${\displaystyle {}n\geq 1}$

${\displaystyle {}x_{n}^{2}\geq c\,}$

und

${\displaystyle {}{\left({\frac {c}{x_{n}}}\right)}^{2}\leq c\,.}$

${\displaystyle {}[{\frac {c}{x_{n+1}}},x_{n+1}]\subseteq [{\frac {c}{x_{n}}},x_{n}]\,}$

für ${\displaystyle {}n\geq 1}$.

${\displaystyle {}\ell _{n}:=x_{n}-{\frac {c}{x_{n}}}\,}$

gilt die Beziehung

${\displaystyle {}\ell _{n+1}={\frac {1}{4x_{n+1}}}\ell _{n}^{2}\,}$

und bei ${\displaystyle {}c\geq 1}$ gilt insbesondere

${\displaystyle {}\ell _{n+1}\leq {\frac {1}{4}}\ell _{n}^{2}\,.}$