Page:Mathematical collections and translations, in two tomes - Salusbury (1661).djvu/181

 West, nor as you would have it, upon the Piece, but rather far distant towards the East. For according to your explanation, it would have two motions, the which would with one consent carry it thitherward, to wit, the common motion of the Earth, which carrieth the Piece and the ball from CA towards ED; and the fire which carrieth it by the inclined line BD, both motions towards the East, and therefore they are superiour to the motion of the Earth.

Not so, Sir. The motion which carrieth the ball towards the East, cometh all from the Earth, and the fire hath no part at all therein: the motion which mounteth the ball upwards, is wholly of fire, wherewith the Earth hath nothing to do. And that it is so, if you give not fire, the ball will never go out of the Piece, nor yet rise upwards a hairs breadth; as also if you make the Earth immoveable, and give fire, the ball without any inclination shall go perpendicularly upwards. The ball therefore having two motions, one upwards, and the other in gyration, of both which the transverse line BD is compounded, the impulse upward is wholly of fire, the circular cometh wholly from the Earth, and is equal to the Earths motion: and being equal to it, the ball maintaineth it self all the way directly over the mouth of the Piece, and at last falleth back into the same: and because it always observeth the erection of the Piece, it appeareth also continually over the head of him that is near the Piece, and therefore it appeareth to mount exactly perpendicular towards our Zenith, or vertical point.

I have yet one doubt more remaining, and it is, that in regard the motion of the ball is very swift in the Piece, it seems not possible, that in that moment of time the transposition of the Piece from CA to AD should confer such an inclination upon the transverse line CD, that by means thereof, the ball when it cometh afterwards into the air should be able to follow the course of the Earth.

You err upon many accounts; and first, the inclination of the transverse line CD, I believe it is much greater than you take it to be, for I verily think that the velocity of the Earths motion, not onely under the Equinoctial, but in our paralel also, is greater than that of the ball whilst it moveth in the Piece; so that the interval CE would be absolutely much bigger than the whole length of the Piece, and the inclination of the transverse line consequently bigger than half a right angle: but be the velocity of the Earth more, or be it less, in comparison of the velocity of the fire, this imports nothing; for if the velocity of the Earth be small, and consequently the inclination of the transverse line be little also; there is then also need but of little inclination to make the