Donc :
1o Si l’on prend le signe supérieur, et qu’on néglige les termes affectés de
on aura
![{\displaystyle \left[\mu _{2}^{2}-(\mu _{2}-2\mu _{1})^{2}\right]\left(\mathrm {A} _{1}+\alpha _{1}{\sqrt {-1}}\right)=0\,;}](https://wikimedia.org/api/rest_v1/media/math/render/svg/29cda8d78fa001f56572e604fddbb9f6b254a4f3)
ce qui donne
![{\displaystyle \mathrm {A} _{1}+\alpha _{1}{\sqrt {-1}}=0\quad {\text{et}}\quad \alpha _{1}{\sqrt {-1}}=-\mathrm {A} _{1}.}](https://wikimedia.org/api/rest_v1/media/math/render/svg/0245541878858f973b345ef0269a7d26a2ea19bd)
2o Si l’on prend le signe inférieur, et qu’après avoir ôté ce qui se détruit on divise toute l’équation par
on aura, en négligeant toujours les termes affectés de
![{\displaystyle {\begin{aligned}(\mathrm {V} )\quad \mu _{2}^{2}\left({\frac {\mu _{1}}{\mu _{2}}}v_{1}-{\text{ϐ}}_{2}\right)&\left(\mathrm {A} _{1}-\alpha _{1}{\sqrt {-1}}\right)-f_{1}\chi _{2}\left[{\overset {\circ }{\Psi }}_{1}(a_{1},a_{2})-\mu _{2}{\overset {\circ }{\Pi }}_{1}(a_{1},a_{2})\right]\\-&{\frac {1}{2}}f_{3}\chi _{2}\left[{\overset {\circ }{\Psi }}_{1}(a_{3},a_{2})-\mu _{2}{\overset {\circ }{\Pi }}_{1}(a_{3},a_{2})\right]\left(\mathrm {B} _{1}-\beta _{1}{\sqrt {-1}}\right)\\-&{\frac {1}{2}}f_{4}\chi _{2}\left[{\overset {\circ }{\Psi }}_{1}(a_{4},a_{2})-\mu _{2}{\overset {\circ }{\Pi }}_{1}(a_{4},a_{2})\right]\left(\mathrm {C} _{1}-\gamma _{1}{\sqrt {-1}}\right)=0.\end{aligned}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/39e3e14bb43f66378f0c30ea05588f968f857a98)
On tirera de même de l’équation
![{\displaystyle \beta _{1}{\sqrt {-1}}=-\mathrm {B} _{1}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/72083155565a51b2ea4186432f93db7b9806fc0f)
et
![{\displaystyle {\begin{aligned}(\mathrm {U} )\quad \mu _{3}^{2}\left({\frac {\mu _{1}}{\mu _{3}}}v_{1}-{\text{ϐ}}_{3}\right)&\left(\mathrm {B} _{1}-\beta _{1}{\sqrt {-1}}\right)-f_{1}\chi _{3}\left[{\overset {\circ }{\Psi }}_{1}(a_{1},a_{3})-\mu _{3}{\overset {\circ }{\Pi }}_{1}(a_{1},a_{3})\right]\\-&{\frac {1}{2}}f_{2}\chi _{3}\left[{\overset {\circ }{\Psi }}_{1}(a_{2},a_{3})-\mu _{3}{\overset {\circ }{\Pi }}_{1}(a_{2},a_{3})\right]\left(\mathrm {A} _{1}-\beta _{1}{\sqrt {-1}}\right)\\-&{\frac {1}{2}}f_{4}\chi _{3}\left[{\overset {\circ }{\Psi }}_{1}(a_{4},a_{3})-\mu _{3}{\overset {\circ }{\Pi }}_{1}(a_{4},a_{3})\right]\left(\mathrm {C} _{1}-\gamma _{1}{\sqrt {-1}}\right)=0\,;\end{aligned}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/8481bc5a80e96f3c0542dbd9245c9f65f084f744)
et de l’équation
![{\displaystyle \gamma _{1}{\sqrt {-1}}=-\mathrm {C} _{1}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/bcad1df625b31406463ad78a98bf9a72c4c2198a)
et
![{\displaystyle {\begin{aligned}(\mathrm {W} )\quad \mu _{4}^{2}\left({\frac {\mu _{1}}{\mu _{4}}}v_{1}-{\text{ϐ}}_{4}\right)&\left(\mathrm {C} _{1}-\gamma _{1}{\sqrt {-1}}\right)-f_{1}\chi _{4}\left[{\overset {\circ }{\Psi }}_{1}(a_{1},a_{4})-\mu _{4}{\overset {\circ }{\Pi }}_{1}(a_{1},a_{4})\right]\\-&{\frac {1}{2}}f_{2}\chi _{4}\left[{\overset {\circ }{\Psi }}_{1}(a_{2},a_{4})-\mu _{4}{\overset {\circ }{\Pi }}_{1}(a_{2},a_{4})\right]\left(\mathrm {A} _{1}-\beta _{1}{\sqrt {-1}}\right)\\-&{\frac {1}{2}}f_{3}\chi _{4}\left[{\overset {\circ }{\Psi }}_{1}(a_{3},a_{4})-\mu _{4}{\overset {\circ }{\Pi }}_{1}(a_{3},a_{4})\right]\left(\mathrm {B} _{1}-\beta _{1}{\sqrt {-1}}\right)=0.\end{aligned}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/d6de23b7cb6b913030c82f794648f38f5f19c04a)