Galileo's 1604 Fragment on Falling Bodies (Galileo Gleanings XVIII)

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Abstract
The first attempted derivation by Galileo of the law relating space and time in free fall that has survived is preserved on an otherwise unidentified sheet bound among his manuscripts preserved at Florence. It is undoubtedly closely associated with a letter from Galileo to Paolo Sarpi, dated 16 October 1604, which somehow found its way into the Seminary of Pisa, where it is still preserved. Those two documents, together with the letter from Sarpi to Galileo which seems to have inspired them, are translated in full below. Sarpi's letter, dated 9 October 1604, suggests that recent oral discussions of problems of motion had recently taken place between the two men. It reads as follows: “In sending you the enclosure, it occurs to me to propose to you a problem to resolve, and another that seems to me paradoxical.

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