On the Acceleration of Falling Bodies

ARTICLES XLIII. XLIV. Regarding the time in which he contends an iron ball would fall from the Moon to the Earth.

While Galileo, assuming there are 196,000 Italian miles original: "milliaria Italica," a unit of distance approximately 1.5 kilometers or 0.93 miles from the Moon to the center of the Earth, calculates from his observations and established ratio that an iron ball dropped from the Moon would cover that distance in 3 hours, 22 minutes, and 4 seconds, the Reverend Father Pierre Cazré concludes something else. Following his own progression in a continuously double ratio original: "ratione continuò dupla," a geometric progression where speed or distance doubles in each successive interval, he claims that same distance would be covered in not even two full minutes. This is truly a monstrous speed, and one which is refuted even by experience. It is established that a falling ball does not travel more than one mile of height in a single half-minute original: "semi-minuto," a period of 30 seconds. Even if we maintain acceleration in a double ratio, the ball could only cover two miles in the second half-minute, four in the third, and eight in the fourth. It is clear that the sum of these parts within two minutes cannot exceed fifteen miles.

How great a discrepancy lies between this number and 196,000 miles. Or rather, the discrepancy is even greater compared to the miles he claims are traversed in two full minutes, which he calculates as 1,677,721 1/2. And what a strange inconsistency this is: he requires that 6 and nearly a third miles be covered in the first half-minute; 403 and one-fifth in the second; 25,804 and four-fifths in the third; and 1,651,507 and one-fifth in the fourth. See pages 79 to 82.

ARTICLES XLV. XLVI. XLVII. Regarding the time to be determined by observation through the first parts; a few words on the physical cause, and on the error committed regarding it.

The Reverend Father indeed frankly admits that he has no means by which the time...