Page:Mathematical collections and translations, in two tomes - Salusbury (1661).djvu/197

 them. From the things premised I gather that the project swiftly swinged round by the projicient, in its separating from it, doth retain an impetus of continuing its motion by the right line, which toucheth the circle described by the motion of the projicient in the point of separation, by which motion the project goeth continually receding from the centre of the circle described by the motion of the projicient.

You know then by this time the reason why grave bodies sticking to the rim of a wheele, swiftly moved, are extruded and thrown beyond the circumference to yet a farther distance from the centre.

I think I understand this very well; but this new knowledg rather increaseth than lesseneth my incredulity that the Earth can turn round with so great velocity, without extruding up into the sky, stones, animals, &c.

In the same manner that you have understood all this, you shall, nay you do understand the rest: and with recollecting your self, you may remember the same without the help of others: but that we may lose no time, I will help your memory therein. You do already know of your self, that the circular motion of the projicient impresseth on the project an impetus of moving (when they come to separate) by the right Tangent, the circle of the motion in the point of separation, and continuing along by the same the motion ever goeth receding farther and farther from the projicient: and you have said, that the project would continue to move along by that right line, if there were not by its proper weight an inclination of descent added unto it; from which the incurvation of the line of motion is derived. It seems moreover that you knew of your self, that this incurvation always bended towards the centre of the Earth, for thither do all grave bodies tend. Now I proceed a little farther, and ask you, whether the moveable after its separation, in continuing the right motion goeth always equally receding from the centre, or if you will, from the circumference of that circle, of which the precedent motion was a part; which is as much as to say, Whether a moveable, that forsaking the point of a Tangent, and moving along by the said Tangent, doth equally recede from the point of contact, and from the circumference of the circle?

No, Sir: for the Tangent near to the point of contact, recedeth very little from the circumference, wherewith it keepeth a very narrow angle, but in its going farther and farther off, the distance always encreaseth with a greater proportion; so that in a circle that should have v. g. ten yards of diameter, a point of the Tangent that was distant from the contact but two palms, would be three or four times as far distant from the circumference