'= (70 = 



cuius veritas fimul ex pulcheirimo confenfu huius Analyfeos 

 elucebit. 



§. 5. His igitur valoribus fubftitutis nancifcimur hanc 

 feriem : 



~lS=^-i-l. 5.?* -H I . £_|! + ^ . ^f -H etc. 



n n ~ n* -^ n° ^ n" 



Quod fi igitur ponamus -?-~jir,vt fit a*~ — , ifta feries hanc 

 induet formam: 



— / S r= A AT a: -f- i B X* H- ^ C Jc' -+- 1 D jc* -f- etc. 



Vt fradiones l, g, ^, etc. abigamus, difFerentiemus, ac facla 

 diuifione per 2dx confequemur. 



— 41- =iAjc-j-Bx^-i-C;c'4-Dj^^-h etc. 



2 S d X 



§. 6. Statuamus hic breuitatis gratia — ^y|^z=:r, vt 

 habeamus,- 



I zrr A jc + B jc' -I- C J*:' 4- D jf^ + etc. 

 vnde fumtis quadratis orietur haec feries: 

 «f rz: A^jcj<--+- ^ABjc'*-)- 2ACa-'-+- 2ADjf'-+- 2AE.v'°-+- etc. 



-+-BB -H2BC -+-2BD -f- etc. 



H- C C H- etc. 

 ficque iam pro quauis poteftate ipfius x eas nadi fumus for- 

 mulas, quibus determinatio litterarum A, B, C, D, contine- 

 tur: defunt tantum coefficientes illi |, |, ^, etc. 



§. 7. Hos autem coefficientes introducemus integran- 

 do, poftquam per 2dx multiplicauerimus. Rcperietur enim 



2judx =IA- x' -^l. zABx' -h}(zAC-^BB)x' 



-h I (2AD-+-2BC)j«:'-f-i\(2AE-+-2BD-+-CC).v"-f-ctc. 

 Cum nunc fit 



|A^ = B, |.2ABz=C, K2AC-f-BB)=i:D, etc. 



liis 



