DE SERIEBVS RECVRREKTIBVS 97 



fzzSY-^-^YV-h 2.v^H-4)"*'- ^^'S^ obtinethaccferies 

 0.0.0. 1 .8. 70.6 1 o. 5 3 1 5i:.4.63 3 2&c.vndej>'=-pV^\^2V 

 eixz^2-f^^y^^-s^ ) qiiae nidix certe longe exadiilima 

 ell: , it.i vt diibitem , pofTe vJla alia methodo iUam 

 tam breiii compendio eademqiieaccuratione obtine- 

 ri. Sit porro radixqiiadrata extrahenda ex 2,5 jerit 

 xxz:z26; ponatur .r— J-I-5 •, erit recfte difpofitaae- 

 quatione izrio) -f-.rr : hinc habetur feries - 

 o. I. 10, loi. 1020. 10301. 104030. ergo 

 — 10301 ^ ,, /g \/ 06 — ^10301 — 



5,0990195 I 3(5o,et per reguhim ordinariam inue- 

 nitur 5. o 99 01951359, qui duo numeri fola vni- 

 tate differunt. 



19. Supereflent quaedam adhuc , circa iam 

 dida monenda , pkirima vero noua dicenda j malo 

 autem haec lecftoris attentioni relinquere •, id fokim 

 fuperaddam , pofTe mcthodo noftra etiam radiccs 

 compofitas inueniri ; vehiti cum aeqiiatio propofita 

 hanc habet radicem compofitam .v"^ -f- <7.v'"~' -j- 



bx^-~- -f-i— 0, poffum proxime ope ferie- 



rum determinare litteras a,b — c modo non fint 

 imaginariae , quod faepe vfui venire potefl, necta- 

 men ab vllo edodum. Patet etiam regulam no- 

 ftram non fubfillcre modo in exemplis'numericis,fed fe 

 extcndere omninoad aequationes algebraicas, veluti 

 fifueritaequatio cubica generalis x — ax-\-bxx-\-cx'^ 

 formeturque feries 0.0.0. i.a.aa-\-b.a'^-^ 2.ab -\-c. 



^'^-\-:iaab-{-2ac-\-bb.a''-\-^a'^b-\-;iaac-\-2(ibb-\-2bc. 



4 

 &:c. erit proxime x—" -4-3ag^-4-2ac-j-6& ^^^5, 



a -+-4-a b-i-3aac-+-3abb-i-2bc 



Tom. 111. JSl fuiit- 



