RePoSS #11: The Mathematics of Niels Henrik Abel: Continuation ...

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408 Appendix B. ABEL’s manuscripts MS:592 Manuscripts and letters (table B.2) MS:434 Fragments from manuscripts (table B.3) MS:435 Note accompaning the Abel manuscripts (fragmentary, 6 pages) MS:969-4 Nogle Bemærkninger om Vinkelfunktionerne (fragmentary, 3 pages) MS:589 Belonging to the Théorie de la résolution algébrique des équations (fragmentary, 2 pages) MS:592 Précis de la théorie des fonctions elliptiques (168 pages) MS:920-4 Niels Abel Berlin-Paris 1825–182? (11 pages) MS:188-8 Note über die Function . . . (2 pages) MS:969-4 Paa Froland og ved Abels grav 4. og 5. august (4 pages) Multiple ABEL’s notebooks (table B.4) Table B.1: Abel manuscript collections in the Manuscript Collection, University Library, Oslo. 1. Mémoire sur une classe particulière d’équations résolubles algébriquement (64 pages) 2. Note sur quelques formules elliptiques (18 pages) 3. Théorèmes sur les fonctions elliptiques (11 pages) 4. Démonstration d’une propriété générale d’une certaine classe de fonctions transcendantes (4 pages) 5. Matematiske uddrag fra N. H. Abel’s breve (13 pages) Table B.2: Abel manuscripts in the Manuscript Collection, University Library, Oslo, MS:592.
1. Précis d’une théorie des fonctions elliptiques (fragmentary, 8 pages) 2. Om transformationer af elliptiske funktioner, hvorved de to perioder divideres med hvert sit tal (fragmentary, 9 pages) 3. Divisionsligningers opløsning (fragmentary, 2 pages) 4. Unidentified (fragmentary, 1 page) 5. Belonging to the Précis or the Recherches (fragmentary, 2 pages) 6. Belonging to the Paris mémoire (fragmentary, 2 pages) 7. Belonging to the Précis (fragmentary, 7 pages) 8. Belonging to the Recherches second part (fragmentary, 2 pages) 9. Table of contents for a work on elliptic functions (fragmentary, 4 pages) 10. Integration ved hjælp af algebraiske, logaritmiske og eksponentielle funktioner (fragmentary, 2 pages) 11. Belonging to the Abelian Theorem for elliptic functions (fragmentary, 2 pages) Table B.3: Abel manuscripts in the Manuscript Collection, University Library, Oslo, MS:434. MS:351:A Notebook A Mémoires de Mathématiques par N. H. Abel. Paris le 9 Août 1826 (202 pages fol.) MS:436 Notebook B Without title (178 pages fol.) MS:351:C Notebook C Without title (215 pages fol.) MS:696 Notebook D Remarques sur divers points de l’analyse par N. H. Abel, 1er Cahier le 3 Sept. 1827 (136 pages 4:o) MS:829 Notebook E Mathematiske Udarbeidelser af Niels Henrik Abel (192 pages 4:o) MS:749 Matematiske Afhandlinger (170 pages 4:o) Table B.4: Abel’s mathematical notebooks in the Manuscript Collection, University Library, Oslo. 409
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RePoSS: Research Publications on Sc
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The Mathematics of NIELS HENRIK ABE
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The Mathematics of NIELS HENRIK ABE
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Contents Contents i List of Tables
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8.3 Refocusing on the equation . .
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V ABEL’s mathematics and the rise
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List of Figures 2.1 NIELS HENRIK AB
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List of Boxes 1 The algebraic reduc
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Summary The present PhD dissertatio
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Preface to the 2004 edition For thi
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in connection with the Abel centenn
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items published in the same year ar
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the Mittag-Leffler archives in Djur
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Chapter 1 Introduction In the after
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1.2. The mathematical topics involv
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1.3. Themes from early nineteenth-c
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1.4. Reflections on methodology 9 l
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1.4. Reflections on methodology 11
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18 Chapter 2. Biography of NIELS HE
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Chapter 3 Historical background The
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3.2. ABEL’s position in mathemati
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3.3. The state of mathematics 43 tr
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3.4. ABEL’s legacy 45 As can be s
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Chapter 4 The position and role of
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4.1. Outline of ABEL’s results an
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4.2. Mathematical change as a histo
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4.2. Mathematical change as a histo
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58 Chapter 5. Towards unsolvable eq
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98 Chapter 6. Algebraic insolubilit
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100 Chapter 6. Algebraic insolubili
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Chapter 7 Particular classes of equ
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7.1. Solubility of Abelian equation
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7.2. Elliptic functions 153 Figure
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7.2. Elliptic functions 155 7.2.1 T
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7.3. The concept of irreducibility
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7.3. The concept of irreducibility
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7.4. Enlarging the class of solvabl
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164 Chapter 8. A grand theory in sp
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Part III Interlude: ABEL and the
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192 Chapter 9. The nineteenth-centu
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194 Chapter 10. Toward rigorization
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208 Chapter 11. CAUCHY’s new foun
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Chapter 12 ABEL’s reading of CAUC
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12.1. ABEL’s critical attitude 22
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12.3. Convergence 229 12.3 Converge
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12.3. Convergence 231 and {εm} was
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12.4. Continuity 233 it followed th
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12.4. Continuity 235 Actually, if t
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12.4. Continuity 237 DIRICHLET intr
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12.5. ABEL’s “exception” 239
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12.6. A curious reaction: Lehrsatz
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12.7. From power series to absolute
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12.7. From power series to absolute
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12.8. Product theorems of infinite
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12.8. Product theorems of infinite
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12.9. ABEL’s proof of the binomia
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12.10. Aspects of ABEL’s binomial
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12.10. Aspects of ABEL’s binomial
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266 Chapter 13. ABEL and OLIVIER on
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Chapter 14 Reception of ABEL’s co
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14.1. Reception of ABEL’s rigoriz
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14.2. Conclusion 281 of basic notio
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Part IV Elliptic functions and the
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286 Chapter 15. Elliptic integrals
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300 Chapter 16. The idea of inverti
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Chapter 17 Steps in the process of
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17.1. Infinite representations 323
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17.2. Elliptic functions as ratios
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17.2. Elliptic functions as ratios
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17.3. Characterization of ABEL’s
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Chapter 18 Tools in ABEL’s resear
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18.1. Transformation theory 333 The
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18.1. Transformation theory 335 Obv
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18.1. Transformation theory 337 Sum
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18.2. Integration in logarithmic te
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18.3. Conclusion 345 Summary. ABEL
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Chapter 19 The Paris memoir N. H. A
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19.1. ABEL’s approach to the Pari
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19.2. The contents of ABEL’s Pari
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Page 434 and 435: 404 Appendix A. ABEL’s correspond
Page 437: Appendix B ABEL’s manuscripts Man
Page 441 and 442: Bibliography Abel (MS:351:A). “M
Page 443 and 444: Bibliography 413 in: Journal für d
Page 445 and 446: Bibliography 415 — (1990). “Geo
Page 447 and 448: Bibliography 417 — (1830). “Mé
Page 449 and 450: Bibliography 419 — (1768). “Ins
Page 451 and 452: Bibliography 421 Grattan-Guinness,
Page 453 and 454: Bibliography 423 Jahnke, H. N. (198
Page 455 and 456: Bibliography 425 Legendre, A. M. (1
Page 457 and 458: Bibliography 427 Rosen, M. (1981).
Page 459: Bibliography 429 Toti Rigatelli, L.
Page 462 and 463: 432 Index of names Frobenius, Georg
Page 465 and 466: Index École Normale, 40, 187 Écol
Page 467: Index 437 Lagrange interpolation, 3
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