Functions, functional relations, and the laws of continuity in Euler

Eulerian functions had two aspects: they were both functional relations bet ween quantities and formulas composed of constants, variables, and operatio nal symbols. The latter were regarded as universal and possessed extremely special properties. Even though Eulerian calculus was based upon the: manip ulation of formulas, mathematicians did not hesitate to use functional rela tions when it was necessary. Besides, functional relations were essential t o the construction ol definition of analytic formulas and application of th e results of calculus. This concept of function led to ambiguity between th e intuitive, geometrical, or empirical nature of concepts and their symboli c representation in analysis. (C) 2000 Academic Press.