54
INTÉGRALES
![{\displaystyle +{\frac {\operatorname {d} .}{\operatorname {d} y}}\left\{{\begin{aligned}\left\{{\begin{array}{r}M-{\frac {\operatorname {d} O}{\operatorname {d} x}}+{\frac {\operatorname {d} ^{2}R}{\operatorname {d} x^{2}}}-\ldots \\\\-{\frac {\operatorname {d} P}{\operatorname {d} y}}+{\frac {\operatorname {d} ^{2}S}{\operatorname {d} x\operatorname {d} y}}-\ldots \\\\+{\frac {\operatorname {d} ^{2}T}{\operatorname {d} y^{2}}}-\ldots \\\\-\ldots \end{array}}\right\}Z+\left\{{\begin{array}{r}P-{\frac {\operatorname {d} S}{\operatorname {d} x}}+\ldots \\\\-{\frac {\operatorname {d} T}{\operatorname {d} y}}+\ldots \\\\+\ldots \end{array}}\right\}{\frac {\operatorname {d} Z}{\operatorname {d} y}}+\left\{{\begin{array}{r}T-\ldots \\\\-\ldots \end{array}}\right\}{\frac {\operatorname {d} ^{2}Z}{\operatorname {d} y^{2}}}+\ldots \end{aligned}}\right\}.(\mathrm {XXVII} )}](https://wikimedia.org/api/rest_v1/media/math/render/svg/9f3fa3ea47974d3f2de5d366da3edcf5f620dd35)
Cette partie étant ainsi supprimée, dans l’équation (XXVI), elle deviendra, en passant aux fonctions primitives,
![{\displaystyle {\begin{aligned}Y=\left\{{\begin{array}{r}L-{\frac {\operatorname {d} N}{\operatorname {d} x}}+{\frac {\operatorname {d} ^{2}Q}{\operatorname {d} x^{2}}}-\ldots \\\\-{\frac {\operatorname {d} O}{\operatorname {d} y}}+{\frac {\operatorname {d} ^{2}R}{\operatorname {d} x\operatorname {d} y}}-\ldots \\\\+{\frac {\operatorname {d} ^{2}S}{\operatorname {d} y^{2}}}-\ldots \\\\-\ldots \end{array}}\right\}Z+\left\{{\begin{array}{r}N-{\frac {\operatorname {d} Q}{\operatorname {d} x}}+\ldots \\\\-{\frac {\operatorname {d} R}{\operatorname {d} y}}+\ldots \\\\+\ldots \end{array}}\right\}{\frac {\operatorname {d} Z}{\operatorname {d} x}}+\left\{{\begin{array}{r}Q-\ldots \\\\-\ldots \end{array}}\right\}{\frac {\operatorname {d} ^{2}Z}{\operatorname {d} x^{2}}}+\ldots \end{aligned}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/1fd9e1e104797b3c605f6c6ae8a81d7b28da8f72)
![{\displaystyle +{\frac {\operatorname {d} .}{\operatorname {d} x}}\left\{{\begin{aligned}\left\{{\begin{array}{r}O-{\frac {\operatorname {d} R}{\operatorname {d} x}}+\ldots \\\\-{\frac {\operatorname {d} S}{\operatorname {d} y}}+\ldots \\\\+\ldots \\\\\end{array}}\right\}Z+\left\{{\begin{array}{r}+R-\ldots \\\\-\ldots \\\\\end{array}}\right\}{\frac {\operatorname {d} Z}{\operatorname {d} x}}+\left\{{\begin{array}{r}S-\ldots \\\\-\ldots \end{array}}\right\}{\frac {\operatorname {d} Z}{\operatorname {d} y}}+\ldots \end{aligned}}\right\}.(\mathrm {XXVIII} )}](https://wikimedia.org/api/rest_v1/media/math/render/svg/54f7d861c79787ff4aac6e94644922119e5eca0f)
47. Or, présentement, les mêmes considérations qui nous ont conduits à partager l’équation (XXrVYI) dans les équations (XXVII) et (XVIII) conduisent également à décomposer chacune, de ces