A Source Book in Mathematics, 1200-1800 (gnv64)

A Source Book in Mathematics, 1200-1800 (Princeton Legacy Library)
by Dirk Jan Struik
Princeton University Press | 1986 | ISBN 0-691-02397-2 | 433 Pages | PDF | 46.6 mb
https://www.amazon.com/Mathematics-1200-1800-Princeton-Library-Paperback/dp/B010TSYFEE

This Source Book contains selections from mathematical writings of authors in the Latin world, authors who lived in the period between the thirteenth and the end of the eighteenth century. The choice was made from books and from shorter writings. Usually only a significant part of the document has been taken, although occasionally it was possible to include a complete text.
The selection has been confined to pure mathematics or to those fields of applied mathematics that had a direct bearing on the development of pure mathematics, such as the theory of the vibrating string. The works of scholastic authors are omitted, except where, as in the case of Oresme, they have a direct connection with writings of the period of our survey. Laplace is represented in the Source Book on nineteenth-century calculus.

CONTENTS
Errata et Addenda vii
Abbreviations of Titles xiv
CHAPTER I ARITHMETIC
Introduction 1
1. Leonardo of Pisa. The rabbit problem 2
2. Becorde. Elementary arithmetic 4
3. Stevin. Decimal fractions 7
4. Napier. Logarithms 11
5. Pascal. The Pascal triangle 21
6. Ferm at. Two Fermat theorems and Fermat numbers 26
7. Fermat. The "Pell" equation 29
8. Euler. Power residues 31
9. Euler. Fermat's theorem for ? = 3, 4 36
10. Euler. Quadratic residues and the reciprocity theorem 40
11. Goldbach. The Goldbach theorem 47
12. Legendre. The reciprocity theorem 49
CHAPTER II ALGEBRA
Introduction 55
1. Al-Khwarizmi. Quadratic equations 55
2. Chuquet. The triparty 60
3. Cardan. On cubic equations 62
4. Ferrari. The biquadratic equation 69
5. Yiete. The new algebra 74
6. Girard. The fundamental theorem of algebra 81
7. Descartes. The new method 87
8. Descartes. Theory of equations 89
9. Newton. The roots of an equation 93
10. Euler. The fundamental theorem of algebra 99
11. Lagrange. On the general theory of equations 102
12. Lagrange. Continued fractions 111
13. Gauss. The fundamental theorem of algebra 115
14. Leibniz. Mathematical logic 123
CHAPTER ?II GEOMETRY
Introduction 133
1. Oresme. The latitude of forms 134
2. Regiomontanus. Trigonometry 138
3. Fermat. Coordinate geometry 143
4. Descartes. The principle of nonhomogeneity 150
5. Descartes. The equation of a curve 155
6. Desargues. Involution and perspective triangles 157
7. Pascal. Theorem on conics 163
8. Newton. Cubic curves 168
9. Agnesi. The versiera 178
10. Cramer and Euler. Cramer's paradox 180
11. Euler. The Bridges of Konigsberg 183
CHAPTER IV ANALYSIS BEFORE NEWTON AND LEIBNIZ
Introduction 188
1. Stevin. Centers of gravity 189
2. Kepler. Integration methods 192
3. Galilei. On infinites and infinitesimals 198
4. Galilei. Accelerated motion 208
5. Cavalieri. Principle of Cavalieri 209
6. Cavalieri. Integration 214
7. Fermat. Integration 219
8. Fermat. Maxima and minima 222
9. Torricelli. Volume of an infinite solid 227
10. Roberval. The cycloid 232
11. Pascal. The integration of sines 238
12. Pascal. Partial integration 241
13. Wallis. Computation of p by successive interpolations 244
14. Barrow. The fundamental theorem of the calculus 253
15. Huygens. Evolutes and involutes 263
CHAPTER V NEWTON, LEIBNIZ, AND THEIR SCHOOL
Introduction 270
1. Leibniz. The first publication of his differential calculus 271
2. Leibniz. The first publication of his integral calculus 281
3. Leibniz. The fundamental theorem of the calculus 282
4. Newton and Gregory. Binomial series 284
5. Newton. Prime and ultimate ratios 291
6. Newton. Genita and moments 300
7. Newton. Quadrature of curves 303
8. L'H6pital. The analysis of the infinitesimally small 312
9. Jakob Bernoulli. Sequences and series 316
10. Johann Bernoulli. Integration 324
11. Taylor. The Taylor series 328
12. Berkeley. The Analyst 333
13. Maclaurin. On series and extremes 338
14. D'Alembert. On limits 341
15. Euler. Trigonometry 345
16. D'Alembert, Euler, Daniel Bernoulli. The vibrating string and its partial differential equation 351
17. Lambert. Irrationality of -p 369
18. Fagnano and Euler. Addition theorem of elliptic integrals 374
19. Euler, Landen, Lagrange. The metaphysics of the calculus 383
20. Johann and Jakob Bernoulli. The brachystochrone 391
21. Euler. The calculus of variations 399
22. Lagrange. The calculus of variations 406
23. Monge. The two curvatures of a curved surface 413
INDEX 421

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