![{\displaystyle {\begin{array}{rr}0=M-{\frac {\operatorname {d} M}{\operatorname {d} a}}.{\frac {\alpha }{1}}+{\frac {\operatorname {d} ^{2}M}{\operatorname {d} a^{2}}}.{\frac {\alpha ^{2}}{1.2}}-\ldots &0=N-{\frac {\operatorname {d} N}{\operatorname {d} a}}.{\frac {\alpha }{1}}+{\frac {\operatorname {d} ^{2}N}{\operatorname {d} a^{2}}}.{\frac {\alpha ^{2}}{1.2}}-\ldots \\\\-{\frac {\operatorname {d} M}{\operatorname {d} b}}.{\frac {\beta }{1}}+2{\frac {\operatorname {d} ^{2}M}{\operatorname {d} a\operatorname {d} b}}.{\frac {\alpha \beta }{1.2}}-\ldots &-{\frac {\operatorname {d} N}{\operatorname {d} b}}.{\frac {\beta }{1}}+2{\frac {\operatorname {d} ^{2}N}{\operatorname {d} a\operatorname {d} b}}.{\frac {\alpha \beta }{1.2}}-\ldots \\\\+{\frac {\operatorname {d} ^{2}M}{\operatorname {d} b^{2}}}.{\frac {\beta ^{2}}{1.2}}-\ldots &+{\frac {\operatorname {d} ^{2}N}{\operatorname {d} b^{2}}}.{\frac {\beta ^{2}}{1.2}}-\ldots \end{array}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a107590289d9d51b8a5a044463de1999e79db0ce)
mais puisque, par l’hypothèse,
et
sont de forts petits nombres, nous pourrons, sans beaucoup d’erreur, écrire simplement
![{\displaystyle {\frac {\operatorname {d} M}{\operatorname {d} a}}\alpha +{\frac {\operatorname {d} M}{\operatorname {d} b}}\beta =M,\qquad {\frac {\operatorname {d} N}{\operatorname {d} a}}\alpha +{\frac {\operatorname {d} N}{\operatorname {d} b}}\beta =N,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/0f072221b1c48d506436f197b7e61ca1d291934b)
d’où nous conclurons
![{\displaystyle {\begin{aligned}&\alpha ={\frac {M{\frac {\operatorname {d} N}{\operatorname {d} b}}-N{\frac {\operatorname {d} M}{\operatorname {d} a}}}{{\frac {\operatorname {d} M}{\operatorname {d} a}}{\frac {\operatorname {d} N}{\operatorname {d} b}}-{\frac {\operatorname {d} N}{\operatorname {d} a}}{\frac {\operatorname {d} M}{\operatorname {d} b}}}},\\\\&\beta ={\frac {N{\frac {\operatorname {d} M}{\operatorname {d} b}}-M{\frac {\operatorname {d} N}{\operatorname {d} a}}}{{\frac {\operatorname {d} M}{\operatorname {d} a}}{\frac {\operatorname {d} N}{\operatorname {d} b}}-{\frac {\operatorname {d} N}{\operatorname {d} a}}{\frac {\operatorname {d} M}{\operatorname {d} b}}}}\end{aligned}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/d7b895a4d41b6428ab5bc85afb8cbae21d71cd91)
ces valeurs ne seront qu’approchées ; mais il n’en résultera pas moins, pour
et
, les valeurs
![{\displaystyle a-{\frac {M{\frac {\operatorname {d} N}{\operatorname {d} b}}-N{\frac {\operatorname {d} M}{\operatorname {d} a}}}{{\frac {\operatorname {d} M}{\operatorname {d} a}}{\frac {\operatorname {d} N}{\operatorname {d} b}}-{\frac {\operatorname {d} N}{\operatorname {d} a}}{\frac {\operatorname {d} M}{\operatorname {d} b}}}},\qquad b-{\frac {N{\frac {\operatorname {d} M}{\operatorname {d} b}}-M{\frac {\operatorname {d} N}{\operatorname {d} a}}}{{\frac {\operatorname {d} M}{\operatorname {d} a}}{\frac {\operatorname {d} N}{\operatorname {d} b}}-{\frac {\operatorname {d} N}{\operatorname {d} a}}{\frac {\operatorname {d} M}{\operatorname {d} b}}}},}](https://wikimedia.org/api/rest_v1/media/math/render/svg/ec7580f88e48b7a7fb5bc216683b358a9a9e9bd9)
généralement plus approchées que ne l’étaient les premières
et