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That the true and real movement of the stone is never accelerated, however alwayes even and uniforme, since that all the equal arches famous in the circumference C D, and their respondent ones marked within the circumference C I, are previous in equal occasions; so that we are left at liberty to hunt new causes of acceleration, or of other motions, seeing that the moveable, as nicely standing upon the Tower, as descending thence, alwayes moveth in the same style, that’s, circularly, with the identical velocity, and with the identical uniformity. And because the angle C E I made within the centre E of the lesser circle, and which insisteth upon the arch CI, is double the angle C A D, made within the centre A of the higher circle, to which the arch C D subtendeth; subsequently the arch C D is half of the arch of the better circle like to the arch C I, and therefore the two arches C D and C I are equal; and in the identical manner we might show of all their elements. A B, the circle B I, representing to me the Terrestrial Globe, and prolonging the semidiameter A B to C, I’ve described the peak of the Tower B C; the which being carried about by the Earth along the circumference B I, describeth with its prime the arch C D: Dividing, in the subsequent place, the line C A in the middle at E; upon the centre E, at the gap E C, I describe the semicircle C I A: In which, I now affirm, that it is extremely possible that a stone falling from the top of the Tower C, doth move, with a motion mixt of the circular, which is in common, and of its peculiar proper movement.
Suppose to your self a line drawn from I to E. And the Semidiameter of the circle C D, that’s, the road C A, being double the Semidiameter C E of the circle C I, the circumference shall be double to the circumference, and every arch of the greater circle double to each like arch of the lesser; and consequently, the half of the arch of the better circle, equal to the entire arch of the lesse. If due to this fact within the circumference C D, sure equal components C F, F G, G H, H L, be marked, and from the points F, G, H, L, right traces be drawn towards the centre A, the parts of them intercepted between the two circumferences C D and B I, shall represent unto us the same Tower C B, transported by the Terrestrial Globe in direction of D I; by which traces the points the place they come to be intersected by the arch of the semicircle C I, are the places by which on occasion the falling stone doth passe; which factors go continually with better and better proportion receding from the top of the Tower.
Tower, or to speak extra correctly, from the circumference of the circle described by the top of the Tower, by way of the Earths conversion; but that such recessions be lesser and lesser in infinitum; by how a lot the moveable finds it self to be lesse and lesse removed from the primary time period the place it rested. Salv.Why then, in discharging the shaft in direction of the course of the chariot, the bow impresseth its three levels of velocity on a shaft that had one diploma of velocity earlier than, via the chariot which transported it so fast in direction of that half; so that in its going off it hath four levels of velocity. For an example, let the flight of it self be three hundred yards, and the course of the chariot in the time whilst the shaft stayeth within the air, an hundred yards, due to this fact taking pictures towards the course, of the three hundred yards of the flight, the chariot may have gone one hundred; so then on the shafts coming to the ground, the house between it and the chariot, shall be however two hundred yards onely; however on the contrary, in the opposite shoot, the chariot operating contrary to the shaft, when the shaft shall have handed its three hundred yards, and the chariot its different hundred the contrary method, the space interposing shall be discovered to be four hundred yards.
And if one accommodate another declining board over in opposition to it, the movement of the Chariot could also be certified so, that the ball, gliding downwards along the board, in its coming to the ground shall rest immoveable, and in addition shall generally run the opposite way to the Chariot. Salv.This is able to essentially follow, if it were concluded that the Terrestrial Globe moveth circularly; a factor, which I pretend to not be completed, but have onely hitherto attempted, as I shall nonetheless, to look at the energy of those reasons, which have been alledged by Philosophers to prove the immobility of the Earth, of which this first taken from issues falling perpendicularly, hath begat the doubts, which were talked about; which I know not of what power they could have appeared to Simplicius; and subsequently earlier than I passe to the examination of the remaining arguments, it can be handy that he produce what he hath to reply to the opposite.