ABSTRACT
CHAPTER I
THEORY OF CONICS AND GEOMETRICAL CONSTRUCTIONS: ‘COMPLETION OF THE CONICS’
1.1.1. Ibn al-Haytham and Apollonius’ Conics
The theory of conics – and this point is worth emphasizing – had never held such an important position before the ninth and tenth centuries. This new importance is not only on account of the properties of the curves, but also because they can they can be applied in areas not foreseen by the original mathematicians, specifically not by Archimedes and Apollonius. That is, the theory of conics has ceased to be simply a powerful instrument in the hands of geometers; it now offers algebraists a means of solving cubic equations.1 Ibn al-Haytham is no exception to the rule. As a geometer he investigates the geometrical properties of conics – as we may see, for example, in his treatise The Measurement of the Paraboloid. As a physicist he is concerned with reflection properties of some of the curves – we may think, for example, of his treatise Parabolic Burning Mirrors. He also uses conics to achieve success in problems of geometrical construction. In short, a glance at his works will show that conics and their properties run through them from beginning to end. So it is easy to understand his taking an interest in Apollonius’ treatise, the more so since – the works of his predecessors having been lost – Apollonius was the only authority. No other Greek mathematical work, apart from Euclid’s Elements, was so much consulted, studied and cited by Arabic mathematicians, among them Ibn alHaytham. Not only did he know the Conics down to the smallest details, but he even went so far as to transcribe the work, as we know from the copy in his handwriting that has survived down the centuries.2
