OF THE LETTERS

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determines by what amount of time the second part and each of the first halves are individually traversed. He therefore challenges others to test the matter in a tower two hundred feet high, even though he himself seemed more likely than others to have conducted the experiment. He does not seem to sufficiently refute Galileo's determination, which was based on his own observations, while he says only that it is to be feared that, since Galileo erred greatly in other things, he might have been deluded here as well. Indeed, it has neither been shown that he erred in other matters, nor does he have anything here that is inconsistent with experience. This is especially true of that saying: if any two spaces are taken from the beginning of the motion, their times will be to each other as one of them is to the mean proportional space In geometry, the mean proportional between two values is the square root of their product. Galileo used this to show that time increases as the square root of the distance. between them. According to this rule, it is easy to determine specifically in what time both the second part and the two first halves are traversed. The Reverend Father Pierre Cazré uses excuses and delays regarding the physical cause, about which the title itself seemed to offer some hope. Concerning this cause, an error was admitted in the Letters on Impressed Motion original: "Epistolis de Motu impresso," a reference to Gassendi's 1642 work where he discussed how motion is maintained in a body: in explaining it, the degrees of velocity were made equal to the distances; and the intercepted triangles, mentioned above, were taken not only for distances but also for degrees. For these, the bases of the triangles should rather have been taken.

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By passing over those things which the Reverend Father exaggerates in a certain summary original: "anacephalæosi," a Greek-derived term for a recapitulation or summary of an argument; not forgetting also how much he lamented that the author had placed faith in Galileo’s principles; and this was not without his usual sign of goodwill.