On the Acceleration of Falling Bodies

OF THE LETTERS.

From page 41 to 53.

...and reach the ground at the same time: even though Aristotle elsewhere judges that the larger body falls more swiftly and arrives sooner.

ART. XXIX. XXX. XXXI. XXXII. XXXIII.

Concerning the Time in which the Reverend Father concludes that individual parts of the space will not be traversed.

From page 53 to 63.

The origin of the error original: "mali", literally "the evil" or "the misfortune" was that the Reverend Father the "Reverend Father" (R.P.) refers to Pierre Cazré accepted a false experiment (or one that did not exist at all) as true. He adopted that definition of uniformly accelerated motion original: "Motus æquabiliter accelerati" which is presented without any mention of time. However, it is impossible to understand speed original: "celeritatem", acceleration, or especially uniform acceleration without comparison to time. By assuming that velocities are acquired in proportion to the distances original: "spatia" traveled, it follows that the second equal space is traversed in half the time of the first. The third would be traversed in one-third the time, the fourth in one-quarter, and so on. This occurs because the time always exists as a submultiple a mathematical term meaning a factor that divides another exactly, here used to describe an inverse ratio to the increasing velocity. Various problems follow from this, specifically that acceleration would happen irregularly in a ratio greater than triple. Therefore, the Reverend Father shows from certain problems that it is impossible for spaces to be traversed in such times. Yet he argues this against his own interests, since such a traversal necessarily follows from his position that velocities relate to each other as distances.

ART. XXXIV. XXXV. XXXVI. XXXVII. XXXVIII.

Concerning the Time in which the Reverend Father concludes individual parts will be traversed.

Having divided the space of the fall into any number of equal parts,