De VSV SUBTRACTIOPHS ETC. 527 



8. ^ n -t- 1 loco n scrihiiur, ex praecedenli numero eruitur, 

 serie inversa , 



1 Jl (1 )_H . . . H-1 ('"-1 )]-f-[l ri )-4- . ."h_1 ("-Hi 1+- . . . -4_[l ( 1 )-t- . "-4-1 ("■*-' J 

 m(wj-+-1 ) . . . (m-^ii) 



~ ~1 .2.3...(«-h1) ' 

 sive ex formula (D) 



1.2....n 2.3....(«-l-1) 3.4....(«^_2) 



■+■ 



1.2....n1.2 n 1.2.... n 



m(m-^-^ ) . . . . (m-+-« — 1 ) w(fft-(-1 ) . . . . (/m-i-m) 

 ■■■"^ 1 .2 « ~ 1 .2.3.... {n^) ' 



Ilaec relatio est eadem , quam perillustris Geometra C^auchy 

 exhibuit , ex qua deducit theorema relatura in nola sexia (1) 

 addila primae paili Cursus Analyseos . 



9. Si vero praecedcnlis aequalionis ainbo membra per 

 1 .2.3 n muliipliccntur , theorema habebimus 



1 .2.3 . . .«H- 2.3.4 . . .(n-Hl)H-3.4.5 . . . («-4-2)-i-. . .H-m(nn-1)...(/7»-t-n_1) 

 1 



= r . TO(TO-f-1 ) . . . (7/j_)_7;). 



n-t-1 



Talis demonslratio est expedita, ac brevis (rebus quae antea 

 exposuimus , bene perspectis), et si lubei, comparari potest 

 cum eaj quam Geometrae Le-Grande, atque Rochat dederunt 

 (2), quamque brevissimam Gergonne nimcupavit, et hac de 

 causa in suis Annalibus retulit. 



10. In formula (C) scribi potest m loco ii, et viceversa, 

 undo oblinetur 



(E) [i (1 )^'7. . -1-1 («)]=[i (1 j-fTT. . -t-1 ("■)] . 



Reapse habcmus ab exposilis 



Ln, ""'' ^, .^ /n(7n-Hl)...(7«-H«— 2) 1.2.3...(m— 1>i...(m-t-«_2) 



L10)-t- f-1(»)J=— — — :: •== ^ ■ ^^ . 



1.2.3 («— 1) 1. 2. 3. ..(«»— 1). 1.2.3. ..(«—1) 



^.M^ "~\. ^l "f«M-1 )...(«-»-'«— 2) 1.2.3...r«— 1)« («-f-m— 2) 



- 1.2.3 (m_1) 1.2.3...(«— 1).1.2.3...(/»— 1) 



(1) Pag. 531. 



(2) Annales de Matliematiques I. 3. pag. 60. 



