154 METHODVS VNIVERSAUS 



res formulas fummatrices erui coniieniet, Sit itaque 

 ifta Series 



a, n-+-&. a-f-i6 st 



A 72" H- B n^-^^ H- C n"-^'^ -\ X n* 



ad iummandum propofita ; ponaturque fumma — S«*. 

 Haec formula autera pofito x—b loco x abibit in hanc 

 «* ( 5 - ,-s^ -f- ,:id^ - rr-dT^ + etc. ) quae aequalis efle 

 debet priori fummae Sn^ demto Yltimo termino X«*. 

 Habebitur ergo ifta aequatio S«^ — X «^ — S — 7;^^+ 



ndr^-iXIdi'-HTTX7dl^- etc. Ex qua aequationc 

 valor ipfius S erui debet. 



§. 13. Ponatur igitur «^ — ;«, eritque S =" -^:z", — 



abdX . e^^ddX 'yb^d^X , ifc*d*X 



«(m—i )*d;c — 1~ 1.2(771— 0'dJi* 1.2.3 (m—O+dx-^ ' ' i.i.3.4(m— j)5d3c* ~~ 



,-;^^^^^^«^^5 H- etc. Hinc terminis homologis com- 

 parandis pofito breuitatis ergo m~iz^p vt fequitur 

 a 3= ?« 



g— 2a-Hw^p 



Szzz^y-\-6^p-\-4.ap-~hmp' 



e — 5 5"-i- 10 Y/j-h 10 gj)--H5 a^'-|-»/p* etc. 



vnde pro litteris a, S, y, (S' etc. fequentes obtinentur 

 valores : 



a ~ m 



^:rz2m -\-mp 

 Y n: 6 //7 -\-67np 4- w/p* 

 ^ — 24. 7» -h 3 (J /z^/) -I- 1 4 w/>' -4- wj!>* 

 ezi:x 20 m-\-2.^Q mp-\-is o mp--\-:^o mp^-\-mp* etc. 



hic 



