I 138 



Problema ^. 



§. i6. Piopofitis binis fcriebus i)ifiiiitis: 

 G - fin. ■'-h[^]uCin.(x~^<P)-t-[l]a'Cm.{a-hi<P)-^eXc. 

 H=cof.aH-[J]ncor.(aH-(I))-H[?,ja'cof.(..-f-2(r>)^elc. 

 utrlusquc Jummam inveftigare. 



Solutio. 

 Ilic fcilicet characloivs tuicinulis inclufi denotant 

 coofncienles pofeftatis binoinii /i'"'. Polito igitur, ut liafle- 

 nus, a — X 4^, ila ut fcries propofitae hanc formam induant: 

 G := fin.XCp-f-[ j Ja fin. (X-f- i,(t)-t-[ 2 Ja' rin.(X-f- 2 )4)-+- ctc. 

 H — cof. X(p-^[^] a cof.(XH- 1 jCp-t-[^Ja'cor (Xh- 2 )cp-^ ctc. 

 habcbinuis 



H-hG /- I =:p'^'^['i]ap'^-^'-h[l]a'p^^--he{c. 



ziz p'^ (i -hapf, 

 H-G/- I =r9^-+-[^]a9^-^^-H[^]a'q^-^^-hetc. 



-q^li-^aii)\ 



confcquenter 



2 H - / ( I -I- a py -hq^^ii -^-nq)", 

 2G\/ ~ i =y {i -I- u pf — r/^ ( i -f- fl r/)\ 



Cum igitur fit 



I H- fl p = I -I- o cof. 4) -t- « / — J fin. Cp, 

 I -+- a 7 = 1 -I- fl cof. Cp — fl >/ — I fin. Cp, 



fi hacc ita rcpracfenlcmMs: 



i-\-ap = { I -f-flCon(|); ( I -I- "1'-;'^:^ )> 



,-t-fl7^(i-i-flC0f.t)(x~--,-^^i^^ 



po- 



