There is a widely acknowledged, albeit still imprecisely defined, connection between the ‘calculatory’ analyses of local motion developed within the fourteenth century ‘Merton School’ and Galileo Galilei's later treatment of natural motion. The present essay is intended to cast some light on the possible sources and significance of Galileo's putative familiarity with the medieval discussions through a study of the fortunes of the most typical representative of the School, Richard Swineshead. Particular attention is paid to the writings of such scholastic (...) philosophers of Galileo's day as Francisco Toledo, Francesco Piccolomini, Iacopo Zabarella, Francesco Buonamico and Scipione Chiaramonte. Somewhat unexpectedly, it emerges that such authors possessed only the most fragmentary and attenuated knowledge of Swineshead's ideas. The implications of this circumstance, especially insofar as it renders Galileo's familiarity with the Merton tradition even more problematical, are discussed briefly. (shrink)