Page:Mathematical collections and translations, in two tomes - Salusbury (1661).djvu/227

 turn round, staying there above, and moving along with the diurnal conversion. Now I tell him, that that same ball falling from the concave unto the centre, will acquire a degree of velocity much more than double the velocity of the diurnal motion of the Lunar concave; and this I will make out by solid and not impertinent suppositions. You must know therefore that the grave body falling and acquiring all the way new velocity according to the proportion already mentioned, hath in any whatsoever place of the line of its motion such a degree of velocity, that if it should continue to move therewith, uniformly without farther encreasing it; in another time like to that of its descent, it would passe a space double to that passed in the line of the precedent motion of descent. And thus for example, if that ball in coming from the concave of the Moon to its centre hath spent three hours, 22 min. prim. and 4 seconds, I say, that being arrived at the centre, it shall find it self constituted in such a degree of velocity, that if with that, without farther encreasing it, it should continue to move uniformly, it would in other 3 hours, 22 min. prim. and 4 seconds, passe double that space, namely as much as the whole diameter of the Lunar Orb; and because from the Moons concave to the centre are 196000 miles, which the ball passeth in 3 hours 22 prim. min. and 4 seconds, therefore (according to what hath been said) the ball continuing to move with the velocity which it is found to have in its arrival at the centre, it would passe in other 3 hours 22 min. prim. and 4 seconds, a space double to that, namely 392000 miles; but the same continuing in the concave of the Moon, which is in circuit 1232000 miles, and moving therewith in a diurnal motion, it would make in the same time, that is in 3 hours 22 min. prim. and 4 seconds, 172880 miles, which are fewer by many than the half of the 392000 miles. You see then that the motion in the concave is not as the modern Author saith, that is, of a velocity impossible for the falling ball to partake of, &c.

The discourse would pass for current, and would give me full satisfaction, if that particular was but salved, ofroof the moving of the moveable by a double space to that passed in falling in another time equal to that of the descent, in case it doth continue to move uniformly with the greatest degree of velocity acquired in descending. A proposition which you also once before supposed as true, but never demonstrated.

This is one of the demonstrations of Our Friend, and you shall see it in due time; but for the present, I will with some conjectures (not teach you any thing that is new, but) remember you of a certain contrary opinion, and shew you, that it may haply so be. A bullet of lead hanging in a long and fine thread fastened to the