Page:Philosophical Transactions - Volume 003.djvu/74

 for, the Ball, going from West to East, hath 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 doth being shot towards the North or South; as, Angeli doeth excellently illustrate by familiar examples of Motion.

To Riccioli his third Argument Angeli answereth, desiring him to prove the sequel of his Major, which Riccioli doeth, 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 is necessary also equal angles of incidence; which in this case he proveth 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 proportion of their velocities, and of the direct proportions of the Sines of their angles of incidence. Supponamus autem sequens principium, nempe, quod percussiones (cæteris paribus,) sint in directa proportione cum velocitatibus, quibus mobile appropinquat planum resistens. Sit planum C F, sintque duo mmobilia omni mode æqualia, & similia, quæ motu æquali accedant à puncto A, ad planum CF, in rectis AD, AF: dico, percussionem in puncto D ad percussionem in puneto F. esse in ratione composita ex ratione velocitatis in recta AD. ad velocitatem in AF, & ex ratione sinus anguli ADE ad sinum anguli AFE. Ex puncto A in planum CF, sit recta AE normalis, sitque recta AC æqualis rectæ AF, & AB æqualis recta AD, & planum BGH, parallelum plano CF: supponamus mobile, prioribus simile & æquale, rnoveri æqualiter in recta AC, eadem velocitate, qua movetur mobile in recta AD: quoniam plana BGH, CF, sunt parallela, & motus in recta AC est æqualis, igitur mobile eadem locitate accedit ad planum BH, qua ad planum CF, & proinde percussiones in punctis B, C, sunt æquales; atque percussio in puncto D, est ad percussionem in puncto B, ut recta AE ad rectam AH, sen (ob æquales rectas AD, AB) ut sinus anguli ADE ad sinum anguli ABH, quod sic probo; velocitas mobilis in recta AD, est æqualis Rh