Abstract
During the collaboration of Beeckman and Descartes at Breda (1618-1619), they studied problems of mixed mathematics by so-called "physico-mathematica". In this paper I clarify the meaning of "physico-mathematica" for Beeckman especially in his musical theory. Beeckman considered the "physico-mathematica" as a way of giving the corpuscular interpretations both to the examples Descartes submitted to him (such as consonance and resonance) and to the problems of the musical theory (division of octave) which have been already demonstrated in the mathematical form by Descartes. This way of philosophizing depended on Beeckman's corpuscular theory of sound which he thought was a sequence of beats (ictus) of corpuscles of air. In those musical problems Beeckman acted as the "physico-mathematician" and Descartes as a traditional mixed mathematician.
