Page:Mathematical collections and translations, in two tomes - Salusbury (1661).djvu/202

 descending groweth less & less in it, the nearer it is to the first term of its descent; that is, to the state of rest; as is manifest from that which you declare unto us, demonstrating that the descending grave body departing from rest, ought to passe thorow all the degrees of tardity comprehended between the said rest, & any assigned degree of velocity, the which grow less and in infinitum. To which may be added, that the said velocity and propension to motion, doth for another reason diminish to infinity; and it is because the gravity of the said moveable may infinitely diminish. So that the causes which diminish the propension of ascending, and consequently favour the projection, are two; that is, the levity of the moveable, and its vicinity to the state of rest; both which are augmentable in infinit. and these two on the contrary being to contract but with one sole cause of making the projection, I cannot conceive how it alone, although it also do admit of infinite augmentation, should be able to remain invincible against the union & confederacy of the others, wch are two, and are in like manner capable of infinite augmentation.

This is a doubt worthy of Sagredus; and to explain it so as that we may more cleerly apprehend it, for that you say that you your self have but a confused Idea of it, we will distinguish of the same by reducing it into figure; which may also perhaps afford us some ease in resolving the same. Let us therefore [in Fig. 4.] draw a perpendicular line towards the centre, and let it be AC, and to it at right angles let there be drawn the Horizontal line AB, upon which the motion of the projection ought to be made; now the project would continue to move along the same with an even motion, if so be its gravity did not incline it downwards. Let us suppose from the point A a right line to be drawn, that may make any angle at pleasure with the line AB; which let be AE, and upon AB let us mark some equal spaces AF, FH, HK, and from them let us let fall the perpendiculars FG, HI, KL, as far as AE. And because, as already hath been said, the descending grave body departing from rest, goeth from time to time acquiring a greater degrees of velocity, according as the said time doth successively encrease; we may conceive the spaces AF, FH, HK, to represent unto us equal times; and the perpendiculars FG, HI, KL, degrees of velocity acquired in the said times; so that the degree of velocity acquired in the whole time AK, is as the line KL, in respect to the degree HI, acquired in the time AH, and the degree FG in the time AF; the which degrees KL, HI, FG, are (as is manifest) the same in proportion, as the times KA, HA, FA, and if other perpendiculars were drawn from the points marked at pleasure in the line FA, one might successively find degrees lesse and lesse in infinitum, proceeding towards the point A, representing the first instant of time, and the first state of rest. And this retreat towards A, representeth the first propension to the