In this text, Durand rejects a common assumption undergirding much of the Latin medieval debate about the relation between the soul and its powers. According to this assumption, which we can call the uniformity assumption, all powers of the soul that bring forth vital operations, such as the intellect and sight, bear the same relation to the soul. Identity theorists maintained that all of these powers are identical to the soul, while distinction theorists held that all of these powers are distinct from the soul. Against this consensus, Durand argues that some powers of the soul are identical to the soul, while others are distinct from it. More precisely, he advocates an identity theory with respect to the vegetative powers but a distinction theory with regard to the sensory and rational powers. He motivates his identity view regarding the vegetative powers with the argument that these powers have substances as their effects and the premise that causes must be like their effects. To motivate his distinction theory regarding the sensory and rational powers, Durand does not draw on Aquinas’ Category Argument, which he thinks is unsound.

Important special functions and their properties are described. In particular, the exponential function and its connection to continuous compounding is discussed, together with the logarithm and trigonometrical functions. It is explained how one can interpret not just integer, but rational and then irrational powers of positive real numbers. The derivatives of exponential, logarithmic and trigonometrical functions are studied.