Additional Bibliography and References

ARY ABHAp\: cf. K. Elfering. L. Aubry, Solution de quelques questions d'analyse indeter­

minee, Sphinx-ffidipe, 7e annee (1912), pp. 81-84. BACHET: Claude Bachet, sieur de Meziriac, Problemes

plaisants et delectables qui se font par les nombres, avec leur demonstration, Lyon, Pierre Rigaud 1612; 2e ed., 1624.

JAC. BERNOULLI: Jacobi Bernoulli ... Ars Conjectandi, Opus Posthumum ... Basileae 1713.

BOMBELLI: (a) L'Algebra, Opera di Rafael Bombelli da Bologna, divisa in tre libri . . . In Bologna, per Giovanni Rossi 1572, con licenza de' Superiori; (b) Rafael Bombelli da Bologna, L'Algebra, Prima edizione' integrate, Feltrinelli, Milano 1966.

S. Chowla and W. E. Briggs, On discriminants of binary quadratic forms with a single class in each genus, Can. J. of Math. 6 (1954) 463-470.

B. Datta and A. N. Singh, History of Hindu Mathematics, A Source Book, 2 vol., Lahore 1935-1938 (vol.II, Algebra).

DIOPHANTUS: (a) Diophanti Alexandrini Arithmeticorum libri sex, et de numeris multangulis liber unus. Nunc pri­mum Gr<ece et Latine editi, atque absolutissimis Com­mentariis illustrati. Auctore Claudio Gaspare Bacheto Meziriaco Sebusiano V.C., Lutetiae Parisiorum, Sumptibus Hieronymi Drouart, via J acob<ea, Sub Scuto Solari

362 Number Theory

M.DC.XXI Cum Privilegio Regis; (b) Diophanti Alexan­drini Arithmeticorum Iibri sex, et de numeris multangulis liber unus. Com Commentariis C.G.Bacheti V.C. et ob­servationibus D.P. de Fermat Senatoris Tolosani. Accessit Doctrinae Analyticae inuentum nouum, collectum ex varijs eiusdem D. de Fermat Epistolis. Tolosce, Excudebat Ber­nardus Bose, e Regione Collegij Societatis Iesu, M.DC.LXX.

DIRICHLET-DEDEKIND: Vorlesungen iiber Zahlentheorie von P.G.Lejeune Dirichlet, herausgegeben und mit Zu­satzen versehen von R.Dedekind, 4te Aufl., Braunschweig, F.Vieweg und Sohn, 1894.

K. Elfering, Die Mathematik des Aryabha~a I, Text, Uber­setzung aus dem Sanskrit und Kommentar, W.Fink Verlag, Miinchen 1975.

ENCYCLOPEDIE, ou Dictionnaire raisonne des Sciences, des Arts et des Metiers, par une Societe de Gens de Lettres. Mis en ordre et publie par M. Diderot, de l'Academie Royale des Sciences et des Belles-Lettres de Prusse; et quant a Ia Partie Mathematique, par M. d'Alembert, de l'Academie Royale des Sciences de Paris, de celle de Prusse, et de Ia Societe Royale de Londres (Tome Quatrieme, a Paris, MDCCLIV, avec approbation et privilege du Roy).

G. Enestrom: (a) Der Briefwechsel zwischen Leonhard Euler undjohann I. Bernoulli, Bibl. Math. 4 (1903) 344-388, 5 (1904) 248-291, 6 (1905) 16-87; Der Briefwechsel zwischen Leonhard Euler und Daniel Bernoulli, ibid. 7 (1906-07) 126-156; Zur Geschichte der unendlichen Reihen urn die Mitte des siebzehnten Jahrhunderts, ibid. 12 (1911-12) 135-148; (b) Verzeichnis der Schriften Leonhard Eulers, Jahresb. d.D.M.V. (Erganzungsband IV), 1910-1913.

A. Enneper, Elliptische Functionen, Theorie und Geschichte, Halle 1876.

EULER: Leonhardi Euleri Opera Postuma Mathematica et Physica, Anno 1844 detecta ... edd. P.-H.Fuss et Nic. Fuss, Petropoli 1862 (Reprint, Kraus 1969).

L. Euler und Chr. Goldbach, Briefwechsel, edd. A.P Juskevic und E. Winter, Berlin 1965.

F AGNANO: Produzioni Matematiche del Conte Giulio Carlo

Additional Bibliography and References 363

di Fagnano, Marchese de' Toschi ... In Pesaro, l'anno del Giubileo M.DCC.L ... con licenza de' Superiori (2 vol. = Fag.l-11).

FERMAT: Varia Cpera Mathematica D.Petri de Fermat Senatoris Tolosani ... Tolosae, Apudjoannem Pech ... juxta Collegium PP. Societatis Jesu M.DC.LXXIX.

FRENICLE: Traite des Triangles Rectangles en nombres ("par M. Frenicle de Bessy", in Memoires de l'Academie Royale des Sciences, tome V, 1729, pp. 127-206; "Ia pre­miere Partie du Traite ... avoit ete imprimee des l'annee 1676, in douze, et reimprimee avec Ia seconde en 1677 au Louvre").

E. GALOIS, Sur la theorie des nombres, Bull. de Ferussac XIII (1830), p. 428-436 = ffiuvres mathematiques d'Evariste Galois, Paris Gauthier-Villars 1897, pp. 15-23.

A. Genocchi, Demonstration d'un theoreme de Fermat, Nouv. Ann. de Math. (Ill) 2 (1883) 306-310.

A. GIRARD: Les ffiuvres Mathematiques de Simon Stevin ... reveu, corrige et augmente par Albert Girard, Leyde, Elzevir 1634.

F. Grube, Ueber einige Euler'sche Satze aus der Theorie der quadratischen Formen, Zeitschr. f. Math. u. Physik 19 (1874) 492-519.

H. Hasse, Kurt Hensels entscheidender Anstoss zur Ent­deckung des Lokal-Global-Prinzips, Crelles J. 209 ( 1962) 3-4.

J. L. Heiberg und H. G. Zeuthen, Einige griechische Auf­gaben der unbestimmten Analytik, Bibl.Math. 8 ( 1907-1908) 118-134.

HURWITZ: Mathematische Werke von Adolf Hurwitz, Basel, Birkhauser, 2 vol. 1932-1933.

]. Itard, (a) Arithmetique et Theorie des Nombres, P.U.F. Paris 1973; (b) Sur Ia date a attribuer a une lettre de Pierre Fermat, Rev.Hist. des Sc. 2 (1948) 95-98.

W. Knorr, Archimedes and the measurement of the Circle, A new interpretation, Arch.Hist.ex.Sc. 15 (1975) 115-140.

J. LANDEN, An investigation of a general theorem for

364 Number Theory

finding the length of any arc of any conic hyperbola, by means of two elliptic arcs, with some other new and useful theorems deduced therefrom, Phil. Trans. LXV (1775) 283-289.

LEGENDRE: (a) Recherches d'Analyse Indetermim!e, Par M. Le Gendre, in: Histoire de l'Academie Royale des Sciences, Annee M.DCCLXXXV, avec les Memoires de Mathematique et de Physique pour Ia meme Annee ... A Paris, de l'lmprimerie Royale M.DCCLXXXVIII, pp. 465-559; (b) Adrien-Marie LeGendre, Memoire sur les Transcendantes elliptiques ... lu ala ci-devant Academie des Sciences en 1792, A Paris, l'an deuxieme de la Re­publique; (c) Essai sur la Theorie des Nombres; par A.M. LeGendre, de l'Institut National, A Paris, Chez Duprat, Libraire pour les Mathematiques, quai des Augustins, An VI; (d) Adrien-Marie Legendre, Theorie des Nombres, troisieme edition. Paris, Firmin-Didot, 2 vol. 1830.

MACLAURIN: Colin MacLaurin, A treatise of fluxions, Edinburgh, 2 vol. 1742.

D. Mahnke, Leibniz auf der Suche nach einer allgemeinen Primzahlgleichung, Bibl. Math. 13 (1912-1913) 29-61.

A. de MOIVRE: (a) The Doctrine of Chances, London 1718; (b) Miscellanea Analytica de Seriebus et Quadraturis ... (1 vol. + Supplementum) Londini 1730.

0. Neugebauer and A. Sachs, Mathematical cuneiform texts, New Haven 1945.

B. PASCAL, ffiuvres CompU~tes, ed. J. Chevalier, Bibl. de Ia Pleiade, Gallimard 1954 (pp. 97-108: Traite du triangle arithmetique; pp. 194-208: Histoire de Ia roulette).

K. Shukla, Acarya Jayadeva the mathematician, Ganita 5 (1954) 1-20.

J. Steinig, On Euler's idoneal numbers, Elem.d.Math. 21 ( 1966) 73-88.

THEON: Theonis Smyrnaei ... Expositio rerum mathe­maticarum ad legendum Platonem utilium, rec. E.Hiller, Lipsiae, Teubner 1878 (and: Theon of Smyrna, Math­ematics useful for understanding Plato, transl. by R. and D. Lawlor ... San Diego, Wizards Bookshelf 1979).

Index Nominum

Abel (N. H., 1802-1829): 251, 298, 299, 306, 338. Archimedes (287 ? -212 B.C.): 3, 16, 17-19, 48, 92, 230. Ariosto (Lod., 1474-1533): 310. Aristotle (384-322 B.C.): 5. Artin (E., 1898-1962): 203. Aryabhata (476-? ): 7, 177. Aubry (L.): 59, 292.

Bacchus (god): 1. Bachet (C. G.- de Meziriac, 1581-1638): 1, 2, 7, 11, 25,

28, 30, 32-34, 44, 46, 48, 51, 52, 59, 61, 93, 94, 110, 177.

Bacon (F., 1561-1626): 119. Barrow (1., 1630-1677): 160. Beaugrand (]. de-, 1600 ?-1640 ?): 38, 41, 42. Beguelin (N. de-, 1714-1789): 188, 223. Berkeley (bishop G., 1685-1753): 4. Bernoulli (Dan., 1700-1782): 163, 164, 169, 170, 171,

172, 174, 180, 223, 237, 257, 262, 264, 311. Bernoulli (Jac., 1654-1705): 48, 49, 162, 184, 257, 260. Bernoulli (Joh., 1667-1748): 65, 162, 163, 169, 170, 182,

184, 243, 244, 257, 258, 262, 264, 265, 270, 309. Bernoulli (Joh. Ill, 1744-1807): 315. Bernoulli (Nic. I, 1687-1759) 170, 174, 203, 237, 264,

271. Bernoulli (Nic. II, 1695-1726): 163, 171. Bhaskara (1115- ? ): 19, 20, 22. Billy(]. de-, 1602-1679): 2, 44, 103, 105, 108, 114, 149. Bolyai (W., 1775-1856): 334. Bombelli (R., 1526-1572): 10, 11, 31-32, 66, 159, 202.

366 Index Nominum

Boncompagni (prince Bald., 1821-1894): 11. Brahmagupta (598-665 ?): 17, 19, 20, 21-22, 24. Briggs (H., 1561-1630 ?): 160. Brouncker (W., viscount-, 1620-1684): 81, 92-97, 98,

100, 160, 161, 174, 229-231.

Campanus (G., thirteenth cent.): 202. Caraccioli (D. Caracciolo, marchese -, 1715-1789): 311,

312. Carcavi (P. de-, 1600 ? -1684): 38, 39, 41, 42, 44, 46,

75, 111, 112, 118-119, 161. Cardano (Hier., 1501-1576): 52, 159. Cassels (j. W. S.): 140. Cassini (J.D., 1625-1712): 161. Catherine II (1729-1791): 163-165, 168. Cauchy (Aug., 1789-1857): 203. Cavalieri (Bon., 1598-1647): 38, 160. Chaptal (j., 1756-1832): 314. Chasles (M., 1793-1880): 124. Chowla (S.): 226. Clairaut (Al.-Cl., 1713-1765): 120, 170, 174, 187, 244,

262, 272, 311. Clerselier ( Cl., 1614-1684): 51. Colbert (j.-B., 1619-1683): 51, 161. Colebrooke (H. T., 1765-1837): 19, 20, 22. Condorcet (j. A. N., marquis de -, 1743-1794): 123,

311, 313, 314. Copernicus (N., 1473-1543): 159. Cramer (G., 1704-1752): 264.

D'Alembert (j. le Rond, 1717-1783): 27, 165, 169, 170, 179,198,203,245,311,312,314,317.

Datta (B.): 7, 17, 19, 22. Dedekind (R., 1831-1916): 320. Delambre (j.-B., 1749-1822): 312, 314. Descartes (R., 1596-1650): 52-54, 61, 65, 121, 160, 199. Digby (Sir Kenelm, 1603-1665): 42, 46, 50, 61, 80, 81,

103, 113, 119, 173, 174.

Index Nominum 367

Diophantus (third cent. A.D.): 1, 3, 10, 11, 13, 17, 19, 25, 27-34, 44, 46, 47, 51, 59, 77, 80, 82, 102, 103, 104-106, 108-109, 121, 180, 181, 233, 243.

Dirichlet (P. G. Lejeune, 1805-1859): 207, 208, 290, 322, 328, 329, 330, 334, 335, 336, 337-338.

Edwards (H. M.): 335. Ehler (K. L.): 175, 202, 262. Eisenstein (G., 1823-1852): 210, 290. Enestrom (G., 1852-1923): 170. Enneper (A., 1830-1885): 123, 244. Espagnet (E. d' -, 1596 ? - ?): 39. Euclid (end of third cent. B.C. ?): 4, 5, 6, 7, 10, 13, 15,

24, 49, 52, 53, 93, 122, 126, 202. Eudemos (fourth cent. B.C.): 4. Euler (Joh. A., 1734-1800): 164. Euler (L., 1707-1783): 1, 2, 3, 15, 25, 48, 56, 57, 58, 61,

62,63,64, 65, 66,67,68, 79, 83,85,97, 100,102,104, 114, 115, 120-123, 134, 135, 138, 139, 147, 155, 159-285, 309, 310-312, 314, 315, 317, 318, 320, 321, 325, 326.

Euler (P., 1670-1743): 162, 165. Eutocius (480 ? - ? A.D.): 16. Evelyn (j., 1620-1706): 81.

Fagnano (G. C. di -, 1682-1766): 1, 122, 182, 245, 246, 247, 251, 284, 298, 305, 306, 307, 310.

Fermat (P. de -, 1601-1665): 1, 2, 3, 6, 7, 14, 24, 25, 28, 29, 30, 32, 34, 37-124, 161, 170, etc.

Fermat (Samuel de-, 1632-1690): 2, 32, 33, 44, 46, 173. Ferro (Sc. del-, 1465-1526): 159. Fibonacci (Leon., 1170 ? - 1240 ?): 11, 12-14. Frederic II (emperor-, 1194-1250): 12, 13. Frederic II (king-, 1712-1786): 163-165, 167, 312. Frenicle (B. -de Bessy, 1612 ? - 1675): 6, 42, 46, 51-

58,62,63,76, 79,80,81,86,90-91,92, 103,105,111, 118, 119, 122, 128, 180.

368

Fuss (N., 1755-1826): 169, 223. Fuss (P.-H., 1798-1855): 165, 170.

Galileo (- Galilei, 1564-1642): 38, 159. Galois (Ev., 1811-1832): 119, 204. Gassendi (P., 1592-1655): 46.

Index Nominum

Gauss (C. F., 1777-1855): 3, 188, 192,203,213,219,225, 248, 285, 309, 313, 319, 320, 326, 327, 328, 330, 331, 332, 335, 336, 353.

Genocchi (A., 1817-1889): 87. Germain (S., 1776-1831): 335, 337, 338. Gillot(]., 1613- ?): 61. Girard (A., 1595-1632): 110. Goldbach (Chr., 1690-1764): 2, 115, 120, 165, 170, 171,

172, etc. Grube (F.): 224. Gsell (G., 1673-1740): 164.

Hasse (H., 1898-1979): 339, 341. Heiberg (J. L., 1854-1928): 13. Hilbert (D., 1862-1943): 124, 284, 345. Hofmann (J. E., 1900-1973): 42, 46, 91. Holzmann (W. - = Xylander, 1532-1576): 10, 28, 31. Hopital (G. F., marquis de I'-, 1661-1704): 162. Hurwitz (A., 1859-1919): 124, 229. Huygens (Const., 1596-1687): 160. Huygens (Chr., 1629-1695): 2, 38, 39, 44, 46, 67, 75, 76,

79, 86, 92, 99, 102, 103, 113, 118, 119, 120, 160, 161, 173, 230, 257.

Itard (J., 1902-1979): 47, 115.

Jacobi (C. G.]., 1804-1851): 1, 122-123, 186, 202, 248, 254, 280, 282, 283, 299, 324, 325, 330, 338.

Jayadeva (eleventh cent. ?): 22. juskevic (A. P.): 165, 170.

Index Nominum

Kepler (j., 1571-1630): 159. Knorr (W.): 16. Kiihn (H., 1690-1769): 202, 262. Kummer (E., 1810-1893): 124.

Lacepede (E. de-, 1756-1825): 314.

369

Lagrange (j. L., 1736-1813): 3, 24, 65, 82, 100, 112, 114, 117, 118, 120, 121, 123, 147, 151, 168, 169, 170, 178-181, 183, 187, 197, 198, 203, 213, 215-219, 224, 225, 228, 233, 234, 236, 239, 240, 253, 283, 284, 309-322, 324, 325, 327, 349, 350-359.

Lalande (J. J., 1732-1807): 311, 314. Lalouvere (A., 1600-1664): 42. Lambert (j. H., 1728-1777): 312. Landen (j., 1719-1790): 123, 147. Laplace (P. S., 1749-1827): 314, 324. Lavoisier (A. L., 1743-1794): 309, 313. Legendre (A.-M., 1752-1833): 3, 102, 172, 244, 250, 275,

285, 290, 302, 315, 319, 322-338, 341-345, 346, 349. Leibniz (G. W., 1646-1716): 25, 56, 57, 65, 66, 99, 121,

123, 160, 161, 163, 182, 184, 203, 257, 258, 265. Le Monnier (P., 1715-1799): 313. Leonardo Pisano: cf. Fibonacci. Lessing (G. E., 1729-1781): 17. Lexell (A.]., 1740-1784): 212. Locke (J., 1632-1704): 4. Lucas (E., 1842-1891): 52.

MacLaurin (Colin, 1698-1746): 184, 245, 257. Maestlin (M., 1550-1631): 159. Mahnke (D.): 56-57, 66. Maupertuis (P.L. de-, 1698-1759): 311. Mengoli (P., 1625-1686): 184. Mersenne (Marin, 1588-1648): 6, 38, 39, 41, 42, 46, 47,

49, 51-56, 59, 60, 61, 62, 67, 71, 76, 80, 103. Mobius (A. F., 1790-1868): 124. Moivre (Abr. de-, 1667-1754): 237, 260, 262.

370

Monge (Gaspard, 1746-1818): 314. Mordell (L. J., 1888-1972): 124, 140. Muller (G. F., 1705-1783): 164.

Napier (J., 1550-1617): 159.

Index Nominum

Naude (Ph., 1684-1745): 185, 262, 276, 277, 278, 283. Neugebauer (0.): 4, 8, 9. Newton (1., 1642-1727): 4, 108, 160, 184, 234, 263.

Olbers (H., 1758-1840): 335, 336. Ozanam (J., 1640-1717): 93.

Pascal (B., 1623-1662): 2, 38, 42, 44, 46, 47, 49, 61, 74, 80, 98, 99, 101.

Pascal (E., 1588-1651): 41, 46. Pell (J., 1611-1685): 174. Peter I (tsar-, 1672-1725): 163. Pfaff (J. F., 1765-1825): 334. Plato (427 ? - 348 B.C.): 5, 53. Poincare (H., 1854-1912): 124. Poisson (S. D., 1781-1840): 324, 325. Poleni (Giov., 1683-1761): 262. Poncelet (J. V., 1788-1867): 124. Proclus (410-485 A.D.): 8. Pythagoras (sixth cent. B.C. ??): 8. Pythagoreans: 5, 8.

Rabelais (F., 1494 ? -1553): 61. Ribenboim (P.): 335. Riccati (J. F., 1707-1775): 183, 230. Ricci (Michelang., 1619-1682): 38. Richelieu (Arm., card. de-, 1585-1642): 161. Riemann (B., 1826-1866): 124, 185, 276. Roberval (G. P. de-, 1602-1675): 41, 46-49, 53, 59, 63,

64, 71, 160. Roomen (Ad. van- = Romanus, 1561-1615): 46.

Index Nominum 371

Saint Martin (P. Bruslart de-, 1584 ? -1659 ?): 51, 53. Sainte Croix (A. Jumeau de-, ? -1646 ?): 51, 61, 76. Schlesinger (L.): 326. Schlomilch (0., 1823-1901): 276. Schooten (Fr. van-, 1615-1660): 39, 81, 160. Schreier (0., 1901-1929): 203. Serre (J.-P.): 290, 340, 345. Shukla (K.): 22. Singh (A. N.): 7, 17, 19, 22. Sluse (R. de-, 1622-1685): 160. Stackel (P., 1862-1919): 265. Stanislas (king-, 1732-1798): 168. Steinig (J.): 224. Stevin (S., 1548-1620): 110, 159. Stifel (M., 1487-1569): 47, 52. Stirling (J., 1692-1770): 262.

Tannery (P., 1843-1904): 5, 19, 46. Taylor (B., 1685-1731): 258. Theon Smyrnaeus (early second cent. A.D.): 16, 90, 92. Torricelli (Evang., 1608-1647): 38, 160.

Viete (Fr., 1540-1603): 10, 12, 25, 26, 28, 31-32, 39, 41, 46, 47, 108-110, 121, 159.

Voltaire (F. M. Arouet, 1694-1778): 4, 165, 311.

Waard (C. de -): 46. Wallis (J., 1616-1703): 2, 7, 50, 51, 81, 92-97, 99, 100,

103, 119, 120, 160, 172, 173, 174, 177. Wilson (J., 1741-1793): 65, 201. Wolff (Chr., 1679-1754): 163, 165.

Xylander: cf. Holzmann.

Zimmermann (A. W. von -): 326.

Index Rerum

Abel's theorem: 251, 298, 307. aliquot parts: 52, 58. amicable numbers: 6, 51-54. ascent: 104-112, 255-256.

Bernoulli numbers: 48, 184, 260, 272. bhavana (cf. composition): 21, 24, 96. binomial coefficients: 46-49. Brahmagupta's identity: 14-17,83,96,204,236,241, 332.

cakrava1a (cf. Pelt's equation): 22-24, 96. canonical equation (Euler's -): 133-134, 156, 249, 254-

256, 301. classes (of quadratic forms: cf. Gaussian, Lagrangian): 317,

319, 320, 321' 334-335. composition (of representations: cf. bhavana): 68-74, 83-

86; (of quadratic forms): 333-335. continued fractions: 7, 120, 183, 231, 315. curves (of genus 0; of genus 1 = elliptic): cf. equations. cyclotomic (polynomials): 199-200; (fields): 336.

definite: 322. determinant (of a "Gaussian" form): 95, 238, 319. descent: 67, 75-77, 79, 101, 113, 114-118, 140-157. diophantine (equations, problems; cf. curves): 1, 25-29,

82, 181. Dirichlet (characters): 207, 267, 287; (series): 264, 267,

272; ( -'s theorem): 208, 329-330. discriminant (of a "Lagrangian" form): 216, 319, 320.

Index Rerum 373

divisor (of a binary quadratic form; cf. prime): 217-218, 320, 332.

double equations: 28-29, 105-107, 138-139, 243, 253.

elastic curve ( = elastica): 182, 244. elliptic (functions, integrals): 1, 122, 130, 182-183, 243-

251, 298-299, 325; (curves = curves of genus 1): cf. equations of genus 1.

equations: cf. diophantine; (of genus 0): 28, 104, 179-180, 233-239, 315, 317, 327-328, 341-344; (of genus 1): 28-29,103-112,130-134,180,242,252-256,296-307, 316.

equivalence (of forms, equivalent·fonns.; cf. classes): 217, 318-319; (of equations): 339.

euclidean algorithm: 5, 7, 94, 126, 177, 193. Euler-MacLaurin (formula, summation): 184, 257-261,

272. Euler's theorem (a""<N> = 1 mod N): 57, 177, 193. eulerian product: 266-267.

factoring: cf. prime number decomposition. Fermat's conjecture (on 22n + 1): 2, 58, 172. Fermat's equation ( = "last theorem": xn + yn = zn): 49,

104, 173, 181; (case n = 4): 61, 77-79, 180, 181; (case n = 3): 61, 116-117, 181, 239, 242; (case n = 5): 335-338.

Fermat's theorem (ap-I = 1 mod p): 55-57, 175-177, 189, 193-194.

figurative numbers: 7. form: cf. Gaussian, Lagrangian, quadratic.

Gaussian (classes, equivalence, forms): 319-320; (field, ring): 66, 125.

Goldbach's conjecture: 2, 170.

Hasse's (or: Hasse-Minkowski) principle: 60, 339, 340-342.

374

heights: 145. Hilbert's formula: 345. hypotenuse: 70, 71.

imaginary: 66, 202, 204, 240. improper (equivalence): 319. indefinite: 322. induction: 49-50. infinite descent: cf. descent. isogeny: 115, 123, 151.

kunaka: 7, 23-24, 94.

Index Rerum

Lagrangian (classes, equivalence, forms): 319-320; (re­duction): 211, 215-217, 317, 321, 346; (transforms): 356-359.

Legendre's theorem: 327-328, 342-344. lemniscate: 182, 244, 246, 304-306.

magic squares: 52. "methodus vulgaris": 105-107, 109, 110. Mordell's theorem: 140-149. m-th power residues: cf. residues.

Partitio numerorum: 185, 276-282. "Pell's equation": 19-24, 42, 51, 81, 83, 92-99, 113, 118,

174, 183, 229-232, 314, 315. perfect numbers: 6, 51-55. porisms: 11, 17, 109. prime, prime factor decomposition: 4-6, 54-55, 58, 74-

75, 187-188, 219-226. prime (divisor of a form): 84, 186-187, 205-209, 288;

(field): 63. primitive (representation): 71, 74; (root): 177, 195, 199-

200. proper (equivalence): 319, 322; (representation): 70, 217,

220, 221, 320; (solution of a congruence): 339.

Index Rerum 375

pythagorean triangles: 8-10, 13, 76-79, 82, 111.

quadratic (fields): 66, 125-129, 202; (forms): 80-81, 83-91, 128, 179, 204-205, 211-218, 222, 292-295, 316, 318-322; (reciprocity): cf. reciprocity; (residues): cf. residues; (rings): cf. quadratic fields.

real: cf. imaginary. reciprocity (quadratic-, law of quadratic-): 62-63, 187,

209, 219, 287-291, 326, 328-330, 344-345. recurrent (sequences): 183, 237. reduced: 95; ("in the Lagrangian sense"): 321; (weakly,

strongly-): 353. reduction: cf. Lagrangian reduction. residue (quadratic -, m-th power -): 61-66, 79, 177,

190-192, 195, 196, 209, 328.

side and diagonal numbers: 16, 90, 92. submultiple numbers: 52-54. sums of n squares (for n = 2): 10-11, 30, 34, 59, 66-74,

177-178, 210-211; (for n = 3): 30, 34, 59, 101-103, 292-294, 331; (for n = 4): 3, 30, 34, 102, 173, 174, 177, 178-179, 226-229, 294-295, 315-316.

sums (of three triangular numbers, four squares, five pen­tagonal numbers, etc.): 3, 61, 79, 101, 119, 173.

Wilson's theorem: 65-66, 201, 316.

Andre Weil, considered one of the leading mathemati­cians of the twentieth century, was Professor Emeritus at the Institute for Advanced Study in Princeton until his death in 1999. He is well known for his work in number theory and algebraic geometry. A lifelong interest in the history of mathematics finds its culmination in this book, which was based on lectures presented at the Institute for Advanced Study and other places.