= (66) == 



dx=d$ cof. C fin. -h a {) fiu. ^ cof. e cof. Cj) ct 

 Bv =: a a cof. & cof. Cp — ^ t^ fin. ^ cof. fin. Cp . 

 Eft vcro fin. t> cof. ? =: i fin. 2 $ , 



fin. p cof. q = i fin. (/>-+- y) -h a Hn. (p — 9) ,' 

 fin. p Cn. y = l cof. (p — q) — i cof. (p -^ q) ^ 

 cof. /> cof. q ~ i cof. (p -^ q) — i cof. (p -I- q). 

 His igitur rcduc^tionibus in fubfidiuin vocatis rcpcricmus : 



^ 1= i fin.((|)-H0; H- i fin.(4)— ^)-H J fin.(2e-+-Cl5; -H i fin.( 2^-4)) 

 i-^ =1 i cof.((|>-^)-+-icof.(Cl)H-0)— icof.(2^-Cp>:jcof.(2^-+-Cl)). 



§. 14. lam vcro cuidcns c([ , finguhis has pnrtcs in- 

 tegr.itioncm cffc admiffuras , fi modo anyuli Cj) ct rationcm 

 intcr fe tcneant rationalcm. Sit igitur CP r: X P, cxillcnte X nu- 

 mcro quocuiujiic, (iuc intcgro, fiuc fracto, fiuc politiuo, fiue 

 nc.;atiu(), c]uin ctiam gcncralius Hatui poterit Cj) ~ X ^ -H a , 

 quo fado iiabcbimus 



J* — i fin. [(X-4- i)0-4.a]-+-ifin. [(X— i) ^ -4- a] 

 -f- i fin. [ (X -4- 2) d -+- a] — i fin [^X — 2) $ -+- a), 



^y zr i cof. [(X - i) e -H a] -4- i cof. [(X -4- i ) e h- a] 

 — i cof. [(X — 2) a -H a] -+- i cof [rx -H 2) ^ -H a] , 

 tum autcm intcgracio nobis pracbcbit illas cxprcirioncs : 



^ co/. [ X-H)»4-a ) co/. [ I X — I ) 9 4- g] eoj. [lX + t) »4-«l 



*" a(X-»-i) ■ ^ — I) 4(A-t-a) 



I . coj. [ ( X — » ) » + a] 



^ 4lX^») ' 



,, — I fin.[ i X — t) » + a] I / i?i. f (X -»- i)»-*-n1 fin. [iX — oK f- g] 



•^ »lX — i) . 1/11-11 41^ — •) 



. I Jin. [ ( X -»- 1 1 ♦ -h_a] 

 ~ 4IX-4-11 ' 



quac formulac fcmpcr crgo crunt algcbraicae, nih fuciit vcl 

 X~_f_i, ^ti Xzz:;_H2. 



§. 15. 



