Functions, Functional Relations, and the Laws of Continuity in Euler

Abstract

Eulerian functions had two aspects: they were both functional relations between quantities and formulas composed of constants, variables, and operational symbols. The latter were regarded as universal and possessed extremely special properties. Even though Eulerian calculus was based upon the manipulation of formulas, mathematicians did not hesitate to use functional relations when it was necessary. Besides, functional relations were essential to the construction or definition of analytic formulas and application of the results of calculus. This concept of function led to ambiguity between the intuitive, geometrical, or empirical nature of concepts and their symbolic representation in analysis. © 2000 Academic Press.