Page:Mathematical collections and translations, in two tomes - Salusbury (1661).djvu/162

 I believe that you very much deceive your self, and am certain, that experience will shew you the contrary, and that the ball being once arrived at the ground, will run together with the horse, not staying behind him, unless so far as the asperity and unevenness of the Earth shall hinder it. And the reason seems to me very manifest: for if you, standing still, throw the said ball along the ground, do you think it would not continue its motion even after you had delivered it out of your hand? and that for so much a greater space, by how much the superficies were more smooth, so that v. g. upon ice it would run a great way?

There is no doubt of it, if I give it impetus with my arm; but in the other case it is supposed, that he who is upon the horse, onely drops it out of his hand.

So I desire that it should be: but when you throw it with your arm, what other remaineth to the ball being once gone out of your hand, than the motion received from your arm, which motion being conserved in the boul, it doth continue to carry it forward? Now, what doth it import, that that impetus be conferred on the ball rather from the arm than from the horse? Whilst you were on horseback, did not your hand, and consequently the ball run as fast as the horse it self? Doubtless it did: therefore in onely opening of the hand, the ball departs with the motion already coceived, not from your arm, by your particular motion, but from the motion dependant on the said horse, which cometh to be communicated to you, to your arm, to your hand, and lastly to the ball. Nay, I will tell you farther, that if the rider upon his speed fling the ball with his arm to the part contrary to the course, it shall, after it is fallen to the ground, sometimes (albeit thrown to the contrary part) follow the course of the horse, and sometimes lie still on the ground; and shall onely move contrary to the said course, when the motion received from the arm, shall exceed that of the carrier in velocity. And it is a vanity, that of some, who say that a horseman is able to cast a javelin thorow the air, that way which the horse runs, and with the horse to follow and overtake the same; and lastly, to catch it again. It is, I say, a vanity, for that to make the project return into the hand, it is requisite to cast it upwards, in the same manner as if you stood still. For, let the carrier be never so swift, provided it be uniform, and the project not over-light, it shall always fall back again into the hand of the projicient, though never so high thrown.

By this Doctrine I come to know some Problems very curious upon this subject of projections; the first of which must seem very strange to Simplicius. And the Problem is this; I affirm it to be possible, that the ball being barely dropt or let fall, by one that any way runneth very swiftly, being arrived at the