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Sur les origines de la géométrie algébrique. (French) Zbl 0552.01004

Verf. erzählt über einige Problemstellungen, die bei der Entwicklung der algebraischen Geometrie eine Rolle gespielt haben, in Äußerungen und Schriften älterer Autoren, wie Diophant, Fermat, Leibniz, Joh. Bernoulli und Euler (mit Originalzitaten).
Reviewer: K.-B.Gundlach

MSC:

01A45 History of mathematics in the 17th century
14-03 History of algebraic geometry
01A50 History of mathematics in the 18th century
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References:

[1] I.G. Bashmakova : Diophante et Fermat , Rev. Hist. Sc. 13 (1966) 289-306. · Zbl 0143.24404
[2] Joh. Bernoulli : Lectiones Mathematicae de Methodo Integralium, aliisque, conscriptae in usum Ill. Marchionis Hospitalii cum Auctor Parisiis ageret Annis 1691 et 1692 , in Opera Omnia, Laus. et Gen. 1742 (réimpr. Georg Olms Verlag, Hildesheim 1968), t.III, 386-558.
[3] Joh. Bernoulli : Briefwechsel , Bd. I, Birkhäuser, Basel 1955.
[4] Diophanti Alexandrini Arithmeticorum libri sex ... cum observationibus D.P. De Fermat... Accessit Doctrinae Analyticae Inventum Novum, collectum ex variis eiusdem D. De Fermat Epistolis, Tolosae 1670.
[5] Diophante , trad. russe par I.N. Vesselovski, réd, et comm. de I.G. Bashmakova , Moscou, Nauka 1974.
[6] ENCYCLOPÉDIE ou Dictionnaire raisonné des Sciences, des Arts et des Métiers , edd. Diderot et D’Alembert, Paris et Neuchâtel, 1751- 1765, 17 vol.
[7] Euler , Opera Omnia: (a) Vollständige Anleitung zur Algebra , St Petersburg 1770 = Op. vol. 11;(b) Demonstratio theorematum quorundam arithmeticorum , Op. vol. 12, pp. 38-58(c) Solutio generalis quorundam problematum Diophanteorum ... , Op. vol. 12, pp. 428-458;(d) Mém. Acad. Sc. St-Pétersbourg 11 (1830), pp. 1-91 = Op. vol. 15, pp. 82-181.
[8] Fermat , Oeuvres , ed. P. Tannery et Ch. Henry, Paris 1891 -1912, 4 vol. · JFM 23.0013.02
[9] P.-H. Fuss : Correspondance Mathématique et Physique , St. Pétersbourg 1843, 2 vol. (réimpr. Johnson Reprint Corp. 1968).
[10] C.G. Jacobi : De usu theoriae integralium ellipticorum et integralium abelianorum in analysi diophantea . J. de Crelle 13 (1835) 353-355= Gesammelte Werke , vol. II, 53-55. · ERAM 013.0500cj
[11] Lagrange : Oeuvres , ed. J.A. Serret, Paris 1867-1892, 14 vol.
[12] Leibniz : Math. Schriften , ed. C.I. Gerhardt; (a) vol. 13, Briefwechsel... , Halle 1856;(b) vol. 111 Halle 1858: no. XXIV, Specimen novum Analyseos pro scientia infiniti, ... , pp. 350-361.
[13] Leibniz : Briefwechsel mit Mathematikern , ed. C.I. Gerhardt, Berlin 1899, vol. I (réimpr. Georg Olms Verlag, Hildesheim 1962). · JFM 29.0025.03
[14] Newton : De resolutione Quaestionum circa numeros , in Mathematical Papers , ed. D.T. Whiteside, vol. IV, Cambridge 1971.
[15] Fr. Viète : Zetetica, in Opera Mathematica , ed. F. Schooten, Lugd. Bat., Elzevir 1646 (réimpr. Georg Olms Verlag, Hildesheim 1970), pp. 42-80. · Zbl 0188.30503
[16] A.P. Youschkevitch , Rev. Hist. Sc. 30 (1977) 338-343.
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