Remarques sur l'Histoire du Texte des ÉlÉments d'Euclide

Rommevaux, Sabine; Djebbar, Ahmed; Vitrac, Bernard

doi:10.1007/s004070000027

Cited by 39 publications

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“…sometimes corresponding almost word for word (e.g., V-12 and VII-12), does not necessarily imply that Book V was modeled after Book VII, because the coincidence may well be the result of later editorial work. Thus the arithmetic books are by no means a simple residue of the mathematics before the discovery of incommensurability (Vitrac 1990(Vitrac -2001. Thus, even if one admits the existence of "commensurable definition" of proportion in early development, its level of sophistication cannot be retrieved from the arithmetic books of Euclid.…”

Section: Testimonymentioning

confidence: 99%

“…Another caveat is that the Greek text of the Elements that we have now is considerably different from the original. Relative credibility of Arabo-Latin tradition, newly advocated by Knorr (1996) for Book XII, then by Rommevaux, Djebbar, and Vitrac (2001) for Book X, has turned out to be the case also for Book V by Acerbi (2003). Though I hope that inauthenticity of some parts of the Greek text would not essentially affect my arguments, one should now be careful of any argument that depends heavily on some small piece of text in the Elements.…”

Section: Book V Of the Elements: Separation From Book Vimentioning

confidence: 99%

“…20(Euclid [1925(Euclid [ ] 1956. I use the numbering in Heiberg's edition, which is followed byVitrac (1990Vitrac ( -2001.4 Though our examination is limited to Becker 1933, there are a lot of studies inspired by this article, among whichFowler (1999) is the most extensive and original. But see also Unguru's critical review(Unguru 2002).5 English translations of the Aristotelian passage are taken from Aristotle 1984.…”

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Phantom Theories of pre-Eudoxean Proportion

Saito

2003

SIC

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This paper proposes an alternative view to Becker's reconstruction of pre-Eudoxean theory of proportion. No extant document explicitly demonstrates the alleged alternation of theories of proportion before Book V of the Elements. Books V and VI of the Elements are not so complete as a theory of proportion in the abstract, and can be interpreted better as a collection of propositions useful in geometry. It follows then that older theories, if they existed at all, must have been less complete. Prevailing interest in geometry on the part of Greek mathematicians is also visible in some expressions in Book VI for specific ratio and proportion used only in definite geometric context. It is therefore more fruitful to consider the "theory" of proportion before Eudoxus as an aggregate of techniques about proportion that are useful in geometry, rather than as the result of a conscious effort to build a logically consistent set of propositions based on a definition.

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Section: Testimonymentioning

confidence: 99%

Section: Book V Of the Elements: Separation From Book Vimentioning

confidence: 99%

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confidence: 99%

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Phantom Theories of pre-Eudoxean Proportion

Saito

2003

SIC

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“…), il semble avoir perdu de vue l'origine eutocienne du texte grec qui nous est parvenu. 70 V. [Rommevaux, S., Djebbar, A., Vitrac, B., 2001]. 71 Dans ce qui suit j'utilise l'abréviation [Gérard Cr., Busard, 1984].…”

Section: B Les Arguments Aristotéliciens De Style Mathématiqueunclassified

“…45-47. 123 V. par exemple[Rommevaux, S., Djebbar, A., Vitrac, B., 2001], en particulier pp. 254-255 et p. 278.…”

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Note Textuelle sur un (Problème de) Lieu Géométrique dans les Météorologiques d'Aristote (III. 5, 375 b 16 - 376 b 22)

Vitrac¹

2002

Archive for History of Exact Sciences

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7 C'est bien entendu le cas si le rapport donné est le rapport identique; les deux droites égales se brisent en un point situé sur la médiatrice du segment qui joint les deux points donnés. Ce cas de figure est exclu dans la citation d'Eutocius puisqu'il suppose deux droites données inégales. 8 V. [Papp., Coll. math.], p. 666, l. 15-19 : « ej a; n aj po; duv o dedomev nwn shmeiv wn euj qei' ai klasqw' sin, kai; h\ / ta; aj p∆ auj tw' n doqev nti cwriv w/ diafev ronta, to; shmei' on a{ yetai qev sei dedomev nh" euj qeiv a": ej a; n de; w\ sin ej n lov gw/ doqev nti, h[ toi euj qeiv a" h] perifereiv a" ». Traduction [Ver Eecke, 1982], pp. 498-499, légèrement modifiée. 9 Pour la commodité des renvois le texte du chapitre III. 5 est divisé en assertions numérotées dans Merker, pp. 00-00. J'utiliserai le même système. 10 [Tannery, MSc, 1929], p. 57 : « En fait, l'interpolateur montre comment, si le rapport MH : MK est donné avec les points H et K, on peut construire une circonférence dont les points soient tels que le rapport de leurs distances à H et K soit égal au rapport donné; sa démonstration présente la plus grande analogie avec la partie correspondante du théorème d'Apollonius sur le même objet, tel qu'Eutocius l'a extrait des Lieux plans du géomètre de Perge et inséré dans son commentaire sur les Coniques (…) Au contraire, l'autre partie du même théorème-à savoir que, si un point M est tel que ses distances à H et K soient dans le rapport donné, ce point sera sur la circonférence construite,-n'est pas démontrée par l'interpolateur ».

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Research on Ancient Greek Mathematical Sciences, 1998-2012

Sidoli¹

2013

From Alexandria, Through Baghdad

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Remarques sur l'Histoire du Texte des ÉlÉments d'Euclide

Cited by 39 publications

References 9 publications

Phantom Theories of pre-Eudoxean Proportion

Phantom Theories of pre-Eudoxean Proportion

Note Textuelle sur un (Problème de) Lieu Géométrique dans les Météorologiques d'Aristote (III. 5, 375 b 16 - 376 b 22)

Research on Ancient Greek Mathematical Sciences, 1998-2012

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