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SUPPLEMENTUM THEORIAE COMBINATIONS OBSERVATIONUM 
nec non 
x' = N 10 {n 00 x°-\-n 01 x'-\-n 02 x'-^-n 03 x w -\- etc.) 
-f- N 11 (w 10 ^°-f- n n x'-\- n { ~x-[- n rs x'"-j- etc.) 
-f- JY 12 (w 20 <2?°-f- n 2[ x-\- n' 2 x"-\- n 23 x'"-\- etc.) 
^N r3 [n M x^-{-n 31 x'-\-n 3 ' 1 x-\-n 33 x'"-{- etc.) etc. 
Quum utraque aequatio manifesto esse debeat aequatio identica, tum in 
priore tum in posteriore pro x°, x, x", x'"etc. valores quoslibet determinatos sub 
stituere licebit. Substituamus in priore 
x° = N 10 , x = N u , x = N n , x"= N 13 etc, 
in posteriore vero 
^^iV 00 , x=№\ x”=№ 2 , x'”=N 03 etc. 
His ita factis subtractio producit 
N 10 — N 01 = {№°N n — N l0 N 0l ){n 01 — n 10 ) 
(jvoo N a _ N io N 02j ( w 02 _ ^20J 
4- (iV 00 N 13 — N 10 N 03 ) (n 03 — n 30 ) 
—j— etc. 
_J_ (iVOl N n _ N n N 02 ) ^12 __ W 21 ) 
+ {№ l N 13 — N n N° 3 ) (w 13 —w 31 ) 
—(— etc. 
+ (.N 02 iV ,s — N n N 03 ) (rc 23 — /* 32 ) 
-(- etc. etc, 
quae aequatio ita quoque exhiberi potest 
N 10 — N m = iV^iV 06 )^ 6 —K 6 '- 1 ) 
denotantibus ab omnes combinationes indicum inaequalium. 
Hinc colligitur, si fuerit 
,01 
n u \ n 02 
w 20 , w 03 = n 30 , w 12 
ra 21 , /i 13 
n 31 . a 23 
w 32 , etc. 
sive generaliter n Uj = n jrx , fore etiam 
N 10 = N 01