Page:Joseph Louis de Lagrange - Œuvres, Tome 7.djvu/545

${\begin{aligned}\mathrm {C} \ \ =&-4a\sin ^{2}{\frac {\varphi }{2}}\sin \alpha ,\\\mathrm {C} _{1}=&-4a\sin ^{2}{\frac {\varphi }{2}}\sin(\alpha +\varphi ),\\\mathrm {C} _{2}=&-4a\sin ^{2}{\frac {\varphi }{2}}\sin(\alpha +2\varphi ),\quad \ldots \,;\\\\{}_{2}\!\mathrm {D} \ \ =&-8a\sin ^{3}{\frac {\varphi }{2}}\cos \left[\alpha -\left(1+{\frac {1}{2}}\right)\varphi \right],\\{}_{1}\!\mathrm {D} \ \ =&-8a\sin ^{3}{\frac {\varphi }{2}}\cos(\alpha -\varphi ),\\\mathrm {D} _{1}=&-8a\sin ^{3}{\frac {\varphi }{2}}\cos \left(\alpha +{\frac {\varphi }{2}}\right),\\\mathrm {D} _{2}=&-8a\sin ^{3}{\frac {\varphi }{2}}\cos \left[\alpha +\left(1+{\frac {1}{2}}\right)\varphi \right],\quad \ldots \,;\\\\{}_{1}\!\mathrm {E} \ \ =&16a\sin ^{4}{\frac {\varphi }{2}}\sin(\alpha -\varphi ),\\\mathrm {E} \ \ =&16a\sin ^{4}{\frac {\varphi }{2}}\sin \alpha ,\\\mathrm {E} _{1}=&16a\sin ^{4}{\frac {\varphi }{2}}\sin \left(\alpha +\varphi \right),\quad \ldots .\end{aligned}}$

De sorte qu’on aura

${\begin{aligned}\mathrm {A} =&a\sin \alpha ,\\\mathrm {B} =&2a\sin {\frac {\varphi }{2}}\cos {\frac {\varphi }{2}}\cos \alpha ,\\\mathrm {C} =&-4a\sin ^{2}{\frac {\varphi }{2}}\sin \alpha ,\\\mathrm {D} =&-8a\sin ^{3}{\frac {\varphi }{2}}\cos {\frac {\varphi }{2}}\cos \alpha ,\\\mathrm {E} =&16a\sin ^{4}{\frac {\varphi }{2}}\sin \alpha ,\\\mathrm {F} =&32a\sin ^{5}{\frac {\varphi }{2}}\cos {\frac {\varphi }{2}}\cos \alpha ,\\.\ldots &\ldots \ldots \ldots \ldots \ldots \ldots \ldots .\end{aligned}}$