![{\displaystyle {\frac {(t-a)^{2}+(u-b)^{2}+(v-c)^{2}}{\lambda ^{2}}}={\frac {t^{2}+u^{2}+v^{2}}{\lambda '^{2}}}\,;}](https://wikimedia.org/api/rest_v1/media/math/render/svg/e75d375360a3da49e0162ab61c4b6c762b4b0c98)
c’est-à-dire,
![{\displaystyle \left(\lambda '^{2}-\lambda ^{2}\right)\left(t^{2}+u^{2}+v^{2}\right)-2\lambda '^{2}(at+bu+cv)+\lambda '^{2}\left(a^{2}+b^{2}+c^{2}\right)=0}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a915e90523698846e1e850ceb08cda9ade8b4ffd)
ou encore
![{\displaystyle \left\{t-{\frac {\lambda '^{2}}{\lambda '^{2}-\lambda ^{2}}}a\right\}^{2}+\left\{u-{\frac {\lambda '^{2}}{\lambda '^{2}-\lambda ^{2}}}b\right\}^{2}+\left\{v-{\frac {\lambda '^{2}}{\lambda '^{2}-\lambda ^{2}}}c\right\}^{2}=}](https://wikimedia.org/api/rest_v1/media/math/render/svg/9c33f4b1e9d5b7e4c333743f981ff2270e53fb76)
![{\displaystyle \left\{{\frac {\lambda '\lambda {\sqrt {a^{2}+b^{2}+c^{2}}}}{\lambda '^{2}-\lambda ^{2}}}\right\}\,;}](https://wikimedia.org/api/rest_v1/media/math/render/svg/4d761e6ddd5d88af026cc006b02e114711d48dac)
équation d’une sphère, comme on pouvait bien s’y attendre.
TRIGONOMÉTRIE.
Note sur l’analise des sections angulaires ;
Par un Abonné.
≈≈≈≈≈≈≈≈≈
Soit posé, avec M. Poisson (Bulletin universel 1825, n.o 9, pag. 142),
![{\displaystyle {\begin{aligned}&X=\operatorname {Cos} .max+{\frac {m}{1}}\operatorname {Cos} .(m-2)x+{\frac {m}{1}}.{\frac {m-1}{2}}\operatorname {Cos} .(m-4)x+\ldots \\\\&X'=\operatorname {Sin} .max+{\frac {m}{1}}\operatorname {Sin} .(m-2)x+{\frac {m}{1}}.{\frac {m-1}{2}}\operatorname {Sin} .(m-4)x+\ldots \,;\end{aligned}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/211b1e2b669ad1986da8b5e7ba61380c50461d1b)
on aura comme l’on sait