m TLVIBO. «5 



Ciii in eo piiriiflo longitiido pcnduli acqualis nccipi 

 debct. Dcniquc cx conftrucflionc colligerc licct, 

 qualcm figuram nollra curua habeat. Sit AB tauto- pj ? 

 chrona dclcenfus, quac continua crit cum AC curua 

 afcenlus. Vltra B ct C continuatur in D et E, ita 

 vt arcus BD, ED fimilcs et aequalcs fint arcui BAC. 

 Atque hoc modo in infinitum producitur. 



§. 31. Pcrpcndamus nunc qualis corporis feu 

 globi, vtpofitumcd, fuper curua tautochrona in- 

 uenta fit motus. Confideremus ofcillationem vnam, 

 quii globus in pundo infimo habeat velocita- 

 tem ex altitudine /' acquifitam. Dicatur, vt ante, 

 altitudo genitrix velocitatis globi in pundo quo- 



ns 



cunque ciiruae defccnfusc;. Erit ex §. 1 3. v—c^\b-t) 



—ns 



vbi eft t—-~fc'^'^dx. Hic vero a altitudinem cylin- 

 dri ofcillantis dcfignat , vt ergo globus introduca- 

 tur pouatur .|^ Joco /7, prout §.17. fa<flum cll ct erit 



v—i^^^^b-t), ett—^fc^^^^^dx, Cum his aequa- 

 tionibus ca quac naturam curuac exprimit efl con- 



jungenda , quac eft haec C^m^^ii^c-^^^^-^^n^^aa— 

 z^m'nas—g{m—7})n-fx ; feu hujus differcntialis , vt 



habeatur dx , z^m'nac^'^ds-:i.^m'nads:=:g{in-ji) 



jns 



fi-fdx, fiuc Im-ac^^^^ds-^m-ads—^^^m-yifdx. 



§. 32. Eft igitur ex poftcriorc acouatione 



3nf 



"^dx-^-i^-Sr^^^^ds-^ils. Vndc erit '!tr\r^'^V.v— 



L 3 



fimrj 

 3ri/ 



