94 



(n) -i-xAn -h x^'A^n + x'''A^n 4- etc — (x ~\-n), 



quarum suinmae, cuni sint nihilo aequales^ omnes quotcun- 

 que fuerint, -cum 2:x junctum sumtae, nihilominus termi- 

 nuni summalorium expriment. Sumantur ergo pio u suc- 

 cessive omnes numeii 1, 2, 3, /\, etc. et tola expressio 

 secundum columnas verticales, singulis valoribus x, x , x', 

 etc. respondentes, sequenti modo disponantur : 



Expressio generalis pro termino summatorio. 



X (1) -I- x^ A 1 -+- x^'' A^ 1 -^ x'^^'A^ 1 -+- etc. 



(1) -^ X A 1 + x' A^ 1-4- x''^ A' 1 4- x^^^ A* 1 -t- — (x 4- 1) 



(2) H- X A 2 4- X^ A^ 2 4- x''' A^ 2 4- x'^'' A-* 2 4- .... . ■ — (x H- 2) 



(3)-hxA3 4-x'A^3 4-x'''A'3-+-x''^A43 4- — (x4-3) 



(n) 4- X An 4- x''A-/z 4- x^'' A^n -+- A'^'^A'^n -h — (xh- n). 



§. 10. Etsi Veritas hujns expressionis nuUi amplius 

 dubio est obnoxia, tamen non parum juvabit, eam ex ipsa 

 forma confirmasse. Colligantar nimirum in imam summaai 

 singulae columnae verticales; ac primae quidem summa erit: 



(i)4-(2)-(3)-^(4)-^....-h(h) = 2:/^ 

 Secunda columna dat : 



X (i 4- A 1 4- A 2 + A 3 4- ... . 4- An). 



