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<title> SUMMARY </title>The classical definitions of ratio (otherwise: λγo&sigmav;, proportio, respect, reason) and proportion (otherwise: αναλoγία, rationes similes, rationes aequales, rationes eaedem, proportionalitas and also proportio, analogy, proportionality), defined respectively by the third and the fifth definitions of the V Book of Euclid's Elements (see I. L. Heiberg, Elementa, vol. II, pp. 2-3), were subjected to a rigorous examination in the Seventeenth century: Among the critics and revisers of those definitions, in this paper we deal with Giovanni Alfonso Borelli and Andre Tacquet (whose definition of «equal reasons» has inspired generations of mathematicians: see Appendixes). Borelli and Tacquet devised refined procedures to figure out the «equality of reasons» by approximation.

Affiliations: 1: Napoli Ricerca eseguita con il contributo del CNR. Il contenuto di questa memoria deriva dalla prosecuzione di una ricerca avviata in preparazione ad una relazione tenuta al convegno «Ratio. La teoria delle proporzioni dall'antichità all'Ottocento», svoltosi presso il CIRM (Centro Internazionale per la Ricerca Matematica), Trento, 9-13 Gennaio 1989. Nel licenziare questo lavoro, un doveroso ringraziamento va alla prof. Angela Carusone, del Liceo scientifico statale di Frattamaggiore, per l'assistenza fornitaci al fine di una più precisa interpretazione dei brani in lingua latina.


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