SE INVICExM PERCFTIENTIFM. 19 



Ponamiis nunc ^ rz S et inueniemus vim viuam qua~ 



drantis circuli ^f^^^^vvfd^V {^"^-^)— (quh Jd^ 

 y(ge-^^)= qiiadranti, quem voco Q)^^^vvQ_-^ 

 crgo vis viua totius circuli zz"-^^^ v v Q. Applicen- 

 tur iam haec ad fphaeram. In hac efl: a zr <? -j- .v , g— 

 V(2l?x-xx ), Qj=^n.(2bx — xx) (per ji intelHgo ex- 

 ponentem rationis inter peripheriam circuli et radium) 



adeoque 7^^^ i"u Q. = ji^Ty'^'^'' ( 8 aabx^i6abxx 

 -h 4-lfbxx — 4.a axx-[- ^.bx' — 8 ax' — 3 x*) , quod du- 

 (ftum in dx altitudinem fcihcet ftrati dabit eius vim viuam 



~ 3(a-+-6)^ '^'^'^''^''v ^aabx-i-i6abxx~\- ^.^lfxx — ^aaxx 

 -\-^bx' — 8ax'—:^x'')^ huius integrale eft z^-^^^—^^» 

 vvi^aabxx-^-^^abx' -^-^bbx^—^aax^-^-bx —zax* 

 — |.v^). In hac exprefiione fi ponatur x~2by obti- 

 nebitur vis viua totius fphaerae ofcillantis —lnb'vv 



(a a -4- 2^b -4- ? /»/A _ 

 (TIjI^^^ ^— (fi hnb^ irtpotc mafla globi YO- 



,,. aa-\-2ab-\-\bb ,, ^ t- t 

 cetur M) — -^ —^ — 'y-yM. Q. E. I. 



Corollarium r. 



VH. Si ponatur fl-rrco, habebitur vls viua globi 

 folo motu progreffiuo moti — i^-yM, plane vt fieri 

 debet. 



Corollarium 2. 



VIII. Vis viua motus compofiti ex progrefliuo et 



gyratoiio , quoiurn velocitates funt inter fe aequales , in- 



C 2 ue- 



