A preliminary survey on the emergence of an arithmetical theory of ratios

Abstract

This article considers competing traditions of theories of ratio and the process which led to the emergence of an arithmetical theory of ratio. Such a complex process, already began in the Ancient Greece, developed throughout the Middle Ages until the Renaissance and received contributions from the Latin and Arabic traditions culminating with the confluence of such traditions, and consequently with its acceleration during the Renaissance. In this context, it must be regarded the Latin translation from the Arabic of Euclid by Campanus of Novara in the thirteenth century, a singular contribution to the structural indefiniteness and to the tension in the history of theories of ratio, inasmuch as Campanus gave to definition 5 of book V concerning proportionality of ratios an arithmetical meaning inserting the concept “denominatio” for ratio not presented in the original Euclid. In theoretical music context, the division of the tone is also not to be overlooked insofar as it molded indirectly the conception of ratio throughout the history of the discussions involving the arithmetization of ratio.