OF THE SECOND LETTER.

ARTICLE I. The Occasion for Writing.

The Reverend Father Father Pierre Cazré, a Jesuit mathematician and critic of Galileo’s laws of fall, having seen the original draft of the previous Letter, did not disapprove of its publication, provided that another was added which he wrote immediately after. He titled this work the Vindication of a Physical Demonstration original: "Vindicias Physicæ Demonstrationis". Because the Reverend Father claims that in this work he reveals a truth previously unknown to the Author Gassendi refers to himself in the third person here, now illustrated with greater clarity and shown to be cleared of error; and because he complains elsewhere that things are frequently attributed to him which he neither said nor could be deduced from the principles he provided; it therefore seemed appropriate to publish the Vindication in such a way that an Exception A formal objection or counter-argument used to challenge a specific point is inserted. This is done to investigate how it is possible that the Author does not see the truth thus illustrated and vindicated, and to wash away that stain with which he felt himself spattered due to the repeated charge of false attribution.

ARTICLE II. III. IV. V. On the State of the Controversy.

Because the Reverend Father persists in holding that letter, against which the previous one was written, to be a Demonstration, it is therefore desirable that the State of the Controversy be made clearer. At the same time, the nature of this Demonstration should be made apparent. It is decided to extract it from the text of his entire Letter and, through analysis, reduce it to a hypothetical syllogism A logical argument formatted as an "if... then" statement, which might be of this kind:

If, in the accelerated motion of falling heavy bodies, the acquired velocities relate to each other as the distances traveled, it is necessary that the distances are traversed in equal times in a continuous double ratio A geometric progression where each value is twice the previous one, such as 1, 2, 4, 8:

But in the accelerated motion of falling heavy...