![{\displaystyle x=x_{0}+ih,\qquad y=y_{0}+ik,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/bda52821387b7759b3b0964700376f51c1287758)
et par suite
![{\displaystyle \operatorname {d} x=i\operatorname {d} h,\qquad \operatorname {d} y=i\operatorname {d} k,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/79fd6641a9edbcb54fefccc71901f612e72f8451)
![{\displaystyle {\begin{aligned}\operatorname {d} 'z=(\operatorname {d} 'z)_{0}&+{\frac {i}{1}}\left\{h\left({\frac {\operatorname {dd} 'z}{\operatorname {d} x}}\right)_{0}+k\left({\frac {\operatorname {dd} 'z}{\operatorname {d} y}}\right)_{0}\right\}\\\\&+{\frac {i^{2}}{1.2}}\left\{h^{2}\left({\frac {\operatorname {d} ^{2}\operatorname {d} 'z}{\operatorname {d} x^{2}}}\right)_{0}+2hk\left({\frac {\operatorname {d} ^{2}\operatorname {d} 'z}{\operatorname {d} x\operatorname {d} y}}\right)_{0}+k^{2}\left({\frac {\operatorname {d} ^{2}\operatorname {d} 'z}{\operatorname {d} y^{2}}}\right)_{0}\right\}\\&+\ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \end{aligned}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/9f1ea980c327f2bf984d588b14bcf948be836dc1)
en dénotant respectivement par
![{\displaystyle (\operatorname {d} 'z)_{0},\quad \left({\frac {\operatorname {dd} 'z}{\operatorname {d} x}}\right)_{0},\quad \left({\frac {\operatorname {dd} 'z}{\operatorname {d} y}}\right)_{0},\ldots }](https://wikimedia.org/api/rest_v1/media/math/render/svg/3ff272c705fd75c0fc6f441b2e743dd17d0cec0b)
ce que deviennent
![{\displaystyle \operatorname {d} 'z,\quad {\frac {\operatorname {dd} 'z}{\operatorname {d} x}},\quad {\frac {\operatorname {dd} 'z}{\operatorname {d} y}},\ldots }](https://wikimedia.org/api/rest_v1/media/math/render/svg/0b7fbf82ff520b91dbb8b98ceca81c391e31b68f)
qui répondent au point ![{\displaystyle \left(x_{0},y_{0},z_{0}\right).}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a4d69dd6ec627d636b41d4510f3e654d9ac90c01)
Substituant ces valeurs dans l’équation (38), et négligeant les termes de plus de deux dimensions en
nous aurons
![{\displaystyle (\operatorname {d} 'z)i^{2}\iint \operatorname {d} h\operatorname {d} k=\theta ,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/ab4034d3c79db5a02218739c17b84b939475a871)
ou encore
![{\displaystyle \varpi \operatorname {d} 'z=\theta ,\qquad }](https://wikimedia.org/api/rest_v1/media/math/render/svg/3d30b5993c75755e58da521f4929ffa89400faa0)
(39)
en observant que
exprime l’aire de la section que l’on considère et représentant cette aire par ![{\displaystyle \varpi .}](https://wikimedia.org/api/rest_v1/media/math/render/svg/708f6611303e54eefbedd289cd48ca2ed16af127)