Long before Ibn al-Haytham, al-Færæbî had proposed a classification of sciences that could not be reduced to the classifications known before him.1 This classification was clearly intended to give an account of the knowledge of the period, to devise a coherent representation of it, and, above all, to explain the new relationships between disciplines. Speaking in terms of the quadrivium could not provide what was required. Perhaps that is why alFæræbî’s successors, among them even Avicenna, adopted this new classification.2 One of its distinguishing characteristics, as indeed of all the later classifications it inspired, is that it includes a complex grouping of several disciplines, whose designation is the significant term: ‘ilm al-Ìiyal (‘science of ingenious procedures’). We have here a complex of disciplines that, for the most part, belong among what would be known, much later, as the ‘mixed sciences’ or ‘mixed mathematics’, which are ‘mixed’ in the sense that in them mathematics is combined with elements that relate to physical matter. The concept underlying these disciplines is that they involve ‘knowledge’ (‘ilm) and ‘action’ (‘amal); that is ‘science’ and ‘art’, the categories being inclusive rather than exclusive. On one hand, it is possible to introduce the ‘rules of the art’ together with its instruments, when we are concerned with defining the specific subject under investigation; on the other hand, this body of knowledge can be applied in the study of objects that lie outside it. Thus if

knowledge aims at action, action must in turn be based on knowledge. Again in accord with this new representation, a body of knowledge can henceforth take on the status of a science without conforming to either the Aristotelian or the Euclidean model. This new relationship between knowledge and action, between science and art, removed the lines of demarkation that a certain kind of Aristotelianism had, at least in theory, established between the two, and conferred a recognized status on the application of mathematics and the sciences.