We define the positive, negative and companion rules. From a given pair of the companion rules we construct a new rule, which we call the combined rule and it has a higher degree of precision. Then we focus separately on families of the companion two-point rules and families of the companion three-point rules and we state some facts which apply to them. In what follows, $\Theta$ denotes the set of rules with degree $m$ and we define the transformation $W: \Theta \times \Theta \to \Theta$. Then we can define the mean rule $W(g)$ and state that it has a degree of at least $m+1$, whereas beginning rules $A(g)$ and $B(g)$ have degree $m$. At the end we focus on the rules of arbitrary degree with rational nodes, where we combine rules of degree 1 and from them we construct a new rule of a higher degree. With that we provide the numerical stability; because of the rationality of the nodes it doesn't come to intermediate rounding.
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