f." ix. Qtio regulae noftrac generali plus lucis at- 

 feratur, ad cafus quosdam fpeciales eam applicare iuvabit. 



Pro factoribus JlmpUcibus y ~ a x -f- b eft n ~ i et 

 A n — " I y — A°y — /, ideoque ipfa faccorum fpecialiurn fe- 

 ries erit progreffio Arithmetica , cuius differentia J — » 

 ($. ic), fietque b ~ h ~ 0, feu factor y valori x zz: o re- 

 fpondens (V. tab. §.■ 5.),. confequenter y ~ B x -+- 0. 



Pro erdendis faftoribus duplicibus y~axx-\-bx 

 -f- c, eft uz: 2, ideoque A n ~~ 2 (ct x x — y) ~ a x x — y, 

 h. e. feries reliduorum progreffio Arithmetica et a ~ a, 

 h~-±_^ 9 c~ — O, ubi fignum fuperius ( -\- ) aut inferi- 

 us ( — ) adhibetur, prout in ferie refiduorum termini fupe- 

 riores ab inferioribus, aut hi ab illis fuerint- fubtracli. Eft 

 itaque vh § — O — 9 c ~ $1 — - m , etc. et — S ~ m. — O 

 ~\ Wl — 9? , etc. unde reperitur facTor duplex 



y~ a x X -f- ( O — W;) x — O. 



Binis hisce cafibus regula Neutoniana ■' continettir (§. 2.), ■ 



Si factores triplices y ~ a x 3 -f- b x x '-+■ c x '+- cZ quae-- 

 rantur, eft /2=5, et A n — 2 (54 x 3 — y) = A (a x 3 — fj pipgfes 

 fio Arithmetica differentiae ?, ideoque a~a, h~ 

 d~ — 0, et d-f- c-*-b~-$l ($. 8.>i h. e.-czzO-i 

 et j=zax ] + ^ >xx-|-(0 — m =h | d) x — O. • 



7 V 



| 



2 ? 



,„4 



Pro inveniendis factoribus hiquadratis y~ a x q 

 li x? H- c x 2 h d x ~f- e, eft . A 2 (% xf — y) progreffio Arithrrie- 

 tica, cuius differentia . fit zz: 5; proinde o- zz a 9 h — -4 \ l , 



