^50 PHILOSOPHICAL TRANSACTIONS. [aNNO 1608. 



semicircle ; which is most true, if the weight fall not to the centre of the earth 

 precisely in 6 hours ; for, in this case of Riccioli, the weight falls to the centre 

 of the earth in 21 minutes and 53 seconds. 



Manfredi, in his answer for Riccioli, affirms, that Angeli understands not 

 the Rule-of-Three, in giving out FS for II596 -v^-rVg-j of which AC is 

 20000000000 : and Angeli, in his reply, affirms his analogy to be so clear, that 

 there can be nothing said more evident than itself to confirm it : referring in 

 the mean time the further determination to geometricians. 



Angeli might have answered Riccioli's argument, granting the weight to 

 move equally in a semicircle, by distinguishing his minor thus : No heavy 

 bodies descend to the earth with a real and notable increase of velocity, if the 

 velocity be computed in the circumference of a semicircle ; then the minor pro- 

 position is true. But the descending motion is not so to be computed : for 

 here the equal motion in the circumference of the semicircle CIA is com- 

 pounded of the equal motion in the quadrant CD, and of the accelerated motion 

 in the moveable semidiameter C A; and this accelerated motion in the semi- 

 diameter is a true and simple descending motion; in which acceptation the 

 minor proposition is most false, and likewise contrary to the experiments of 

 Riccioli. But it seems that Angeli answers otherwise, to make Riccioli sensible 

 that CI A is no semicircle; concerning the nature of which line they debate 

 very much throughout the whole dispute. 



The second argument is much insisted on by Angeli, to make his solution 

 clear to vulgar capacities ; but the substance of all is, that the cannon ball has 

 not only that violent motion impressed by the fire, but also all those motions 

 proper to the earth, which were communicated to it by the impulse received 

 from the earth; for the ball, going from w^est to east, has indeed two impulses, 

 one from the earth, and another from the fire ; but this impulse from the earth 

 is also common to the mark, and therefore the ball hits the mark only with that 

 simple impulse received from the fire, as it does when shot towards the north 

 or south ; as Angeli excellently illustrates by familiar examples of motion. 



To Riccioli's third argument Angeli answers, desiring him to prove the sequel 

 of his major, which Riccioli does, supposing the curve in which the heavy body 

 descends to be composed of many small right lines ; and proving that the 

 motion is almost always equal in these lines ; and after some debate concerning 

 the equality of motion in these right lines, Angeli answers, that the equality of 

 motion is not sufficient to prove the equality of percussion and sound, but that 

 there are necessary also equal angles of incidence; which in this case he shows 

 to be very unequal. To illustrate this more, let us prove that, other things 

 being alike, the proportion of two percussions is composed of the direct propor- 



