Lagrange The metaphysics of the calculus
383
Johann and Jakob Bernoulli The brachystochrone
391
Euler The calculus of variations
399
Lagrange The calculus of variations
406
Monge The two curvatures of a curved surface
413
INDEX
421
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