![{\displaystyle \left.{\begin{aligned}&\quad x{\frac {\operatorname {d} M'}{\operatorname {d} x}}+y{\frac {\operatorname {d} M'}{\operatorname {d} y}}+z{\frac {\operatorname {d} M'}{\operatorname {d} z}}-mM'\\\\+\lambda &\left(x{\frac {\operatorname {d} M''}{\operatorname {d} x}}+y{\frac {\operatorname {d} M''}{\operatorname {d} y}}+z{\frac {\operatorname {d} M''}{\operatorname {d} z}}-mM''\right)\\\\+\mu &\left(x{\frac {\operatorname {d} M'''}{\operatorname {d} x}}+y{\frac {\operatorname {d} M'''}{\operatorname {d} y}}+z{\frac {\operatorname {d} M'''}{\operatorname {d} z}}-mM'''\right)\end{aligned}}\right\}=0\,;\quad }](https://wikimedia.org/api/rest_v1/media/math/render/svg/68f34969a030bfa9a5670019f790128e0e5dfde9)
(12)
or, quelles que soient les valeurs attribuées aux deux constantes arbitraires
et
, cette surface polaire passe évidemment par les
points donnés par les trois équations
![{\displaystyle {\begin{aligned}&x{\frac {\operatorname {d} M'}{\operatorname {d} x}}\ \ +y{\frac {\operatorname {d} M'}{\operatorname {d} y}}\ \ +z{\frac {\operatorname {d} M'}{\operatorname {d} z}}=mM'\\\\&x{\frac {\operatorname {d} M''}{\operatorname {d} x}}\ +y{\frac {\operatorname {d} M''}{\operatorname {d} y}}\ +z{\frac {\operatorname {d} M''}{\operatorname {d} z}}=mM''\\\\&x{\frac {\operatorname {d} M'''}{\operatorname {d} x}}+y{\frac {\operatorname {d} M'''}{\operatorname {d} y}}+z{\frac {\operatorname {d} M'''}{\operatorname {d} z}}=mM'''\,;\end{aligned}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/faf26b2045861bce9beb76b3ce88eb104292a8f3)
on a donc ces deux théorèmes :
C’est là, comme l’on voit, la première partie des deux théo-