r= (207) 



Ponatur brcnitatis crgo '"^"^f- — 2 w , critquc 



{a -\- by zn 2 m a b. 

 Hinc igitur euoluendo fit 



aa-\-2ab-\~bb::izzmab 

 Tniic colligitur a a zn 1 {m — i)ab — bb^ 'lincquc 



a zzz {m — i)^±:V^('/^ — \ y b b — b b ^ 

 ita vt fit 



~ zn m — I 2t 1/ w ;// — 2 m. 



Qno autcm quacllio fit ponibilis , ratio a : (5 ita cfl fiimcnda, 

 vt fjt "~^'\ - > i/n. Nam cum fit w numcrus rcaJis, ncccfTc 



cft vt practcrca flt w > 2, hoc cft '- ''"^'l' > 2, iiue ^^^—r- > i, 



lcu i±l.^/n. 



Corollarium i. 



5. 9. Si ambo corpora ftatuantur aequalia, ct quacra- 

 tur ratio filorum ita, vt tcmpor.i ofcillationum fint in data ra- 

 tione , ob « — 2 pro hoc cafu conditio adimplenda ita fe 

 habcbit: '-^-^~ > 2, fuic a. a — 6a^-}-(3p>o. Statuatur cr- 

 go a ar: 6 a p — f? p-t- (3 (3 w, critquc ara ^-^-V (8 P^3-t-^l3o.), 

 fuic -^ =:: 3 Hi /(8 -f-w), hoc eft ratio data a : [3 ita compa- 

 rata cire dcbct, vt fit vel " > 3 -f •/ g vel -" << 3 — V ^ -> 

 quae conditioncs ita cnunciari poffunt: Po/ttis anibnbus corpuS' 

 culis A et B acqualibus^ nuUa itucr tempora ofcillatiomm }/ % et 



\f i3 ratio fubfijkre potejl , nifi extra limites l/ 3 -h V S ^' ' 

 ■/3 — V >i' Quaedio igitur impo']"ibilis ell , quoties fradiof 

 -" continetiur intra limitcs 3 -h V 8 — V ct 3 — V 8 — i 

 proximc. 



Corol- 



