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Article ID: CBB058221761

Apollonius de Perge, Serenus d'Antinoe, Thabit Ibn Qurra et les recherches sur les sections coniques et cylindriques (2013)

Nikolantonakis, Konstantinos (Author)

Bollettino di Storia delle Scienze Matematiche
Volume: 33
Issue: 1
Pages: 9-38

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In the context of this paper we are presenting a comparative study between definitions and propositions of Book I of "The Conics" of Apollonius of Perga (propositions 1-21), of the treatise "On the Section of a Cylinder" of Serenus of Antinoeia (propositions 1-19) and of the treatise "On the Section of a Cylinder and its lateral surface" of Thabit ibn Qurra (propositions 1-11). From this study we are deducing firstly the continuity of Apollonius' studies on conical sections into this treatise of Serenus and in the first part of the treatise of Thabit, and secondly that Serenus has animated a tradition with his works on cylindrical sections and has influenced Thabit. The originality of Serenus is based on the fact that he has transcribed properties from the cone to the cylinder and has developed his proper theory on cylindrical sections. Thabit has found in "Section of a Cylinder" of Serenus and "The Conics" of Apollonius a model for the elaboration of his theory on cylindrical sections. After the first group of propositions he has developed the study on geometrical transformations for the needs of his theory. From this point, we notice the divergence of the development between these three treatises because Thabit uses geometric projections and works on different kinds of problems.

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