24 
SUMMATIO QUARUMDAM 
fir, n—1) = 1-J-r 1 —|— r 3 —[-r 6 -f-etc, -\-r *)“ 
= (1 — r) (1 — r 3 ) (1 — r 5 ) .... (1 — r n ~ 2 ) 
Eadem aequatio etiamnum valebit, si pro r substituitur r\ designante X 
integrum quemcunque ad n primum: tunc enim etiam erit radix propria ae 
quationis x n —1 = 0. Scribamus itaque pro r, r n ~~' 3 sive quod idem est r~ 2 , 
eritque 
1 r 2 -f- /' -f- r 12 -)- etc. -f- r( n ~^ n = (l — r -2 ) (1 — r —1B ) (1 — r~ l0 ) . . . (1 — t 2 ( n 2 )j 
Multiplicemus utramque partem huius aequationis per 
r r 3 , r 5 . . 2 ^ = r^ n ~^ 2 
prodibitque, propter 
r 2+l(^-l) 2 _ r i(n-3f r (n-l)n+i(w-l) 2 __ r |-(n+l) 2 
r 6-H(w-l) B __ r i(«-5)^ r (w-2)(w-l)+i(n-l) 2 __ r i(w+3) 2 
r 12+l(w-l) 2 __ r i(n-7)^ r (w-3)(n-2)+A(w-l) 2 __ r l(«+5) 2 et( . 
aequatio sequens 
r i(n-l) 2 _|_ r i(w-3) 2 _|_ , r -t(«-5) 2 _j_ etc _ _|_ r I 
r i(«+l) 2 _)_ r i(w+3) 2 _|_ r i(«+5) 2 _|_ etc> _|_ r i(2n-2y- 
— r — l )(r*—r —3 )(r 5 — r —5 ) .... [r n ~ 2 ?~ n + 2 ) 
aut. partibus membri primi aliter dispositis , 
1 —f— r —[— r* —etc. _/•(«—*)* — — r -1 ) (r 3 —r~ 3 ) . . . [r n ~ 2 — r ~ n+2 ) . . [5] 
13. 
Factores membri secundi aequationis [5] ita quoque exhiberi possunt 
r — r~ l = — [r n ~ l — r~ n+l ) 
/• :5 r —' 3 — 3 r —«+S\ 
r 5 —r —0 = —(r n—5 — r~ w+5 ) etc. 
usque ad 
r n ~ 2 — r“ n+2 = — [r 2 — r” 2 ) 
quo pacto aequatio ista hanc formam assumit: