Page:Mathematical collections and translations, in two tomes - Salusbury (1661).djvu/171

 Tower. And this is the cause why the right motion made along the side of the Tower apeareth to us more and more accelerate. It appeareth also, how by reason of the infinite acutenesse of the contact of those two circles D C, C I, the recession of the cadent moveable from the circumference C F D; namely, from the top of the Tower, is towards the beginning extream small, which is as much as if one said its motion downwards is very slow, and more and more slow in infinitum, according to its vicinity to the term C, that is to the state of rest. And lastly it is seen how in the end this same motion goeth to terminate in the centre of the Earth A.

I understand all this very well, nor can I perswade my self that the falling moveable doth describe with the centre of its gravity any other line, but such an one as this.

But stay a little Sagredus, for I am to acquaint you also with three Observations of mine, that its possible will not displease you. The first of which is, that if we do well consider, the moveable moveth not really with any more than onely one motion simply circular, as when being placed upon the Tower, it moved with one single and circular motion. The second is yet more pleasant; for, it moveth neither more nor lesse then if it had staid continually upon the Tower, being that to the arches C F, F G, G H, &c. that it would have passed continuing alwayes upon the Tower, the arches of the circumference C I are exactly equal, answering under the same C F, F G, G H, &c. Whence followeth the third wonder, That the true and real motion of the stone is never accelerated, but alwayes even and uniforme, since that all the equal arches noted in the circumference C D, and their respondent ones marked in the circumference C I, are past in equal times; so that we are left at liberty to seek new causes of acceleration, or of other motions, seeing that the moveable, as well standing upon the Tower, as descending thence, alwayes moveth in the same fashion, that is, circularly, with the same velocity, and with the same uniformity. Now tell me what you think of this my fantastical conjecture.

I must tell you, that I cannot with words sufficiently expresse how admirable it seemeth to me; and for what at present offereth it self to my understanding, I cannot think that the business happeneth otherwise; and would to God that all the demonstrations of Philosophers were but half so probable as this. However for my perfect satisfaction I would gladly hear how you prove those arches to be equal.

The demonstration is most easie. Suppose to your self a line drawn from I to E. And the Semidiameter of the circle C D, that is, the line C A, being double the Semidiameter C E of the