XCVI.
Qu’on multiplie l’équation (2o) par 
et qu’on y ajoute l’équation (3o), on aura
![{\displaystyle {\begin{aligned}(\mathrm {Q} )\ &\left[\mathrm {M} _{2}^{2}-\left(\mu _{2}-\mu _{1}\pm \mathrm {V} _{1}{\sqrt {-1}}\right)^{2}\right]\left(\mathrm {A} _{1}\pm \alpha _{1}{\sqrt {-1}}\right)\\&-nf_{1}\chi _{2}\left[{\overset {\circ }{\Psi }}_{1}(a_{1},a_{2})-\left(\mu _{2}-\mu _{1}\pm \mathrm {V} _{1}{\sqrt {-1}}\right){\overset {\circ }{\Pi }}_{1}(a_{1},a_{2})\right]\\&-{\frac {n}{2}}f_{3}\chi _{2}\left[{\overset {\circ }{\Psi }}_{1}(a_{3},a_{2})-\left(\mu _{2}-\mu _{1}\pm \mathrm {V} _{1}{\sqrt {-1}}\right){\overset {\circ }{\Pi }}_{1}(a_{3},a_{2})\right]\left(\mathrm {B} _{1}\pm \beta _{1}{\sqrt {-1}}\right)\\&-{\frac {n}{2}}f_{4}\chi _{2}\left[{\overset {\circ }{\Psi }}_{1}(a_{4},a_{2})-\left(\mu _{2}-\mu _{1}\pm \mathrm {V} _{1}{\sqrt {-1}}\right){\overset {\circ }{\Pi }}_{1}(a_{4},a_{2})\right]\left(\mathrm {C} _{1}\pm \gamma _{1}{\sqrt {-1}}\right)=0.\end{aligned}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a7fba76eb3dec0dd744a4e849e59322778edb879)
De même, en multipliant l’équation (4o) par et y ajoutant l’équation (5o), on aura
![{\displaystyle {\begin{aligned}(\mathrm {R} )\ &\left[\mathrm {M} _{3}^{2}-\left(\mu _{3}-\mu _{1}\pm \mathrm {V} _{1}{\sqrt {-1}}\right)^{2}\right]\left(\mathrm {B} _{1}\pm \beta _{1}{\sqrt {-1}}\right)\\&-nf_{1}\chi _{3}\left[{\overset {\circ }{\Psi }}_{1}(a_{1},a_{3})-\left(\mu _{3}-\mu _{1}\pm \mathrm {V} _{1}{\sqrt {-1}}\right){\overset {\circ }{\Pi }}_{1}(a_{1},a_{3})\right]\\&-{\frac {n}{2}}f_{2}\chi _{3}\left[{\overset {\circ }{\Psi }}_{1}(a_{2},a_{3})-\left(\mu _{3}-\mu _{1}\pm \mathrm {V} _{1}{\sqrt {-1}}\right){\overset {\circ }{\Pi }}_{1}(a_{2},a_{3})\right]\left(\mathrm {A} _{1}\pm \alpha _{1}{\sqrt {-1}}\right)\\&-{\frac {n}{2}}f_{4}\chi _{3}\left[{\overset {\circ }{\Psi }}_{1}(a_{4},a_{3})-\left(\mu _{3}-\mu _{1}\pm \mathrm {V} _{1}{\sqrt {-1}}\right){\overset {\circ }{\Pi }}_{1}(a_{4},a_{3})\right]\left(\mathrm {C} _{1}\pm \gamma _{1}{\sqrt {-1}}\right)=0.\end{aligned}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/273aba64b475375fccfbef92024743edaf2bd628)
Enfin, multipliant l’équation (6o) par et y ajoutant l’équation (7o), on aura
![{\displaystyle {\begin{aligned}(\mathrm {S} )\ &\left[\mathrm {M} _{4}^{2}-\left(\mu _{4}-\mu _{1}\pm \mathrm {V} _{1}{\sqrt {-1}}\right)^{2}\right]\left(\mathrm {C} _{1}\pm \gamma _{1}{\sqrt {-1}}\right)\\&-nf_{1}\chi _{4}\left[{\overset {\circ }{\Psi }}_{1}(a_{1},a_{4})-\left(\mu _{4}-\mu _{1}\pm \mathrm {V} _{1}{\sqrt {-1}}\right){\overset {\circ }{\Pi }}_{1}(a_{1},a_{4})\right]\\&-{\frac {n}{2}}f_{2}\chi _{4}\left[{\overset {\circ }{\Psi }}_{1}(a_{2},a_{4})-\left(\mu _{4}-\mu _{1}\pm \mathrm {V} _{1}{\sqrt {-1}}\right){\overset {\circ }{\Pi }}_{1}(a_{2},a_{4})\right]\left(\mathrm {A} _{1}\pm \alpha _{1}{\sqrt {-1}}\right)\\&-{\frac {n}{2}}f_{3}\chi _{4}\left[{\overset {\circ }{\Psi }}_{1}(a_{3},a_{4})-\left(\mu _{4}-\mu _{1}\pm \mathrm {V} _{1}{\sqrt {-1}}\right){\overset {\circ }{\Pi }}_{1}(a_{3},a_{4})\right]\left(\mathrm {B} _{1}\pm \beta _{1}{\sqrt {-1}}\right)=0.\end{aligned}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/efed900c07499ad06b23cee45a4f277a7b29e522)
Chacune de ces trois équations en vaut deux, comme on voit, à cause de l’ambiguïté du signe de 
