 In his Enumeration of the Sciences (ʾIḥṣāʾ al-ʿulūm), al-Fārābī puts forward a more detailed discussion of the ontology of mathematics. He distinguishes applied/practical (ʿamalī) mathematics from pure/theoretical (naẓarī) mathematics. The objects of applied arithmetic are numbers as they are associated with sensible things. Applied arithmetic considers the number of sensible things existing in the material world. By contrast, pure arithmetic considers an absolute conception of number and plurality. It studies numbers that are abstracted from all the numbered things in the sensible world. Similarly, applied geometry considers the geometrical properties of specific physical objects, whereas pure geometry deals with geometrical shapes regardless of whether or not they are attached to specific physical objects (al-Fārābi [Enum]: chap. 3; Endress 2003: 139–40).