158 METHODVS VNIFERSALIS 



poaatur rumma rzS.ABC VX. Abibit erga 



haec fumma pofito x-b loco x in hanc ABC - - V 



(S-fl^-i-^.-rSetc.) quae aequahs efle de- 

 bet priori fummae demto termino vltimo, id eft huic 

 quantitati AB V(SX — X). Hanc ob rem ha- 



bebitur ifta aequatio b X — X iz:: o — 775* ~H ndw*""7md3c* 



b*d*S 



i.i.z.\dx* etC. 



Ex hac aequatione valor ipfuis S crutus erit ifte 

 S~xzr, H-E-|-F-t-G-4-etc. qui termini ita progre- 



progrediuntur , vt pofito xirT = D fit E=z: |^_,)^^ ^Fz=: 



— 6aE , b^ddP f~< — 6ctF_ _■ ^»^dd E 



i(X— i)d»:~i~i.2(X— i)dK» 7 ^ i(X— i)d*~T-,.2(X— i)dx* 



7.' 2 ^[x—iTdx' i atque ita porro. Adeo vt fumma feriei 



propofitae fit :=ABC VX(D-|-E -i-F-f-G 



etc). Seriei vero in infinitum continuatae 



ABC VX-+-ABCD VXY-f-etc. 



fumma erit z=ABC VX(i-D-E-F-G 



etc. )H-Conft. Vt fi quaeratur fumma huius 



feriei -,-7^:771 irrs" -+- ,.2.z ---- «(«-t-T; H- etc. in infinitum 

 crit ^zri, X— ^, atque D—.—. Tum vero E — 

 (TE^ i F — *73^etc. fumma ergo feriei propofitae ob 

 conftantem euanefcentem erit — rTizrni i -1- ^^-(iziTr. 

 -4- (Sryi' etc). h"x his vero traditis facile intelligitiir, 

 cuiusmodi fummae formam afliimere oporteat in quouis 

 cafu oblato, quo fumma minimo labore inueniatur. 



CVR- 



