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

152 
DE FORMIS SECUNDI GRADUS. 
reliquae totidem sunt multitudine et ex illis oriuntur, tribuendo terminis exteris 
signa opposita; idemque valet de formis ex reductis reiiciendis et remanentibus. 
176. 
Ecce itaque pro determinantibus quibusdam negativis tabulam formarum, 
secundum quas omnes reliquae eiusdem determinantis in classes distingui possunt; 
apponimus autem, ad annotat, art. praec., semissem tantum, scilicet eas quarum 
termini exteri positivi. 
D 
1 (1, 0, 1). 
2 (1, 0, 2). 
3 {1,0, 3), (2, 1, 2). 
4 (1, 0, 4), (2, 0. 2). , 
5 (1,0, 5), (2, 1, 3). 
6 (1,0, 6), (2, 0, 3). 
7 (1, 0, 7), (2, 1, 4). 
8 (1, 0, 8), (2, 0, 4), (3, 1, 3). 
9 (1, 0, 9), (2, 1, 5), (3, 0, 3). 
10 (1, 0, 10), (2, 0, 5). 
11 (1, 0. 11), (2, 1, 6), (3, 1, 4), (3,-1, 4). 
12 (1, 0, 12). (2, 0, 6), (3, 0, 4), (4, 2, 4). 
Superfluum foret hanc tabulam hic ulterius continuare, quippe quam infra 
multo aptius disponere docebimus. 
Patet itaque, quamvis formam determinantis —1, formae xx-\-yy pro 
prie aequivalere, si ipsius termini exteri sint positivi, vel huic —xx—yy, si 
sint negativi; quamvis formam determinantis — 2 , cuius termini exteri positivi, 
formae xx-\- ‘lyy etc.; quamvis formam determinantis —11, cuius termini ex 
teri positivi, alicui ex his xx-\- Wyy, ‘Ixx-^lxy 6 yy, Zxx-^-^xy-^X yy, 
%xx—lLxy-\-\yy etc. 
177. 
Problema. Habetur series formarum, quarum quaevis praecedenti a parte poste- 
riori contigua: desideratur transformatio aliqua propria primae in formam quamcun 
que seriei.
	        
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