Theory of Conics, Geometrical Constructions and Practical Geometry: A History of Arabic Sciences and Mathematics Volume 3, provides a unique primary source on the history and philosophy of mathematics and science from the mediaeval Arab world. The present text is complemented by two preceding volumes of A History of Arabic Sciences and Mathematics, which focused on founding figures and commentators in the ninth and tenth centuries, and the historical and epistemological development of ‘infinitesimal mathematics’ as it became clearly articulated in the oeuvre of Ibn al-Haytham.
This volume examines the increasing tendency, after the ninth century, to explain mathematical problems inherited from Greek times using the theory of conics. Roshdi Rashed argues that Ibn al-Haytham completes the transformation of this ‘area of activity,’ into a part of geometry concerned with geometrical constructions, dealing not only with the metrical properties of conic sections but with ways of drawing them and properties of their position and shape.
Including extensive commentary from one of world’s foremost authorities on the subject, this book contributes a more informed and balanced understanding of the internal currents of the history of mathematics and the exact sciences in Islam, and of its adaptive interpretation and assimilation in the European context. This fundamental text will appeal to historians of ideas, epistemologists and mathematicians at the most advanced levels of research.
Introduction: Conic sections and geometrical constructions Chapter 1: Theory of conics and geometrical constructions: 'completion of the conics' Chapter 2:Correcting the Bana Masa's Lemma for Apollonius' conics Chapter 3: Problems of geometrical construction Chapter 4: Practical Geometry: Measurement Appendix 1: A Research Tradition: the regular heptagon Appendix 2: Sinan ibn Al-Fati and Al-Qabisi:Optical Mensuration Supplementary notes Bibliography Indexes