ABSTRACT
IBN AL-HAYTHAM AND THE GEOMETRISATION OF PLACE
As we have seen, the emergence of geometrical transformations – the
operations as well as the transformed objects of geometry – spurred Ibn alHaytham into conceiving a new mathematical discipline: the discipline of the knowns. This discipline was designed to justify the operations, and to provide a basis for the existence of the objects by its introduction of motion. And the same is true of its method: the technique of analysis. In truth Euclid’s Common Notions, Postulates and Definitions seem no longer to be enough, being unsuitable for the new representation of the objects of geometrical knowledge that are envisaged. In the Elements, this object was simply the figure, without any consideration either of its place or, in general, of the space that contained it. From now on, figures are no longer the sole objects of geometry; moreover, a figure can move, undergo translation, dilatation, contraction, inversion and projection. Thus, the figure moves, and motion even comes into the way the object is conceived. For example, it is relevant to the concept of parallelism, and for the process of deriving figures by the transformation of other figures. So it is clear that it was no longer possible to think about the relationships between elements of a single figure, any more than about the relationships between figures and still less about the relationships used in finding these figures, without raising questions about the notion of spatial relationships itself. This is precisely what Ibn al-Haytham is doing in the treatise On Place.
