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

✍ Scribed by Giovanni Ferraro

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
132 KB
Volume
27
Category
Article
ISSN
0315-0860

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✦ Synopsis

La nozione euleriana di funzione presenta un duplice aspetto: essa era, a un tempo, relazione funzionale tra quantitΓ  e formula composta da simboli operazionali, da costanti, e da variabili. Queste ultime erano concepite come universali e pertanto godenti di particolari proprietΓ . Anche se il calcolo di Euler era basato sulla manipolazione delle formule, egli non esitΓ² a ricorrere alle relazioni funzionali se necessario. Inoltre le relazioni funzionali erano essenziali per la costruzione o definizione delle formule analitiche e per le applicazioni dei risultati. Ovviamente un tale modo di intendere le funzioni provocΓ² ambiguitΓ  tra l'aspetto intuitivo, geometrico, o empirico dei concetti e la loro rappresentazione simbolica in analisi. C 2000 Academic Press 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.

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