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Arithmetic of algebraic curves from Diophantus to Poincaré. (English) Zbl 0471.01003


MSC:

01A05 General histories, source books
11-03 History of number theory
14-03 History of algebraic geometry
11D25 Cubic and quartic Diophantine equations
01A20 History of Greek and Roman mathematics
01A55 History of mathematics in the 19th century
01A45 History of mathematics in the 17th century
51-03 History of geometry

Citations:

Zbl 0388.01002
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References:

[1] Bashmakova, I. G., Diophante et Fermat, Revue d’histoire des sciences et de leurs applications. Revue d’histoire des sciences et de leurs applications, Istoriko-mathematicheskie issledovania, 17, 283-306 (1966), Original Russian version in
[2] Bashmakova, I. G., Arithmetic of algebraic curves (from Diophantus to Poincaré), Istoriko-mathematicheskie issledovania, 20, 104-124 (1975), [in Russian] · Zbl 0388.01002
[3] Heath, T. L., Diophantus of Alexandria, 129-246 (1910), Cambridge, England
[4] Euler, L., Vollständige Anleitung zur Algebra, Opera omnia, 1, 1, 209-498 (1770), Leipzig and Berlin
[5] Fermat, P., Observations sur Diophante, Oeuvres, 3, 241-276 (1670), Paris
[6] Fermat, P., Inventum novum (compiled by J. de Billy from Fermat’s letters), Oeuvres, 3, 325-400 (1670), Paris
[7] Hilbert, D.; Hurwitz, A., Über die diophantischen Gleichungen vom Geschlecht Null, Acta Mathematica, 14, 217-224 (1890) · JFM 23.0190.01
[8] Hofmann, J. E., Über zahlentheoretische Methoden Fermats und Eulers, …, Archive for History of Exact Sciences, 1, 2, 122-159 (1961) · Zbl 0094.00302
[9] Jacobi, C. G.J, Gesammelte Werke, 2, 53-55 (1882), Berlin
[10] Mordell, L. J., On the rational solutions of the indeterminate equations of the third and fourth degrees, (Proceedings of the Cambridge Philosophical Society, 21 (1922)), 179-192 · JFM 48.1156.03
[11] Newton, I., (Whiteside, D. T., Mathematical papers, Vol. 4 (1971)), Cambridge, England
[12] Poincaré, H., Sur les propriétés arithmétiques des courbes algébraiques, Journal des mathématiques pures et appliquées, Series V, 7, 161-233 (1901) · JFM 32.0564.06
[13] Weil, A., L’arithmétique sur les courbes algébraiques, Acta Mathematica, 52, 281-315 (1921) · JFM 55.0713.01
[14] Zeuthen, H. G., Geschichte der Mathematik im Altertum und Mittelalter (1896), Kopenhagen · JFM 26.0002.01
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