SEV OSCILLATORIIS. * 1 3 



cenferl poteft, (i corpus nec minimum fit nec 

 admodum leue) eflfe modo denfiorem modo ra- 

 riorcm, poterit ratio grauitatum fpecificarum ha- 

 beri ex numero ofcillationum dati penduli, poft 

 quem ofcillationes dato arcu diminutae fuerint, 

 Et hinc mcnfura caloris ifixa haberi poteft, vt 

 alia occafione monftrabo* 



Problema, 



§. 9. Si corpus in medio fubtiliflimo ofcil- 

 letur arcus defcribens cycloidieos, inuenire ex pri- 

 mo arcu defcenfus arcum afcenfus, quem eorpus 

 poft magnum ofcillationum numerum datum de- 

 fcribet, aut vicifiim ex vtroque arcu dato inuc- 

 nire numerum ofcillationum. 



Solutlo* 



Sit primus arcus defcenfus zzzt^ erit per §,6". 

 arcus fubfequentis afcenfus — t — ^ntt: fimiliter re- 

 peritur arcus fecundi afcenfus zzzt^^ntt-\- 3 -^nnt $ 

 — 1^« 3 /+, et pofito vltimo numero ofcillatio- 

 num /, erit arcus vltimo afcenfu defcriptus :rr 



t-I(*n)tt+(ll-l)(%n)H*-(l 3 -^ll-iril)(%n) 3 t+ 



-4- etc. , cui feriei fine notabili errore fubftitui 

 poteft haec altera geometrica t— (%nl)tt-\-(§nl) z 

 t 3 — (fyil) 3 t+-\- etc. tum ob paruitatem numeri n 

 cuius dimenfiones inferiores prae maxima quafi 

 cuanefcunt. Eft autem fumma huius feriei geo- 

 metricae — t: (i-f-^«//)j vnde fi arcus afcenfus 

 poft numerum ofcillationum / dicatur r, erit 

 Tom. V. P I. 



