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A Programmatic Note: on two Types of Intertextuality

Reviel Netz (2005)

Revue d'histoire des mathématiques

The note addresses briefly some reactions to a previous article “Deuteronomic Texts: Late Antiquity and the History of Mathematics”. In particular it looks at the question: if indeed any text must depend on previous texts, what makes the dependency of commentary and commentary-like text so special to justify my emphasis on this form of writing ? A suggestion is developed, trying to define Deuteronomic texts through their precise semiotics of intertextuality: in general, it is argued, intertextuality...

An objective and practical method for describing and understanding ratios

D. H. Fowler (1993)

Mathématiques et Sciences Humaines

This article explores the use of the euclidian algorithm as a most useful way of handling ratios, especially when good rational approximations are required. Illustrations are taken from a discussion of the analysis of greek architecture by J.J Coulton. Although this is intended as a practical account, some discussions of theoretical aspects are included, and also of the relationship of this procedure to a new interpretation of early greek mathematics.

Archimédés [Book]

Bečvář, Jindřich, Bečvářová, Martina, Halas, Zdeněk, Bártlová, Tereza, Moravcová, Vlasta (2012)

Caustics in Greek antiquity

Alain Joets (2008)

Banach Center Publications

The word caustic was introduced by Tschirnhausen in 1686, in the Latin expression caustica curva. We show that the study of the optical caustics goes back well before, at least to the hellenistic period. We present a small Greek text, whose author is perhaps Geminus (1st cent. B.C.), describing an optical phenomenon called achilles. We show that the term achilles, which has appeared only once, to our knowledge, in the literature, means caustics by reflection. We complete the description of the achilles...

Comment définir la nature des textes mathématiques de l’Antiquité grecque tardive ? Proposition de réforme de la notion de ‘textes deutéronomiques’

Alain Bernard (2003)

Revue d'histoire des mathématiques

J’examine dans cet article la proposition faite par Reviel Netz de caractériser les textes mathématiques de l’Antiquité grecque tardive comme « deutéronomiques ». J’en critique tout d’abord d’importantes faiblesses. D’une part, elle s’appuie, tout en la réformant, sur l’idée d’une « décadence » qui serait propre à la période considérée. Or j’argumente que cette idée, même réformée, ne constitue ni un bon point de départ pour l’étude des travaux de cette époque, ni même une bonne description de ces...

It’s not that they couldn’t

Reviel Netz (2002)

Revue d'histoire des mathématiques

The article offers a critique of the notion of ‘concepts’ in the history of mathematics. Authors in the field sometimes assume an argument from conceptual impossibility: that certain authors could not do X because they did not have concept Y. The case of the divide between Greek and modern mathematics is discussed in detail, showing that the argument from conceptual impossibility is empirically as well as theoretically flawed. An alternative account of historical diversity is offered, based on self-sustaining...

Le rôle des diagrammes dans quelques traités de la «Petite astronomie»

Guy Le Meur (2012)

Revue d'histoire des mathématiques

Cet article porte sur les diagrammes de traités de la « Petite astronomie » . On entend sous ce nom un ensemble de traités anciens transmis par la tradition manuscrite grecque, dont la composition pourrait remonter aux environs du quatrième siècle de notre ère, à Alexandrie. Elle a pu servir d’introduction pédagogique à l’étude de l’Almageste de Ptolémée. Elle comprend, entre autres, des ouvrages d’Autolycos (vers 330 av. J.-C.), d’Euclide (vers 300 av. J.-C.) et de Théodose de Bithynie (vers 125...

Proposta di ricostruzione di un ragionamento incompleto nell’opera di Archimede Sulla sfera e sul cilindro (in occasione del ritrovamento di una dimostrazione nei manoscritti di Giacomo Bernoulli)

Clara Silvia Roero, Tullio Viola (1981)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

This paper discusses from a historical standpoint the incomplete reasoning of Book I proposition 9 of Archimedes' On the sphere and cylinder and gives a proof, which only uses means available to Archimedes himself. This paper also discusses some demonstrations which, through the centuries, have been proposed to solve this problem. One of these is the previously unpublished proof by Jakob I Bernoulli, which is here reported, recently discovered at the Universitätsbibliothek of Basel.

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