Abstract
In this essay, I will scrutinize the differences between Galileo's and Huygens's demonstrations of free fall, which can be found respectively in the Discorsi and the Horologium, from a mathematical, representational and methodological perspective. I argue that more can be learnt from such an analysis than the thesis that Huygens re-styled Galilean mechanics which is a communis opinio. I shall argue that the differences in their approach on free fall highlight a significantly different mathematical and methodological outlook.
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