PROPORTIONALIVM. ^ot 



erlt ex earum indole i»^"^— Lb-{'M.c~\-Nraet 

 e'^"-'Zz:Lc-\~Mra-i~Nrb at lcx progreflionis prae- 

 bet fcquentes terminos : 



^(n-^o__jL4-Mr+Nr)^+(L+M+Nr)<:+(L-fM+N)m 

 ^nH-T)__^L+Mr+Nr)^+(L+M4-Nr)ra4-(L-i-M4-N)r^. 

 Hinc fi generaiius ftatuamus : n 



a-i-a^x-i-a^^x^-lr-a^^^^x^-^-etc, zzVa+Qb+Kc eilt ^ 

 b^yx^y^x^-^-y^^x^ + etc, —P^+Q^^+Rr^J 

 c^c^x-^-c^^^x^-i-c^^^x^ + ctc.zziTc+Qra+Rrb, 

 Addantur hae feries inuicem , et quia eft 

 a-\-b-i-cz=a^, a^^y-hc^zna'', a'^+b^^+c^^z:a^^^ crit 

 /?''4-«^^A:4-fl''^V>4-etc.-(P4-Q.?'-i-Rr)^+(P+Q4-Rr)^ 



^-(P-i-^i-i-R)*^ 



qnae per x multiplicata et a prima fubtrada dat 



ti—Ta-hQb-^-Kc - (P-4-Qr^- Kr)ax- (P-f-Q-f-Rr) b x 



-(^-\-Qs\-r)cx, 



Quia autem quantitates P, Q , R litteras ^, b^ c 

 non inuoluunt , hinc nafcuntur tres aequationes : 



I. irP-Pjt-QrA-Rnv i=P-Q-Q(r-i)jkr 



II. o:zQ:-P.t-Qjt: -Rr^; hincque orQ-R-R(r-i)x 

 lU: OT,K-?x~q_x -Kx i-P-R-(Q+R)(r-i)T. 



Pro faciliori refolutione {latuamus i^x-^-rxzzz 

 et fequens combinatio praebebit t 



i Tom. XIV. Nou. Comin. C c I-II 



