tK PtRCrsSIOUE. 125 



Sit maiTa corporls in Arrw, eius velocitas AB-=zp ; Fis. 7 • 

 malTa corporis Cznn, eius velocitas CB— </. Mutentur 

 velocitates AB & BC poft occurfum in alteras §a , 6c 



§Y , fitquc ^a=i.r , gy— J=^ (P^'' P^^P^^^^^^"^"^ ^•) 

 •]/ mpp_^ nq qirv^ _ Ponantur iam eadem corpora reverti 



ad fecundum impulfum velocitatibus ^? & $&, ita utfit 

 ^&. $? :: BA. BC, <^a. Cpy :: n. »?, feu reciproce ut 

 maflae corporum in A oc L : repcnetiir 6 a-zz-^^zzqir ? oc 

 (py — f^^^J^^. His ita pofitis exprimantur veloci- 

 tates poft hunc fecundum idum in ? per lineas BD & 

 BF , & apparebit per lecundam partem hypothefeos 

 tertiic quod AB. ga :: ^g. DB— ^^^^P , & CB, ^Y- ^ 

 $?. BF=^Eg?. Confideratis porro velocitatibus 

 partialibus a^, Y^ ' patet per hyp. 4 degenerare hasin 

 BA & BC, reliquas vero ^a. & (pY (P^^ P^^P- 2.)ma- 

 nere easdem , & per confequens ADz=:(5^a, ficut & CF 

 mY'^- Elicitur ergo etiam(per primam partem hypo» 

 thefeos 3) quod BDrrBA-f-AD-/)-!-'-;^^:^;^, & BF 

 BC^CF^^^ ^^Zg^ unde provenit "^7^^^^r=p-|- 



mnx — pny „ mxy — n^y , qmx — ■pm.y i 



^fml^qn^y ^ -pn-qn =^-^>m-^ » ^^^^ ^'"32 aSquatlO. 



nes per fubftitutionem valoris ^y fupra exhibiti fimilem 

 producunt aequationcm. Primam ergo reduxiffe hic 

 fufficiat, & prodibitper debitam terminorum difpofitio- 

 nem mxx—nxj' — qnx-\-pny — ppm-^pqmzo , quae «- 

 quatio divifa per x — p (radicem mantfefte inutilem dat 

 vix—ny~\-mp—qni:zo , vel , furrogato pro jy valore fuo, 

 mmxx -+- mnxx -f- 2 mmpx — Qmnqx^mmpp — mnpp — 

 Smnpq—o , vel tandem dividendo per x--\-p , radicem 



Q 3 etiam 



