Full text: [Disquisitiones arithmeticae] (1. Band)

FORMAE TERNARIAE. 
315 
277. 
Eegulae, per quas omnes formae in I et II art. praec. erui possunt, ex 
ipsarum explicatione sponte defluunt; quare sufficiet quaedam exempla apposuisse. 
p r0 D = 1, formae I hae sex (per ambiguitatem signorum) prodeunt 
(0, 1, 0\ /0, 1, ±1\ 
'0, +1, 0' ’ '0, +1, 0/ 
in formis II a et A" alios valores quam +1 et —1 habere nequeunt, pro sin 
gulis quatuor combinationum hinc oriundarum h”, B et B' poni debent — 0, 
unde emergunt quatuor formae 
f 1 ’- 1 ’ l ) 
v 0, 0, o' ’ 
/—i, i, i\ C’ h 
^ 0, 0,0'’ ^ ’ 
(.—1, —1, 
v 0, o, 
"i) 
Simili modo pro D = — I. 
sex formae I quatuorque II habentur, 
/0, — 1, 0 \ /0, -1, ±l\. 
\0, +1, 0' ’ U, +1, o' 5 
/1, —i, -n (—1,1,— 
^0, 0, o' ’ V 0, 0, 
i), (i: 
i, 1\ 
0, 0/ ’ 
Pro B — 2 sex formae I proveniunt 
/0, 2, 0\ /0, 2, ±i\ 
''O, +1, o' ’ 1 0, +1, 0 ' 
octoque formae II 
(b - 1 ’ 2 ) 
v 0, 0, 0 ' ’ 
1, 2\ /1, 1, —2\ 
v o, o, o' ’ v o, o, o' ’ 
("i: 'i; 
- 2 .), 
f 1, —2, n 
' 0, 0, o' ’ 
f—u 2, n fl, 2, —1\ 
' 0, 0, o' ’ '0,0, o' ’ 
f— 1, —2, 
v 0, 0, 
-i) 
Ceterum multitudo classium ex his formis in his tribus casibus prodeuntium 
formarum multitudine multo minor est. Scilicet facile confirmatur 
I. Formam (°’ 1 » 0 ) transire in 
v o, i, o/ 
/0, i, 0\ (0, 1, 1\ 
' 0, —1, O'’ U, ±1, 0' ’ 
f0, i, —1\ 
W, +1, o' ’ 
1, 
0, 
— 1 N 
0 ' 
resp. per substitutiones 
1, 
0, 
0 
0, 0, 1 
0, 
0, 
1 
0, 
1, 
0 
0, 1, —1 
0, 
1, 
1 
0, 
0, 
—1 
±1, 1, 0 
+1, 
—1, 
—1 
formam i 1 ’ 1 ) autem in i 1 » — 1 > 1 ) (—M per solam indeterminatarum pei 
v °’ °» . v o, o, o'’ v 0, o, o' ^ , . 
mutationem. Quare illae decem formae ternariae det. 1 ad has duas reducuntui 
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