myself, the patient being the same, double force in the agent shall worke upon it double effect. In the same letter you require a better explication of y^e proportion I gather betweene wayght and swiftnesse: wherein, because you have not my figure, I imagine you have mistaken me very much. And first, you thinke, I suppose, D E equall to A B: w^{ch} I am sure is a mistake. For I put A B for any line you will to expresse a _minutū secundum_. I will, therefore, go over againe the demonstration I sent you before, and see if I can do it cleerer. [Illustration] Let A B stand for the time knowne wherein the waight D descendeth to E. And let there bee a cylinder of the same matter the waight D consisteth of, and let the altitude of that cylinder be D C: w^{ch} I shew before was the swiftnesse wherew^{th} that cylinder _presseth_, not wherew^{th} it _falleth_. And wee are now to enquire how farre such matter as the cylinder is made of must descend from D, before it attayne a swiftnesse equall to this pressing swiftnesse D C. And I say it must fall to L. For in the time A B it is knowne that the waight in D will fall to E: and it is demonstrated by Gallileo, that when such waight comes to E, it shall be able to go twice the space it hath fallen in the same time. Therefore the waight D being in E, hath velocity to carry him the space D K (w^{ch} I put double to D E) in the same time A B. But I put B F equall to D K. Therefore, in the time A B, the waight’s velocity acquired in E shall be such as to go from B to F without decrease of velocity by the way. Hence I go on to finde in what point the waight in D comes to where it getteth a velocity equall to C D. Therefore, I apply D C to G H, parallel to B F: and then it is, as the time A B to the time A G, so the velocity acquired at the end of the time A B to the velocity acquired at the end of the time A G. For the swiftnesse acquired from time to time (I say, not from place to place, but from time to time) are proportionable to the times wherein they are acquired: w^{ch} is the postulate on w^{ch} Galileo builds all his doctrine. And as A B to A G, so the line B F to the line G H. But, at the end of the time A B, the waight D is by supposition in E, in that degree of velocity as to go B F or D K in the same time A B. The question therefore is, where the waight D shall be at the end of the time A G. For there it hath the velocity of going G H or D C in the same time, because the velocity G H is to the velocity B F as the line G H to the line B F, or as the time of descent A G to the time A B. But, because the spaces of the descent are in double the proportion of the times of descent, make it as B F to G H, that is, D K to D C, so D C to another, D L. The velocity, therefore, acquired in the point of descent E, namely the velocity D K or B F, is to the velocity acquired in the point L, namely, the velocity G H or D C, (w^{ch} is the velocity of the cylinder’s waight), as D K to D L. And