COMMENTATIO SECUNDA. 
145 
— 2 hy = 6 
stit in tribus 
i — 6)r] + aC, 
numeros po- 
»rro quum sit 
im F [a — 6), 
icare tertiam 
— b), condi- 
bus ipsius X 
et £ positivi 
valore itaque 
- iM+S[«->”] 
Sed fit. scribendo terminos inverso ordine, 
’ / 
- [f.] + [H] + [n]+ • • • • ■+[ (S T S ’ , 1 = ») 
Formula itaque nostra sequentem induit formam: 
g = cp(a— 6, a+6) + <p(2 6, a) — <p(«, 6) —cp(6, a)+£6 6 
Consideremus primo terminum cp(« — 6, a -f- 6), qui protinus transmutatur 
in cp(^ — 6, 2 6) —(— 1 —|— 2 —|— 3 —|— etc. —(— — 6 —l) sive in 
?(« — &. 2b)-\-i({a—6) 2 — 1) 
sumus (Conf. 
r. de residuis 
4( a — 
concilientur, 
— 2 a x 
20 : q^re 
Uein quum per theorema generale fiat cp(i, w)-|-cp(w, i) = [F^] • [F^]» dum 
t, u sunt integri positivi inter se primi, habemus 
cp(« — 6, 2 6) = ±b{a — 6—1) — cp(26, a—b) 
adeoque 
<p(a — b, a-{-b) = ^[aa-\-1ab—3bb — 4 6—1) — cp(2 6, a — 6) 
Disponamus partes ipsius cp(2 6, a — 6) sequenti modo 
se 
l^J+[% 1) ] + l%- ) ]+ etc. + [fcil£zJ] 
+[“7 i ]+[ 2( T i) ]+[ 3( T i) ]+ etc - +[^F J) ] 
Series secunda manifesto fit 
itegros ipsius 
ad i {a —i), 
— cp(6, a — b) = cp(6, a) — 1 — 2 — 3— etc. —\b = cp(6, a) — i(66-|-26) 
seriem primam ordine terminorum inverso ita exhibemus: 
itato (Theore- 
[$■(«+1—b)— ^] + [4(«+ 3 — & )—+ — 6 )~2l] + etc - ^ 26 ] 
quae expressio, quum denotante t numerum integrum, u fractum, generaliter sit 
i t — u\ = t—1 — \u ", mutatur in sequentem 
m [-fi], ter- 
indus vero fit 
*6(a«—4 —6)—[|g—[‘-3— etc. -[<V1 
= i-b (2 a — 4 — 6) — 9 (2 6, a) -|- (6, a) 
19