enfin
12. La valeur de n {\displaystyle n} est ici égale à 1 − 1 z 3 2 , {\displaystyle 1-{\frac {1}{z^{\frac {3}{2}}}},} ce qui donne
Par ces substitutions la formule des inégalités dues à Vénus deviendra
![{\displaystyle {\begin{alignedat}{2}r'''[r''',r^{\scriptscriptstyle {\text{IV}}}]_{6}=&0{,}089538\qquad \qquad &\log .\quad &8{,}9520073,\\r'''[r''',r^{\scriptscriptstyle {\text{IV}}}]_{7}=&0{,}059894&&8{,}7773862,\\r'''[r''',r^{\scriptscriptstyle {\text{IV}}}]_{8}=&0{,}040119&&8{,}6033502,\\\ldots \ldots \ldots \ldots &\ldots \ldots \ldots &&\ldots \ldots \ldots ,\end{alignedat}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a8aeba2b12aca9bbdf77cd1bc6f3c7e1a45fc5d5)
![{\displaystyle {\begin{alignedat}{2}2r'''^{2}{\frac {d[r''',r^{\scriptscriptstyle {\text{IV}}}]}{dr'''}}\ \,=&-3{,}556045\qquad \qquad &\log .\quad &{\overline {0}}{,}5932815,\\2r'''^{2}{\frac {d[r''',r^{\scriptscriptstyle {\text{IV}}}]_{1}}{dr'''}}=&-5{,}171886&&{\overline {0}}{,}7136489,\\2r'''^{2}{\frac {d[r''',r^{\scriptscriptstyle {\text{IV}}}]_{2}}{dr'''}}=&-4{,}049450&&{\overline {0}}{,}6073961,\\2r'''^{2}{\frac {d[r''',r^{\scriptscriptstyle {\text{IV}}}]_{3}}{dr'''}}=&-3{,}162854&&{\overline {0}}{,}5000790,\\2r'''^{2}{\frac {d[r''',r^{\scriptscriptstyle {\text{IV}}}]_{4}}{dr'''}}=&-2{,}451637&&{\overline {0}}{,}3894561,\\2r'''^{2}{\frac {d[r''',r^{\scriptscriptstyle {\text{IV}}}]_{5}}{dr'''}}=&-1{,}887421&&{\overline {0}}{,}2758688,\\2r'''^{2}{\frac {d[r''',r^{\scriptscriptstyle {\text{IV}}}]_{6}}{dr'''}}=&-1{,}445683&&{\overline {0}}{,}1600731,\\2r'''^{2}{\frac {d[r''',r^{\scriptscriptstyle {\text{IV}}}]_{7}}{dr'''}}=&-1{,}104162&&{\overline {0}}{,}0430328,\\2r'''^{2}{\frac {d[r''',r^{\scriptscriptstyle {\text{IV}}}]_{8}}{dr'''}}=&-0{,}843539&&{\overline {9}}{,}9261051,\\\ldots \ldots \ldots \ldots \ldots \ldots &\ldots \ldots \ldots \ldots &&\ldots \ldots \ldots ,\end{alignedat}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/4e58c5f62e2910446ac0dade7afe86170e81e622)
est ici égale à 
ce qui donne
![{\displaystyle {\begin{aligned}-\mathrm {T} ^{\scriptscriptstyle {\text{IV}}}&\left[+9{,}820869\sin \ \ (p'''-p^{\scriptscriptstyle {\text{IV}}})-11{,}168298\sin 2(p'''-p^{\scriptscriptstyle {\text{IV}}})\right.\\&-1{,}379716\sin 3(p'''-p^{\scriptscriptstyle {\text{IV}}})-\ \ 0{,}418198\sin 4(p'''-p^{\scriptscriptstyle {\text{IV}}})\\&-\left.0{,}169076\sin 5(p'''-p^{\scriptscriptstyle {\text{IV}}})-\ \ 0{,}079229\sin 6(p'''-p^{\scriptscriptstyle {\text{IV}}})-\ldots \right].\end{aligned}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/796bc055c3374398eb98f4bf17b1be5115f3d738)
