(195) 



qn.ne qnntnor exprcffioncs fequcnti modo conciniiius repracfcn- 

 tari poHunt : 



^ r. ,n ( cof. X t -i- cof. 2 X r ) i 



>5 r /f ( cof. X f — cof. z\i)\ 



if r ir, X ( fin. X ; 4- :i fm. 2 X f ) ; 



I J = i' X ( Cu. X / — 2 fin. 2 X O • 



§. 14. Qno nnnc in motns pendiili noftri plincnomc- 

 pa nccurratius inquiraiiius , quaeramus tcmporis ca momenta , 

 quibus corpus fuperius rctrogreditur, quod fit \bi ccleritiis an- 

 guhiris euaiicfcit. Ponatur igitur ^^ = o , critque fm. X ; r - 

 afin. 2X/, cui acquationi fatisfit pofito X / r tt , 2 tt , 3 tt , 

 4 7r, etc. , fiuc ;r 1,2,3,4, etc. min. fcc. ; tum vero eidcm 

 acquationi proximx fatisfit cafibns X / r --^ , '-i^ , '-^-^ , etc. hoc 

 crt tcmporc / r /, , ?i , ?| , ctc. min. fcc. Corpus autcm in- 

 fcrius rctrogrcdi incipict \bi -^r o, hoc cft fin. X / r -+- 2 fin.X''/, 

 qnod fit cafibus X / r ^, 2 -r, 3 t, etc. hoc eft tempore /ri, 

 2,3, etc. min. fec. tnm vcro huic aeqnaiioni fatisfaciunt 

 proxime valores X / r '3 , !13 , IlJI , ctc. Hic autcm probc 

 caucndu)n cft nc corpns infcrius his portrcmis tcmporis mo- 

 mcntis ccnfcatur rctrogrcdi : cx fcqucntibus cnim patcbit hoc 

 ficri omnino non polfc, qnod paradoxon infra diluctiir. 



§. i^. Quacramus porro quibnsnam tcmporis momcn- 

 tis corpus fupcrius A in axcm O V incidit, quod cum cucniat 

 quando anguhis ^ cuancfcir, ficri dcbcbit cof. X/r-cof. 2 X /, 

 quod cucnit cafbiis quibus c(l X/r"^-, H', 5- - , ~, — , ctc. 

 hoc cfl tcmpore /rj, 1, -J , ^, 3, ctc. min. fcc. Quod au- 

 icm corpus infcrius attinet, id pcr axcm rranfit quando aiii;u- 

 ius B A y abit in Q A ^, hoc crt vbi v; r - P, f»iic, quia ambo fila 



B b 2 acqua- 



