X 14 METIH. FACIL. ATQVE EX?ED1T. INTECR. 



autem \ltcrius progrcflliri indu<flionc non indigemus ; fi 

 cnim dcnominiuoris N tador {n (p-i-</-v)"; hincquc in- 



tcgnlis pars oriunda ponatur — A r, >,_. 77^ "^ 



N 

 ratiocinio fupra adhibito patcbit , pofito S ~ — — 7:;; 



per (p-f-^-v)" diuifibilcm cflc dcbcrc hanc cxprcllioncm 



f-A-B(p-i-^.v)-C(p-i-fvf-D(/)+^.v)'-E(p-t-^.v)*-etc. 



Tam igitur hacc ipfa exprclfio , quam cius diflfcrcntialia 



ordinis primi, fccundi, tcrtii,ctc. vsquc ad ordincm tj-i 



inclufiuc fingula per p-h^.v diuifibilLi cflTe oportet , 



I - A - B (p-i-f v) - C ip-\-gxy - D ( p-^qxY- E ( p-^-qx)*- ctc. 



d.^-'Bqdx-:LC{p-\-qx)qdx-:iE>{p-{-qxyqdx-ct.c. 



dd.^-^C qdx- 6 D [p->t-q.x)qdx"- x i E (p-f-f v) V V.v'-ctc. 



d"l-6 Dq'd.x' - z^E{p-\-q.x)q"dx- 60 F (p-f^ v)^V.v'-etc. 



d:~-24Eq*d.x*-izo¥ip-\-qx)q*dx*-ctc. 



d!^-i2o¥q'd.x'-ctc. 



Qiiod fi inm pon.itur p-H^.v— o (cu .v — =^ , finguhc 

 iltac cxprcfiioncs cuauclcunt ; indcquc rcpcritur 





D aqfdx' ^' S 



E ~ t*q*dx* "■ S" 

 i.,flMjc» "• S" 



etc 



Ex 



