Page:Mathematical collections and translations, in two tomes - Salusbury (1661).djvu/225

 ball got to the ground, when the little one is still within less than a yard of the top of the Tower.

That this proposition is most false, I make no doubt in the world; but yet that yours is absolutely true, I cannot well assure my self: nevertheless, I believe it, seeing that you so resolutely affirm it; which I am sure you would not do, if you had not certain experience, or some clear demonstration thereof.

I have both: and when we shall handle the business of motions apart, I will communicate them: in the interim, that we may have no more occasions of interrupting our discourse, we will suppose, that we are to make our computation upon a ball of Iron of an hundred (a) pounds, the which by reiterated experiments descendeth from the altitude of an hundred (b) yards, in five second-minutes of an hour. And because, as we have said, the spaces that are measured by the cadent moveable, increase in double proportion; that is, according to the squares of the times, being that the time of one first-minute is duodecuple to the time of five seconds, if we multiply the hundred yards by the square of 12, that is by 144, we shall have 14400, which shall be the number of yards that the same moveable shall pass in one first-minute of an hour: and following the same rule because one hour is 60 minutes, multiplying 14400, the number of yards past in one minute, by the square of 60, that is, by 3600, there shall come forth 51840000, the number of yards to be passed in an hour, which make 17280 miles. And desiring to know the space that the said ball would pass in 4 hours, let us multiply 17280 by 16, (which is the square of 4) and the product will be 276480 miles: which number is much greater than the distance from the Lunar concave to the centre of the Earth, which is but 196000 miles, making the distance of the concave 56 semidiameters of the Earth, as that modern Author doth; and the semidiameter of the Earth 3500 miles, of 3000 * Braces to a † mile, which are our Italian miles.

Therefore, Simplicius, that space from the concave of the Moon to the centre of the Earth, which your Accomptant said could not be passed under more than six days, you see that (computing by experience, and not upon the fingers ends) that it shall be passed in much less than four hours; and making the computation exact, it shall be passed by the moveable in 3 hours, 22 min. prim. and 4 seconds.

I beseech you, dear Sir, do not defraud me of this exact calculation, for it must needs be very excellent.

So indeed it is: therefore having (as I have said) by diligent tryal observed, that such a moveable passeth in its descent, the height of 100 yards in 5 seconds of an hour, we will say, if 100 yards are passed in 5 seconds; in how many seconds shall