Page:Mathematical collections and translations, in two tomes - Salusbury (1661).djvu/223

 may have erred in rehearsing his Argument, and to avoid running into the same mistakes for the future, I could wish I had his Book; and if you had any body to send for it, I would take it for a great favour.

You shall not want a Lacquey that will runne for it with all speed: and he shall do it presently, without losing any time; in the mean time Salviatus may please to oblige us with his computation.

If he go, he shall finde it lie open upon my Desk, together with that of the other Author, who also argueth against Copernicus.

We will make him bring that also for the more certainty: and in the interim Salviatus shall make his calculation: I have dispatch't away a messenger.

Above all things it must be considered, that the motion of descending grave bodies is not uniform, but departing from rest they go continually accelerating: An effect known and observed by all men, unlesse it be by the forementioned modern Authour, who not speaking of acceleration, maketh it even and uniforme. But this general notion is of no avail, if it be not known according to what proportion this increase of velocity is made; a conclusion that hath been until our times unknown to all Philosophers; and was first found out & demonstrated by the * Academick, our common friend, who in some of his * writings not yet published, but in familiarity shewn to me, and some others of his acquaintance he proveth, how that the acceleration of the right motion of grave bodies, is made according to the numbers uneven beginning ab unitate, that is, any number of equal times being assigned, if in the first time the moveable departing from rest shall have passed such a certain space, as for example, an ell, in the second time it shall have passed three ells, in the third five, in the fourth seven, and so progressively, according to the following odd numbers; which in short is the same, as if I should say, that the spaces passed by the moveable departing from its rest, are unto each other in proportion double to the proportion of the times, in which those spaces are measured; or we will say, that the spaces passed are to each other, as the squares of their times.

This is truly admirable: and do you say that there is a Mathematical demonstration for it?

Yes, purely Mathematical; and not onely for this, but for many other very admirable passions, pertaining to natural motions, and to projects also, all invented, and demonstrated by Our Friend, and I have seen and considered them all to my very great content and admiration, seeing a new compleat Doctrine to spring up touching a subject, upon which have been written hundreds of