ABSTRACT
The historical development of the abstract portion of mathematical science has, since the time of Descartes, been for the most part determined by that of the concrete. The concrete portions of the science depend on the abstract, which are wholly independent of them. The chapter reviews the leading conceptions of the analysis. The business of concrete mathematics is to discover the equations that express the mathematical laws of the phenomenon under consideration; and these equations are the starting point of the calculus, which must obtain from them certain quantities by means of others. It is only by forming a true idea of an equation that political theorists can lay down the real line of separation between the concrete and the abstract part of mathematics. In order to establish the equations of phenomena, political theorists must conceive of their mathematical laws by the aid of functions composed of the few analytical elements.
