On the Acceleration of Falling Bodies

...half is not valid, lest the ratio of accelerated motion not be perfectly understood. The question here again is not whether the velocity through the second part is precisely double the velocity through the first: but whether that follows (as well as other absurdities) from the Reverend Father's original: "R. P." referring to Marin Mersenne principles. The Reverend Father avoids the challenge of calculations, lest the flaws become more clearly evident, especially the objection that a third and a fourth part do not compose a whole; nor likewise the fifth, sixth, seventh, and eighth parts. With a useless effort, he tries to excuse the double ratio as the only appropriate one, for the reason that it also overturns itself whenever the assumed times are greater or smaller than what is given, even if those times are equal to each other: since these also ought to correspond to the spaces in the same ratio: which, however, does not happen: as is shown in the example brought by the Reverend Father concerning the fall of a ball from the Moon. From page 191 to 208.

TO ARTICLES 43. 44. Regarding the time in which he contends an iron ball would fall from the Moon to the Earth.

Nothing seems necessary to be added here to those things which were objected: since the Reverend Father admits that the rapid speed, which he had previously asserted, cannot be so insane that the ball would traverse that space in not even two full minutes: although he seeks to soften the matter, saying that nature indeed requires it, but the condition of the medium medium: the substance through which an object moves, such as air or water, which creates resistance stands in the way. From page 208 to 209.

TO ARTICLES 45. 46. 47. Regarding a certain correction to be made about the physical cause of the accelerated motion of weights.

What the Reverend Father in his Vindications original: "Vindicÿs," likely referring to a defensive text or section written by Mersenne regarding Article 40 about Physics...