pour abréger,
![{\displaystyle {\begin{alignedat}{3}\Theta &={\Bigl [}t-f\left[(x')(x'')(x''')\right]{\Bigr ]}&&\times {\Bigl [}t-f\left[(x'')(x')(x''')\right]{\Bigr ]}&&\times {\Bigl [}t-f\left[(x''')(x'')(x')\right]{\Bigr ]}\\&\times {\Bigl [}t-f\left[(x')(x''')(x'')\right]{\Bigr ]}&&\times {\Bigl [}t-f\left[(x''')(x')(x'')\right]{\Bigr ]}&&\times {\Bigl [}t-f\left[(x'')(x''')(x')\right]{\Bigr ]},\\\\\theta \ &={\Bigl [}t-f\left[(x')^{3}\right]{\Bigr ]}&&\times {\Bigl [}t-f\left[(x'')^{3}\right]{\Bigr ]}&&\times {\Bigl [}t-f\left[(x''')^{3}\right]{\Bigr ]},\\\\\theta _{1}&={\Bigl [}t-f\left[(x')^{2}(x'')\right]{\Bigr ]}&&\times {\Bigl [}t-f\left[(x'')^{2}(x')\right]{\Bigr ]}&&\times {\Bigl [}t-f\left[(x''')^{2}(x'')\right]{\Bigr ]}\\&\times {\Bigl [}t-f\left[(x')^{2}(x''')\right]{\Bigr ]}&&\times {\Bigl [}t-f\left[(x''')^{2}(x')\right]{\Bigr ]}&&\times {\Bigl [}t-f\left[(x'')^{2}(x''')\right]{\Bigr ]},\\\\\theta _{2}&={\Bigl [}t-f\left[(x')(x'')^{2}\right]{\Bigr ]}&&\times {\Bigl [}t-f\left[(x'')(x')^{2}\right]{\Bigr ]}&&\times {\Bigl [}t-f\left[(x''')(x'')^{2}\right]{\Bigr ]}\\&\times {\Bigl [}t-f\left[(x')(x''')^{2}\right]{\Bigr ]}&&\times {\Bigl [}t-f\left[(x''')(x')^{2}\right]{\Bigr ]}&&\times {\Bigl [}t-f\left[(x'')(x''')^{2}\right]{\Bigr ]},\\\\\theta _{3}&={\Bigl [}t-f\left[(x')(x'')(x')\right]{\Bigr ]}&&\times {\Bigl [}t-f\left[(x'')(x')(x'')\right]{\Bigr ]}&&\times {\Bigl [}t-f\left[(x''')(x'')(x''')\right]{\Bigr ]}\\&\times {\Bigl [}t-f\left[(x')(x''')(x')\right]{\Bigr ]}&&\times {\Bigl [}t-f\left[(x''')(x')(x''')\right]{\Bigr ]}&&\times {\Bigl [}t-f\left[(x'')(x''')(x'')\right]{\Bigr ]},\\\\\end{alignedat}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/02d39b4e3fa840fa27f660bdb3a7096563be91a4)
on aura
![{\displaystyle \mathrm {T} =\Theta \theta \theta _{1}\theta _{2}\theta _{3}.}](https://wikimedia.org/api/rest_v1/media/math/render/svg/d31fb63d4b5bb8c7f296c1f4a0f55df99b48dcc9)
Maintenantje remarque que, si l’on suppose
![{\displaystyle t-f\left[(x)^{3}\right]=0,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/6c89a8e4fea635fd2091a56eb5141bfc1883f744)
et qu’on élimine
par le moyen de l’équation en ![{\displaystyle x,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/feff4d40084c7351bf57b11ba2427f6331f5bdbe)
![{\displaystyle x^{3}+mx^{2}+nx+p=0,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/7eba1a74ae4b01bcd214ca28edf7fc5e14448c71)
on trouvera, comme dans le numéro précédent, l’équation finale
de sorte que
sera nécessairement une fonction rationnelle de
et des coefficients ![{\displaystyle m,n,p.}](https://wikimedia.org/api/rest_v1/media/math/render/svg/969d7c9f0c18de01b74f86ea7cb3c0742aaebcd8)
On trouvera, par les mêmes principes, que si l’on fait
![{\displaystyle t-f\left[(x)^{2}(y)\right]=0,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a22823851a984029c940d00bb474b051018a84c9)
et qu’on élimine successivement
et
par le moyen des deux équations en
et en
savoir
![{\displaystyle {\begin{aligned}x^{3}+mx^{2}+nx+p=0,\\y^{3}\,+my^{2}+ny+p=0,\end{aligned}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/5120c10fe2be1dabf0cc2aab25eda266c530cb2d)