III. -- Mathematics.

48. Object of Mathematics. -- While metaphysics deals with what is immaterial either by abstraction or of its nature, mathematics deals with extension in the abstract, and with the relations this gives rise to. It passes over all corporeal attributes in so far as these are subject to change, and deals with aspects that are in a sense immovable, aspects isolated by mental abstraction from the corporeal substance whose permanent and inseparable attributes they are. Besides pure mathematics -- arithmetic and geometry -- Aristotle also mentions applications of mathematics to the practical arts, such as surveying, and to the natural sciences, optics, mechanics, harmonics, astrology. His mathematical works are lost.^{1}

Descending another step in the scale of abstraction, we find ourselves in the domain of physics.

{1} Cf. BOUTROUX, op. cit., p. 146.