Salv.Neither doth this suffice, but its requisite to know according to what proportion such accelleration is made; a Problem, that I believe was never hitherto understood by any Philosopher or Mathematician; although Philosophers, and particularly the Peripateticks, have writ great and entire Volumes, touching motion.
Simpl.Philosophers principally busie themselves about universals; they find the definitions and more common symptomes, omitting certain subtilties and niceties, which are rather curiosities to the Mathematicians. And Aristotle did content himself to define excellently what motion was in general; and of the local, to shew the principal qualities, to wit, that one is natural, another violent; one is simple, another compound; one is equal, another accellerate; and concerning the accelerate, contents himself to give the reason of acceleration, remitting the finding out of the proportion of such acceleration, and other particular accidents to the Mechanitian, or other inferiour Artist.
Sagr.Very well Simplicius. But you Salviatus, when you descend sometimes from the Throne of Peripatetick Majesty, have you ever thrown away any of your hours in studying to find this proportion of the acceleration of the motion of descending grave bodies?
Salv.There was no need that I should study for it, in regard that the Academick our common friend, heretofore shewed me a Treatise of hisThis is that excellent tract which we give the first place in our second Volume.De Motu, where this, and many other accidents were demonstrated. But it would be too great a digression, if for this particular, we should interrupt our present discourse, (which yet it self is also no better than a digression) and make as the Saying is, a Comedy within a Comedy.
Sagr.I am content to excuse you from this narration for the present, provided that this may be one of the Propositions reserved to be examined amongst the rest in another particular meeting, for that the knowledg thereof is by me very much desired; and in the mean time let us return to the line described by the grave body in its fall from the top of the Tower to its base.
Salv.If the right motion towards the centre of the Earth was uniforme, the circular towards the East being also uniforme, you would see composed of them both a motion by a spiral line, of that kind with those defined by Archimedes in his Book De Spiralibus; which are, when a point moveth uniformly upon a right line, whilest that line in the mean time turneth uniformly about one of its extreme points fixed, as the centre of his gyration. But because the right motion of grave bodies falling, is continually accelerated, it is necessary, that the line resulting of thecom-
