What is new and what is old in Viète’s analysis restituta and algebra nova, and where do they come from ? Some reflections on the relations between algebra and analysis before Viète

• Volume: 13, Issue: 1, page 85-153
• ISSN: 1262-022X

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Abstract

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François Viète considered most of his mathematical treatises to be part of a body of texts he entitled Opus restitutæ mathematicæ analyseos seu algebra nova. Despite this title and the fact that the term “algebra” has often been used to designate what is customarily regarded as Viète’s main contribution to mathematics, such a term is not part of his vocabulary. How should we understand this term, in the context of the title of his Opus, where “new algebra” is identified with “restored analysis”? To answer this question, I suggest distinguishing between two kinds of problematic analysis: the former is that described by Pappus at the beginning of the 7th book of his Mathematical Collection, which I will call “intra-configurational”; the latter is the one Viète applied, which I will call “trans-configurational”. In order to apply the latter kind of analysis, Viète relies on his new formalism. I argue, however, that the use of this formalism is not a necessary condition for applying it. I also argue that the same kind of analysis was largely applied before Viète for solving geometrical problems, by relying on geometrical inferences of a special sort which I call “non-positional”, since they do not depend on a diagram. As an example of a similar systematic application of trans-configurational analysis, I consider al-Khayyām’s Treatise of Algebra and Al-muqābala. Finally, I suggest that Viète, when speaking of algebra in the title of his Opus, refers to the system of techniques underlying trans-configurational analysis, that is, to the art of transforming the conditions of certain purely quantitative problems, using either an appropriate formalism relative to the operations of addition, subtraction, multiplication, division, root extraction and solving polynomial equations applied to indeterminate numbers, or appropriate geometrical, non-positional inferences.

How to cite

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Panza, Marco. "What is new and what is old in Viète’s analysis restituta and algebra nova, and where do they come from ? Some reflections on the relations between algebra and analysis before Viète." Revue d'histoire des mathématiques 13.1 (2007): 85-153. <http://eudml.org/doc/274895>.

@article{Panza2007,
abstract = {François Viète considered most of his mathematical treatises to be part of a body of texts he entitled Opus restitutæ mathematicæ analyseos seu algebra nova. Despite this title and the fact that the term “algebra” has often been used to designate what is customarily regarded as Viète’s main contribution to mathematics, such a term is not part of his vocabulary. How should we understand this term, in the context of the title of his Opus, where “new algebra” is identified with “restored analysis”? To answer this question, I suggest distinguishing between two kinds of problematic analysis: the former is that described by Pappus at the beginning of the 7th book of his Mathematical Collection, which I will call “intra-configurational”; the latter is the one Viète applied, which I will call “trans-configurational”. In order to apply the latter kind of analysis, Viète relies on his new formalism. I argue, however, that the use of this formalism is not a necessary condition for applying it. I also argue that the same kind of analysis was largely applied before Viète for solving geometrical problems, by relying on geometrical inferences of a special sort which I call “non-positional”, since they do not depend on a diagram. As an example of a similar systematic application of trans-configurational analysis, I consider al-Khayyām’s Treatise of Algebra and Al-muqābala. Finally, I suggest that Viète, when speaking of algebra in the title of his Opus, refers to the system of techniques underlying trans-configurational analysis, that is, to the art of transforming the conditions of certain purely quantitative problems, using either an appropriate formalism relative to the operations of addition, subtraction, multiplication, division, root extraction and solving polynomial equations applied to indeterminate numbers, or appropriate geometrical, non-positional inferences.},
author = {Panza, Marco},
journal = {Revue d'histoire des mathématiques},
keywords = {algebra; analysis; Viète; Al-Khayyām; Pappus},
language = {eng},
number = {1},
pages = {85-153},
publisher = {Société mathématique de France},
title = {What is new and what is old in Viète’s analysis restituta and algebra nova, and where do they come from ? Some reflections on the relations between algebra and analysis before Viète},
url = {http://eudml.org/doc/274895},
volume = {13},
year = {2007},
}

TY - JOUR
AU - Panza, Marco
TI - What is new and what is old in Viète’s analysis restituta and algebra nova, and where do they come from ? Some reflections on the relations between algebra and analysis before Viète
JO - Revue d'histoire des mathématiques
PY - 2007
PB - Société mathématique de France
VL - 13
IS - 1
SP - 85
EP - 153
AB - François Viète considered most of his mathematical treatises to be part of a body of texts he entitled Opus restitutæ mathematicæ analyseos seu algebra nova. Despite this title and the fact that the term “algebra” has often been used to designate what is customarily regarded as Viète’s main contribution to mathematics, such a term is not part of his vocabulary. How should we understand this term, in the context of the title of his Opus, where “new algebra” is identified with “restored analysis”? To answer this question, I suggest distinguishing between two kinds of problematic analysis: the former is that described by Pappus at the beginning of the 7th book of his Mathematical Collection, which I will call “intra-configurational”; the latter is the one Viète applied, which I will call “trans-configurational”. In order to apply the latter kind of analysis, Viète relies on his new formalism. I argue, however, that the use of this formalism is not a necessary condition for applying it. I also argue that the same kind of analysis was largely applied before Viète for solving geometrical problems, by relying on geometrical inferences of a special sort which I call “non-positional”, since they do not depend on a diagram. As an example of a similar systematic application of trans-configurational analysis, I consider al-Khayyām’s Treatise of Algebra and Al-muqābala. Finally, I suggest that Viète, when speaking of algebra in the title of his Opus, refers to the system of techniques underlying trans-configurational analysis, that is, to the art of transforming the conditions of certain purely quantitative problems, using either an appropriate formalism relative to the operations of addition, subtraction, multiplication, division, root extraction and solving polynomial equations applied to indeterminate numbers, or appropriate geometrical, non-positional inferences.
LA - eng
KW - algebra; analysis; Viète; Al-Khayyām; Pappus
UR - http://eudml.org/doc/274895
ER -

References

top
1. [Abgrall 2004] Abgrall ( Philippe) – Le développement de la géométrie aux ixe-xie siècles. Abū Sahl al-Qūhī, Paris: A. Blanchard, 2004. Zbl1059.01004MR2123808
2. [Anaritius 1994] Anaritius – The Latin Translation of Anaritius Commentary on Euclid’s Elements of Geometry Books I-IV, edited by P. M. J. E. Tummers, Nijmegen: Ingenium Publisher, 1994.
3. [Apollonius 1706] Apollonius – De sectione rationis libri duo. Ex Arabico Msto. Latine Versi, Opera & studio E. Halley, Oxonii: E Theatro Sheldoniano, 1706.
4. [Apollonius 1988] Apollonius – On Cutting off of a Ratio: An Attempt to Recover the Original Argumentation Through a Critical Translation of the Two Extant Medieval Arabic Manuscripts, translated by E. M. Macierowski, and edited by R. H. Schmidt, Fairfield, Conn.: Golden Hind Press, 1988.
5. [Archimedes 1972-1975] Archimedes – Archimedis Opera Omnia, Iterum editit I.L. Heiberg; corrigenda adiecit E. S. Stamatis (for vols. I–III). 4 vols., Stuttgart: Teubner, 1972-1975.
6. [Barrow 1683] Barrow ( Isaac) – Lectiones mathematicæ XXIII, Londini: Typis J. Playford, pro G. Wells, 1683; English translation by J. Kirkby: The Usefulness of Mathematical Learning explained and demonstrated: Being Mathematical Lectures ..., London: S. Austen, 1734 (I refer to this translation). Zbl0225.01005
7. [Beaney 2002] Beaney ( Michael) – Decomposition and Transformations: Conceptions of Analysis in the Early Analytic and Phenomenological Traditions, The Southern Journal of Philosophy, 40 (2002), p. 53–99.
8. [Behboud 1994] Behboud ( Ali) – Greek Geometrical Analysis, Centaurus, 37 (1994), p. 52–86. Zbl0815.01001MR1306339
9. [Berggren & Brummelen 2000] Berggren ( J. Lennart) & Brummelen ( Glen Van) – The Role and Development of Geometric Analysis and Synthesis in Ancient Greece and Medieval Islam, in Suppes (P.), Moravcsik (J. M.) & Mendell (H.), eds., Ancient and Medieval Traditions in the Exact Sciences. Essays in Memory of Wilbur Knorr, Stanford: CSLI Pubblications, 2000, p. 1–31. Zbl1011.01003MR1827650
10. [Bombelli 1572] Bombelli ( Rafael) – L’Algebra[;] parte maggiore dell’Aritmetica, Bologna: G. Rossi, 1572.
11. [Bos 2001] Bos ( Henk J. M.) – Redefining Geometrical Exactness. Descartes’ Transformation of the Early Modern Concept of Construction, New York, Berlin, etc.: Springer, 2001. Zbl0972.01020MR1800805
12. [Cardano 1545] Cardano ( Girolamo) – Ars Magna sive de regulis algebraicis liber unus, Norimbergæ: J. Petreius, 1545; Second ed.: Officina Henricpetrina, Basilea, 1570. Third ed.: in Hieronymi Cardani Mediolanensis philosophi ac medici celeberrimi Opera omnia, Lugdunis sumptibus I. A. Huguetan et M. A. Ravaud, 1663, vol. IV, pp.221–302 (I refer to this edition).
13. [Clavius 1608] Clavius ( Christopher) – Algebra, Romæ: B. Zannettum, 1608; Second ed.: Genevæ, S. Gamonetus, 1609 (I refer to this edition).
14. [Cornford 1932] Cornford ( Francis M.) – Mathematics and Dialectics in the Republic VI-VII, Mind, 41 (1932), p. 37–52 and 173–190. Zbl0004.19301
15. [Descartes 1637] Descartes ( René) – Discours de la méthode .... Plus la Dioptrique. Les météores. Et la Géométrie qui sont des essais de cette Méthode, Leyde: I. Maire, 1637.
16. [Descartes 1897-1910] Descartes ( René) – Œuvres de Descartes, édités par C. Adam et P. Tannery. 12 vols., Paris: Vrin, 1897-1910.
17. [Diophante 1984] Diophante – Les Arithmétiques, vol. III and IV (books IV–VIII), texte établi et traduit par R. Rashed, Paris: Les Belles Lettres, 1984.
18. [Diophantus 1575] Diophantus – Diophanti Alexandrini rerum arithmeticarum libri sex ..., A Guil. Xilandro Augustano incredibili labore latine redditum, et commentariis explanatum, inque lucem editum, Basilæ: E. Episcopium et Nicolai Fr. hæredes, 1575.
19. [Diophantus 1893-1895] Diophantus – Diophanti Alexandrini opera omnia cum græcis commentariis, 2 vols. Edidit et latine interpretatus et Paulus Tannery, Lipsiæ: B. G. Teubner, 1893-1895. JFM25.0014.01
20. [Euclid 1969-1977] Euclid – Elementa ..., post J. L. Heiberg edidit E. S. Stamatis. 5 volumes in 6 tomes, Leipzig: B. G. Teubner, 1969-1977. Zbl0191.00203
21. [Euclid 1883-1889] Euclid – Opera Omnia, editerunt I. L. Heiberg et H. Menge. 8 vols. + 1 vol. supl., New York, Heidelberg: Teubner, 1883-1889. JFM15.0002.04
22. [Euclid 1926] Euclid – The Thirteen Books of Euclid’s Elements, translated from the text of Heiberg with introduction and commentary by T. L. Heath; Second edition revised with additions; 3 vols., Cambridge: Cambridge Univ. Press, 2nd edition, 1926. Zbl1026.01024MR1304053
23. [Fournarakis & Christianidis 2006] Fournarakis ( Philippos) & Christianidis ( Jean) – Greek geometrical analysis: A new interpretation through the ‘givens’-terminology, Bollettino di Storia delle Scienze Matematiche, 26 (2006), p. 33–56. Zbl1202.01021
24. [Freguglia 1988] Freguglia ( Paolo) – Ars analytica. Matematica e methodus nella seconda metà del Cinquecento, Busto Arsizio: Bramante editrice, 1988.
25. [Freguglia 1999] Freguglia ( Paolo) – La geometria fra tradizione e innovazione ..., Torino: Bollati Boringhieri, 1999. MR2218331
26. [Freguglia 2005] Freguglia ( Paolo) – L’interprétation de l’œuvre de Diophante: les Zeteticorum libri quinque, in Barbin (Évelyne) & Boyé (Anne), eds., François Viète un mathématicien français de la Renaissance, Paris: Vuibert, 2005, p. 75–86. MR1893131
27. [Freguglia forthcoming] Freguglia ( Paolo) – Viète reader of Diophantus, Bollettino di Storia delle Scienze Matematiche, forthcoming. Zbl1202.01035
28. [Gardies 2001] Gardies ( Jean-Louis) – Qu’est-ce que et pourquoi l’analyse? Essai de définition, Paris: Vrin, 2001. Zbl0999.00006MR1863960
29. [Ghetaldi 1607] Ghetaldi ( Marino) – Variorum problematum collectio, Venice: V. Fiorina, 1607.
30. [Ghetaldi 1630] Ghetaldi ( Marino) – De resolutione et compositione mathematica libri quinque opus posthumus, Romae: Ex Typographia Reuerendæ Cameræ Apostolicæ, 1630.
31. [Giusti 1992] Giusti ( Enrico) – Algebra and Geometry in Bombelli and Viète, Bollettino di Storia delle Scienze Matematiche, 12 (1992), p. 303–328. Zbl0784.01006MR1238362
32. [Hankel 1874] Hankel (Hermann) – Zur Geschichte der Mathematik in Alterthum und Mittelalter, Leipzig: B. G. Teubner, 1874. JFM06.0001.01
33. [Heath 1921] Heath ( Tomas L.) – A History of Greek Mathematics, Oxford: Clarendon Press, 1921; 2 vol. Zbl0001.11301JFM48.0046.01
34. [Heiberg 1903] Heiberg ( Johan L.) – Paralipomena zu Euklid, Hermes, 38 (1903), p. 46–74, 161–201, 321–356.
35. [Hintikka & Remes 1974] Hintikka ( Jakko) & Remes ( U.) – The Method of Analysis. Its Geometrical Origin and Its General Significance, Dordrecht: Reidel, 1974. Zbl0344.01002MR505178
36. [Hintikka & Remes 1976] Hintikka ( Jakko) & Remes ( U.) – Ancient Geometrical Analysis and Modern Logic, in Cohen (R. S.) & al., eds., Essays in Memory of Imre Lakatos, Dordrecht: Reidel, 1976, p. 253–276. Zbl0354.02003
37. [Khayyām 1851] Khayyām ( Umar al) – L’algèbre d’Omar al-Khayyāmī, publiée, traduite et accompagnée d’extraits de manuscrits inédits par F. Woepcke, Paris: Duprat, 1851.
38. [Khwārizmi 1831] Khwārizmi ( Mohammed ibn Musa al) – The algebra of Mohammed ben Musa, edited and translated by F.Rosen, London: printed for the Oriental Translation Fund. and sold by J. Murray, 1831.
39. [Klein 1934-1936] Klein ( Jacob) – Die griechische Logistik und die Entstehung der Algebra, Quellen und Studien zur Geschichte der Mathematik, Astronomie und Physik; Abteilung B : Studien, 3 (1934-1936), p. n. 1 (1934), 18–105 and n. 3 (1936), 122–235; english (slightly amended) translation by E.Brann: Greek Mathematical Thought and the Origin of Algebra, MIT Press, Cambridge (Mass), 1968 (I refer to this translation). Zbl0014.04902MR472317
40. [Knorr 1986] Knorr ( Wilbur) – The Ancient Tradition of Geometric Problems, Boston, Basel, Stuttgart: Birkhäuser, 1986. Zbl0588.01002MR884893
41. [Luckey 1941] Luckey ( Paul) – Tābit b. Qurra über den geometrischen Richtigkeitsnachweis der Auflösung der quadratischen Gleichungen, Berichte über die Verhandlungen der Sächsischen Akademie der Wissenschaften zu Leipzig. Mathematisch-physikalische Klasse, 93 (1941), p. 93–114. Zbl0063.03671MR31430JFM68.0008.03
42. [Mäempää 1997] Mäempää ( Petrü) – From Backward Reduction to Configurational Analysis, in [Otte & Panza 1997, pp. 201–226], 1997. MR1800646
43. [Mahoney 1968-1969] Mahoney ( Michael S.) – Another Look at Greek Geometrical Analysis, Archive for History of Exact Sciences, 5 (1968-1969), p. 318–348. Zbl0175.25402MR1554119
44. [Netz 1999a] Netz ( Reviel) – The Shaping of Deduction in Greek Mathematics. A Study in Cognitive History, Cambridge, New York, Melbourne: Cambridge University Press, 1999. Zbl1025.01002MR1683176
45. [Netz 1999b] Netz ( Reviel) – Archimedes Transformed: The case of a Result Stating a Maximum for a Cubic Equation, Archive for History of Exact Sciences, 54 (1999), p. 1–47. Zbl0928.01004MR1697182
46. [Netz 2000] Netz ( Reviel) – Why Did Greek Mathematicians publish Their Analyses?, in Suppes (P.), Moravcsik (J. M.) & Mendell (H.), eds., Ancient and Medieval Traditions in the Exact Sciences. Essays in Memory of Wilbur Knorr, Stanford: CSLI Pubblications, 2000, p. 139–157. Zbl0999.01002MR1827654
47. [Netz 2004] Netz ( Reviel) – The Transformation of Mathematics in the Early Mediterranean World: From Problems to Equations, Cambridge, New York, etc.: Cambridge University Press, 2004. Zbl1106.01004MR2072579
48. [Neugebauer 1938] Neugebauer ( Otto) – Über eine Methode zur Distanzbestimmung Alexandria-Rom bei Heron, Kongelige Danske Videnskabernes selskabs Skriften, 26 (1938), p. 21–24. Zbl0019.10001JFM64.0010.03
49. [Otte & Panza 1997] Otte ( Michael) & Panza ( Marco), eds. – Analysis and Synthesis in Mathematics. History and Philosophy, by Otte (Michael) & Panza (Marco), Dordrecht: Kluwer A. P., 1997. MR1800638
50. [Pacioli 1494] Pacioli ( Luca) – Summa de Arithmetica, Geometria, Proportioni et Proportionalità, Venezia: Paganino de’ Paganini, 1494.
51. [Panza 1997a] Panza ( Marco) – Mathematics Acts of Reasoning as Synthetic a priori, in [Otte & Panza 1997, pp. 261–326], 1997. MR1800650
52. [Panza 1997b] Panza ( Marco) – Classical Sources for the Concepts of Analysis and Synthesis, in [Otte & Panza 1997, pp. 365–414], 1997. MR1800652
53. [Panza 2005] Panza ( Marco) – Newton et les origines de l’analyse: 1664-1666, Paris: Blanchard, 2005. Zbl1080.01004MR2153198
54. [Panza forthcoming] Panza ( Marco) – The role of algebraic inferences in Na‘īm ibn Mūsā’s Collection of geometrical propositions, forthcoming. Zbl1169.01005
55. [Pappus 1588] Pappus ( of Alexandria) – Pappi Alexandrini MathematicaeCollectiones à Federico Commandino Urbinate in Latinum Conversæ, et commentariis illustratæ, Pisauri: Apud H. Concordiam, 1588.
56. [Pappus 1876-1878] Pappus ( of Alexandria) – Pappi Alexandrini Collectionis ..., edited with Latin translation and commentary by F. Hultsch, Berolini: Weidmann, 1876-1878; 3 vols.
57. [Pappus 1986] Pappus ( of Alexandria) – Book 7 of the Collection, translation and Commentary by A.Jones. 2 vols., Leipzig: Springer, 1986. Zbl0588.01014MR816533
58. [Ramus 1560] Ramus ( Petrus) – Algebra, Parisiis: apud A. Wechelum, 1560.
59. [Rashed 1984] Rashed ( Roshdi) – Entre arithmétique et algèbre. Recherches sur l’histoire des mathématiques arabes, Paris: Les Belles Lettres, 1984. Zbl0944.01019MR791215
60. [Rashed 1993] Rashed ( Roshdi) – Géométrie et dioptrique au xe siècle : Ibn Sahl, al-Qūhī and Ibn al-Haytham, Paris: Les Belles Lettres, 1993. Zbl0946.01003MR1731497
61. [Rashed 2003] Rashed ( Roshdi) – Al-Qūhī et al-Sijzī : sur le compas parfait et le tracé continu des sections coniques, Arabic Sciences and Philosophy, 13 (2003), p. 9–43. Zbl1063.01006MR1971782
62. [Rashed 2004] Rashed ( Roshdi) – Œuvre mathématique d’al-Sijzī. Volume I, Géométrie des coniques et théorie des nombres au xe siècle, Louvain, Paris: Peeters, 2004. Zbl1208.01009MR2264417
63. [Rashed & Houzel 2004] Rashed ( Roshdi) & Houzel ( Christian) – Recherche et enseignement des mathématiques au ixe siècle. Le recueil de propositions géométriques de Na‘īm ibn Mūsā, Louvain, Paris: Peeters, 2004. Zbl1062.01007MR2142636
64. [Rashed & Vahabzadeh 1999] Rashed ( Roshdi) & Vahabzadeh ( B.) – Al-Khayyām mathématicien, Paris: Blanchard, 1999.
65. [Ritter 1868] Ritter ( Frédéric) – Introduction à l’art analytique par François Viète. Traduit par M. F. Ritter, Bullettino di bibliografia e di storia delle scienze matematiche e fisiche [Bullettino Boncompagni], 1 (1868), p. 223–276. JFM01.0009.01
66. [Ritter 1895] Ritter ( Frédéric) – François Viète, inventeur de l’algèbre moderne, 1540–1603. Essai sur sa vie et son œuvre, La Revue occidentale philosophique, sociale et politique, 2e série, 10 (1895), p. 234–274 and 354–415. JFM24.0008.03
67. [Tartaglia 1556] Tartaglia ( Niccolò) – La prima parte del General Trattato di numeri et misure, Vinegia: C. Troiano dei Navò, 1556.
68. [Thomas 1957] Thomas ( Ivar) – Selections Illustrating the History of Greek Mathematics, Cambridge (Mass.): Harvard Univ. Press, 1957. Zbl0045.14506JFM65.1079.01
69. [Timmermans 1995] Timmermans ( Benoît) – La résolution des problèmes de Descartes à Kant, Paris: PUF, 1995.
70. [Tūsī 1986] Tūsī ( Sharif al-Dīn al) – Œuvres mathématiques. Algèbre et Géométrie au xiie siècle, texte établi et traduit par R. Rashed. 2 vols., Paris: Les Belles Lettres, 1986.
71. [Vasset 1630] Vasset ( A.) – L’algèbre nouvelle de Mr. Viète ... trad. en françois par A. Vasset, Paris: chez Pierre Rocolet, 1630.
72. [Vaulézard 1630a] Vaulézard ( Jean-Louis) – Les cinq livres des zététiques de François Viette mis en françois, commentez et augmentez des exemples .... Par I.-L. Sieur de Vav-Lezard ..., Paris: J. Jacquin, 1630; new edition: La nouvelle algèbre de M. Viète, Fayard, Paris, 1986, 67-267.
73. [Vaulézard 1630b] Vaulézard ( Jean-Louis) – Introduction en l’art analytic, ou Nouvelle algèbre ..., traduict en nostre langue et commenté et illustré d’exemples par I.-L. Sieur de Vav-Lezard ..., Paris: J. Jacquin, 1630; new edition : La nouvelle algèbre de M. Viète, Fayard, Paris, 1986, 7-66.
74. [Viète 1591a] Viète ( François) – In artem analiticem isagoge: seorsim excussa ab Opere restitutae mathematicae analyseos, seu Algebra nova, Turonis: apud I. Mettayer, 1591; republished in [Viète 1646, sheets 5v.-6r. (dedicatory letter to princess Catherine de Parthenay) and 1-12 (In artem analiticem isagoge)]. Both the Isagoge and the dedicatory letter to princess Catherine de Parthenay are translated into English by J. W. Smith in [Klein 1934-1936, pp. 313-353] and in French in [Ritter 1868, pp. 225-244]. The Isagoge is translated into English in [Viète 1983, pp. 11-32] and into French in [Vaulézard 1630b] and in [Vasset 1630, pp. 1-36].
75. [Viète 1591b] Viète ( François) – Zeteticorum libri quinque..., Turonis: apud I. Mettayer, 1591.
76. [Viète 1591c] Viète ( François) – Effectionum geometricarum Canonica Recensio, Without publisher [probably I. Metteyer, Turonis], 1591; without date [probably between 1591 and 1593. In [Viète 1646, pp. 229–239]. English translation in [Viète 1983, pp.371–387].
77. [Viète 1593a] Viète ( François) – Supplementum geometricae ..., Turonis: apud I. Mettayer, 1593; in [Viète 1646, pp. 240-257]. English translation in [Viète 1983, pp. 388-417].
78. [Viète 1593b] Viète ( François) – Variorum de rebus mathematicis responsorum liber VIII ..., Imonis, apud I. Mettayer, 1593; in [Viète 1646, pp. 347-435].
79. [Viète 1600] Viète ( François) – De numerosa potestatum ad exegesim resolutione ..., Parisiis: D. Le Clerc, 1600; in [Viète 1646, pp. 162-228]. English translation in [Viète 1983, pp. 311-370].
80. [Viète 1615a] Viète ( François) – De aequationum recognitione et emendatione tractatus duo ..., Parisiis: Ex typographia Ioannis Laqvehay, 1615; in [Viète 1646, pp. 82–161]. English translation in [Viète 1983, pp. 159-310].
81. [Viète 1615b] Viète ( François) – Ad angularium sectionum analyticen theoremata ... a Francisco Vieta ... primum excogitata, at absque ulla demonstratione ad nos transmissa, jam tandem demonstrationibus confirmata, opera et studio Alexandri Andersoni ..., Parisiis: apud O. de Varennes, 1615; in [Viète 1646, pp. 286-304]. English translation in [Viète 1983, pp. 418-450].
82. [Viète 1631] Viète ( François) – Ad logisticem speciosam notæ priores, Parisiis: G. Baundry, 1631; in [Viète 1646, pp. 13-41]. French Translation in [Ritter 1868, pp. 245-276]. English translation in [Viète 1983, pp. 33-82].
83. [Viète 1646] Viète ( François) – Francisci Vietæ Opera Mathematica, In unum Volumen congesta, ac recognita, Operâ atque studio Francisci à Schooten Leydensis [...], Lugduni Batavorum: B. & A. Elzevirorum, 1646.
84. [Viète 1983] Viète ( François) – The analytic art. Nine studies in algebra, geometry and trigonometry from the Opus Restitutæ Mathematicæ Analyseos, seu algebrâ novâ, Kent (Ohio): The Kent State Univ. Press, 1983. Zbl0558.01041MR731262
85. [Woepcke 1874] Woepcke ( Franz) – Trois traités arabes sur le compas parfait, Notices et extraits des manuscrits de la Bibliothèque Impériale et autres bibliothèques, 22 (1874), p. 9–43; réédité dans [Woepcke 1986, vol. II, pp.560–734].
86. [Woepcke 1986] Woepcke ( Franz) – Études sur les mathématiques arabo-islamiques, Frankfurt am Main: Inst. für Geschichte der Arabisch-Islamischen Wissenschaften an der Johann Wolfgang Goethe-Universität, 1986; 2 vols. Zbl0649.01035MR917734

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