DE FRJCTIONIBrS CONTIl<lFIS OBSERK $$ 



§.42. Qiio autem vfiis harum formularum in inter- 

 polationibus pateat , propofita fit haec feries : j~ -H 



p'p-h2r) p(p-h^r){p-^ r) ^ '^ . 



(p-+-2'L.p-H-^-H:r) "^ Cf)-f-^'?Xp-4-2j-H:r);f-+-3:j-+-+r) "i- etC. CUIUS 



terminus indicis | fit zz: A ; terminus indicis | z= ABCj 

 terminus indicis | = ABCDE; et ita porro. His pofi- 

 ns erit ad _ ^^^ , ^u _ p-^,.i-i.,r ^ ^^^ — pri--+-.r» 

 etc. Ponatur nunc A = ^zp^; B =: ^i^i^ ; C--^; 

 D zr ^-I^^IJI^T: ; etc. eritqsc ab—p{p^iq-r)-^ bcz=l 

 {p-^r){p-\-^q)\ cd—{p^2r){p-\-2q-^r); de 

 i:r(p4-3^) (p-l-2^-4-2r) ; etc. lam fiat vlterius a 

 —p-^-q-r-^l ; bzzp + q-^^'^ ; c-=zp+q-\^r^ 

 ^ ; //=z_p -4- ^ -4- 2 r -h I ; etc. quibus valoribus fubftitutis 

 emergent fequentes aequationes , Eidlo g — q^r—q)', 

 « (3 - [p-\-q-r) ^ - [p-^-q) ^-q [r-q) - o 

 P y - (? ^- ^) P ~ (P+^-H^) V -^ (r-^) = o 

 y$- ip-^-q-^r) y -{p-J^q^^y) $-q {r-q) — q 



^ e - ip-^q-h- 2.r) $ - {p~\-q-{-:^r) e-q {r-q):=zo 



etc. 

 §.43. Comparatis his aequationibus cum iis , quas 

 5. 38. aflfumfimus , reperietur: 



m^p-^-q-r '^ n—p-^-q-^ Kznqr—qq-^ et j-^zrrvnde 

 fiet ss—ms-^-ns-^-K-zznrr-^qr—qq'^ ^ss—^ms-^-ins 

 '^K—6rr-\-qr—qq ; 9SS — 3ms-\-3ns-\-Kzzi2rr-\- 

 qr — qq\ etc. Qiiibiis valoribus omnibus fiibftitutis obti- 

 nebuntur fequentes fradiones continuae , quibus litterae a^ 

 h^ Cy d, etc. exprimentur. 



hIZp-i.q-r^ qr-qq 



2(P-H3— ^)4- 2 -^qr—qq 



2{p-i^l—rj ^■^rr-j-qr—^q) 



6= 



