Pagina:Gauss, Carl Friedrich - Werke (1870).djvu/110

100

de congruentiis secundi gradus.

collato theoremate fundamentali cum theorematibus art. 111, sequentes propositiones facile deducentur.

	Si		erit
1.	$\quad \pm aRa'$	$\ldots \ldots$	$\quad \pm a'\!Ra$
2.	$\quad \pm aNa'$	$\ldots \ldots$	$\quad \pm a'\!Na$
3.	$\left\{{\begin{matrix}+aRb\\-aNb\end{matrix}}\right\}$	$\ldots \ldots$	$\quad \pm bRa$
4.	$\left\{{\begin{matrix}+aNb\\-aRb\end{matrix}}\right\}$	$\ldots \ldots$	$\quad \pm bNa$
5.	$\quad \pm bRa$	$\ldots \ldots$	$\left\{{\begin{matrix}+aRb\\-aNb\end{matrix}}\right.$
6.	$\quad \pm bNa$	$\ldots \ldots$	$\left\{{\begin{matrix}+aNb\\-aRb\end{matrix}}\right.$
7.	$\left\{{\begin{matrix}+bRb'\\-bNb'\end{matrix}}\right\}$	$\ldots \ldots$	$\left\{{\begin{matrix}+b'\!Nb\\-b'\!Rb\end{matrix}}\right.$
8.	$\left\{{\begin{matrix}+bNb'\\-bRb'\end{matrix}}\right\}$	$\ldots \ldots$	$\left\{{\begin{matrix}+b'\!Rb\\-b'\!Nb\end{matrix}}\right.$

132.

In his omnes casus, qui, duos numeros primos comparando, occurrere possunt, continentur: quae sequuntur, ad numeros quoscunque pertinent: sed harum demonstrationes minus sunt obviae.

	Si		erit
9.	$\quad \pm aRA$	$\ldots \ldots$	$\quad \pm ARa$
10.	$\quad \pm bRA$	$\ldots \ldots$	$\left\{{\begin{matrix}+ARb\\-ANb\end{matrix}}\right.$
11.	$\quad +aRB$	$\ldots \ldots$	$\quad \pm BRa$
12.	$\quad -aRB$	$\ldots \ldots$	$\quad \pm BNa$
13.	$\quad +bRB$	$\ldots \ldots$	$\left\{{\begin{matrix}-BRb\\+BNb\end{matrix}}\right.$
14.	$\quad -bRB$	$\ldots \ldots$	$\left\{{\begin{matrix}+BRb\\-BNb\end{matrix}}\right.$