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