Studies on the problem of minimum and maximum in conic sections' traditions.: Apollonios of Perga and Serenos of Antinoeia

• Autores: Konstantinos Nikolantonakis
• Localización: The Circulation of Science and Technology: Proceedings of the 4th International Conference of the European Society for the History of Science. Barcelona, 18-20 November 2010 / coord. por Antoni M. Roca Rosell, 2012, ISBN 978-84-9965-108-8, págs. 272-280
• Idioma: inglés
• Texto completo no disponible (Saber más ...)
• Resumen

  • The treatise of Apollonios of Perga Conics has put its sign on the development of mathematical sciences in the Arabic world since the 9th century and Apollonios is the most referenced and studied mathematician after Euclid. The Arabic translation of the 7 books of the Conics has been done in Baghdad in the 9th century, after the demand of Banu Musa from Hilal ibn Hilal al-Himsi and has been controlled by Thabit Ibn Qurra. This translation has inaugurated a tradition, and has influenced the interest on solid problems –especially the trisection of an angle and the construction of a regular heptagone– the application of the conics on problems from other fields like the optics (burning mirrors and lenses), geometric resolution of the 3rd degree equations (works of AlKhayyam and Sharaf al-Din al-Tusi) or even the theory of astrolabes, sun clocks or the perfect compass. All these applications will lead to the reinvention of new properties on these curves – focus properties, study of asymptotes, local and harmonic properties. In the 5th book of the Conics which survived only in Arabic, Apollonios studies the problem of minimum and maximum. The treatise Section of a Cone of Serenos of Antinoeia (4th century A.C.) deals with the areas of triangular sections of right or scalene cones made by planes passing through the vertex and either through the axis or not through the axis, showing when the area of a certain triangle of a particular class is a maximum, under what conditions two triangles of a class may be equal in area.

    In the context of this paper we are going to present a comparative study of these two treatises and show the influence of the work of Apollonios on the level of some enunciations to the approach of Serenos.