44 DE FRACTIOmBFS CONTINnS OBSERF. , 



§.23. Ex his igitur aequationibus emergent (equen- 

 tes litterarum a, ^, y , <5^, etc. comparationes inter fe. a :zi 



Pg-(m-r) P ~T~— (m- r) ig>^ (PH-a.)>-w P^^^ "T^ 



P '^ 

 {?-»-r)(p- 



V — (P-^»^)5-(m-»-r) PH-2(i "t- 



p::Ml+r 



(P->-2' )(^-f-?g-4-r):(PH-2a>* 



p-4--'a ^^ 



Si ergo breuitatis gratia ponatur p*'+'2pq—mp'-mq^ 

 qr ~K Qt pr -\- qr -- mr ZZ.S , atque valores litterarum 

 aflumtarum continuo in praecedentibus furrogentur , proue- 

 niet (equens fraclio continua 



** P ~t~ .rR- , (f)H-r] (p-4-2^):(P-f>a)* 



P(P=Ha) ~r- ~^f(R"-4-S) ( j,H-r) ( j)-f-2g-f-r):(P-h 2a)* ^ 



(P-f-g ,(P-i-2a) "T^ . r ( R.4 -2 S) 



(p-+-2a)(p-H3a) "T" ^^c* 



§. 54. Cum igitur fit ^=1«/— r-f- ~ habebitur 

 p 



zm-r 



in^p[p-^-q-r){?-\-(:L) 



2rR-H(p-f->-)(p-i-2g).-(P-H:a) 



2r(R-t-Sj-4-(j^-H2r)(p-f-i?.4- r)(P-4-a)(P-h5a ) 

 2r(R-f-2S>4- *,c. 



Hinc igitur feriei propofitae ■^q-\-jf^^^~;:p^-]r 

 j^^^f^^^pz^^ -H etc. terminus cuius index eft § 

 erit A — ^ip-gi^- Qiioniam vero huius feriei terminus ge- 



neralis indicem habens « eft = ^ ^ , , / ^ — ^,Tn= — erit 

 fradio continua inuenta feu valor litterae ^jfznfp-f-s^-r) 

 ]^^^(i^r^^^'^^ poft vtramque integrationem j=i. 



