INTER SE GOMFARANDIS. 43 



Problema 5. 



Si ellipfis ADBFA per diametrnm quamcunque Tib. 1. 

 ECF faerit bifeda , femicircumferentiam EBF ita fe- ^'S' ^" 

 care in puncflo M, vt partium EM er FM difFeren- 

 tia fit geometrice affignabilis. 



S o 1 u t i o. 



Etfi hoc problema in praecedente continetur , 

 tamen folutio inde deduci nequit , propterea quod tam 

 p-i-r". o, quam Ph-R— o; pecuiiari ergo modo 

 foiutio debet inueftig;u-i. Pofitis ergo femiaxibus 

 CArr^; CD—l?z--aVii — m) fit pro altero termino 

 E nrcus propofiti abfciflli CVzzp, crit applicata 

 FEz:z'-V{aa~pp): quae coordinatae negatiiie fumtae 

 ad alterum terminum F pertinebunt , quae autem fint 

 r et -^V^a a — rr), ita "vt fit rzz-p et V{aa-rr) 

 z:^ — V{aa—pp). Cum nuuc fumta quadam noua 

 abfciffi k, pofitaque quaefita CQ^zi^, fit ex CoroU. 2. 

 Probl. 11. 



aaV{aa-kk)-pqV{aa-?nkk)zz:aV{aa-pp){aa-qq) 

 aaV{aa-kk)-qrV{aa-mkk:]-=zaV{aa-qq){aa-rr) 



haec \ltima aequatio ob rzr-^ et V{aa-rr)~-V{aa-pp) 

 abit in hanc : 



aaV{aa~-kk)-\-pqV{aa-mkk)z=:-aV{aa—pp)[aa'qq) 

 quae ad primam addita dat: 



!iaaV{aa — kk) zi: o ideoque kzzai 

 qui valor in altera fubftitutus dat : 



—pqV{i -m)zzV{aa-pp) {aa—qq) 



F 2 ideoque 



