Bashmakova, Isabella G. Arithmetic of algebraic curves from Diophantus to Poincaré. (English) Zbl 0471.01003 Hist. Math. 8, 393-416 (1981). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 3 Documents 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 Keywords:Diophantine equations; curves of genus 0, of genus 1; elliptic functions; Poincare; Diophantus; Euler; Fermat; Jacobi Citations:Zbl 0388.01002 PDFBibTeX XMLCite \textit{I. G. Bashmakova}, Hist. Math. 8, 393--416 (1981; Zbl 0471.01003) Full Text: DOI 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 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.