Page:Joseph Louis de Lagrange - Œuvres, Tome 5.djvu/258

${\begin{alignedat}{3}&&[3,0]{\frac {\lambda \ \ \ \cos(\varphi \ \ \ -\varphi ''')}{\lambda '''}}=&0''{,}1489m&[3,0]\lambda \ \ \ \sin(\varphi \ \ \ -\varphi ''')=&-0''{,}0004m\\&&&\ \ 9{,}1728747,&&\quad \ \ \,6{,}6055191,\\&&[3,1]{\frac {\lambda '\ \ \cos(\varphi '\ \ -\varphi ''')}{\lambda '''}}=&0''{,}1542m'&[3,1]\lambda '\ \ \sin(\varphi '\ \ -\varphi ''')=&-0''{,}0801m'\\&&&\ \ 9{,}1881213,&&\quad \ \ \,8{,}9035026,\\&&[3,2]{\frac {\lambda ''\ \cos(\varphi ''\ -\varphi ''')}{\lambda '''}}=&-1''{,}1131m''&[3,2]\lambda ''\ \sin(\varphi ''\ -\varphi ''')=&-0''{,}0247m''\\&&&\quad \ \ \,0{,}0465464,&&\quad \ \ \,8{,}3923443,\\&&[3,4]{\frac {\lambda ^{\scriptscriptstyle {\text{IV}}}\cos(\varphi ^{\scriptscriptstyle {\text{IV}}}-\varphi ''')}{\lambda '''}}=&2''{,}2610m^{\scriptscriptstyle {\text{IV}}}\quad &[3,4]\lambda ^{\scriptscriptstyle {\text{IV}}}\sin(\varphi ^{\scriptscriptstyle {\text{IV}}}-\varphi ''')=&-0''{,}0209m^{\scriptscriptstyle {\text{IV}}}\\&&&\ \ 0{,}3543074,&&\quad \ \ \,8{,}3200893,\\&&[3,5]{\frac {\lambda ^{\scriptscriptstyle {\text{V}}}\ \cos(\varphi ^{\scriptscriptstyle {\text{V}}}\ -\varphi ''')}{\lambda '''}}=&0''{,}5141m^{\scriptscriptstyle {\text{V}}}&[3,5]\lambda ^{\scriptscriptstyle {\text{V}}}\ \sin(\varphi ^{\scriptscriptstyle {\text{V}}}\ -\varphi ''')=&-0''{,}0040m''\\&&&\ \ 9{,}7110457,&&\quad \ \ \,7{,}6048069,\\&&[4,0]{\frac {\lambda \ \ \ \cos(\varphi \ \ \ -\varphi ^{\scriptscriptstyle {\text{IV}}})}{\lambda ^{\scriptscriptstyle {\text{IV}}}}}=&0''{,}1261m&[4,0]\lambda \ \ \ \sin(\varphi \ \ \ -\varphi ^{\scriptscriptstyle {\text{IV}}})=&-0''{,}0007m\\&&&\ \ 9{,}1007967,&&\quad \ \ \,6{,}8370840,\\&&[4,1]{\frac {\lambda '\ \ \cos(\varphi '\ \ -\varphi ^{\scriptscriptstyle {\text{IV}}})}{\lambda ^{\scriptscriptstyle {\text{IV}}}}}=&-2''{,}2446m'&[4,1]\lambda '\ \ \sin(\varphi '\ \ -\varphi ^{\scriptscriptstyle {\text{IV}}})=&-0''{,}0308m'\\&&&\quad \ \ \,0{,}3511444,&&\quad \ \ \,8{,}4886625,\\&&[4,2]{\frac {\lambda ''\ \cos(\varphi ''\ -\varphi ^{\scriptscriptstyle {\text{IV}}})}{\lambda ^{\scriptscriptstyle {\text{IV}}}}}=&-1''{,}0372m''&[4,2]\lambda ''\ \sin(\varphi ''\ -\varphi ^{\scriptscriptstyle {\text{IV}}})=&-0''{,}0032m''\\&&&\quad \ \ \,0{,}0158706,&&\quad \ \ \,7{,}5090316,\\&&[4,3]{\frac {\lambda '''\cos(\varphi '''-\varphi ^{\scriptscriptstyle {\text{IV}}})}{\lambda ^{\scriptscriptstyle {\text{IV}}}}}=&11''{,}7487m'''&[4,3]\lambda '''\sin(\varphi '''-\varphi ^{\scriptscriptstyle {\text{IV}}})=&-0''{,}0451m'''\\&&&\quad 1{,}0699903,&&\quad \ \ \,8{,}6543635,\\&&[4,5]{\frac {\lambda ^{\scriptscriptstyle {\text{V}}}\ \cos(\varphi ^{\scriptscriptstyle {\text{V}}}\ -\varphi ^{\scriptscriptstyle {\text{IV}}})}{\lambda ^{\scriptscriptstyle {\text{IV}}}}}=&4''{,}7266m^{\scriptscriptstyle {\text{V}}}&[4,5]\lambda ^{\scriptscriptstyle {\text{V}}}\ \sin(\varphi ^{\scriptscriptstyle {\text{V}}}\ -\varphi ^{\scriptscriptstyle {\text{IV}}})=&-0''{,}0451m^{\scriptscriptstyle {\text{V}}}\\&&&\ \ 0{,}6745476,&&\quad \ \ \,8{,}6540571,\\&&[5,0]{\frac {\lambda \ \ \ \cos(\varphi \ \ \ -\varphi ^{\scriptscriptstyle {\text{V}}})}{\lambda ^{\scriptscriptstyle {\text{V}}}}}=&0''{,}0011m&[5,0]\lambda \ \ \ \sin(\varphi \ \ \ -\varphi ^{\scriptscriptstyle {\text{V}}})=&-0'',0001m\\&&&\ \ 7{,}0378060,&&\quad \,\ \ 5{,}8041101,\end{alignedat}}$