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Joseph Louis de Lagrange - Œuvres, Tome 5.djvu/258
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[
3
,
0
]
λ
cos
(
φ
−
φ
‴
)
λ
‴
=
0
″
,
1489
m
[
3
,
0
]
λ
sin
(
φ
−
φ
‴
)
=
−
0
″
,
0004
m
9,172
8747
,
6,605
5191
,
[
3
,
1
]
λ
′
cos
(
φ
′
−
φ
‴
)
λ
‴
=
0
″
,
1542
m
′
[
3
,
1
]
λ
′
sin
(
φ
′
−
φ
‴
)
=
−
0
″
,
0801
m
′
9,188
1213
,
8,903
5026
,
[
3
,
2
]
λ
″
cos
(
φ
″
−
φ
‴
)
λ
‴
=
−
1
″
,
1131
m
″
[
3
,
2
]
λ
″
sin
(
φ
″
−
φ
‴
)
=
−
0
″
,
0247
m
″
0,046
5464
,
8,392
3443
,
[
3
,
4
]
λ
IV
cos
(
φ
IV
−
φ
‴
)
λ
‴
=
2
″
,
2610
m
IV
[
3
,
4
]
λ
IV
sin
(
φ
IV
−
φ
‴
)
=
−
0
″
,
0209
m
IV
0,354
3074
,
8,320
0893
,
[
3
,
5
]
λ
V
cos
(
φ
V
−
φ
‴
)
λ
‴
=
0
″
,
5141
m
V
[
3
,
5
]
λ
V
sin
(
φ
V
−
φ
‴
)
=
−
0
″
,
0040
m
″
9,711
0457
,
7,604
8069
,
[
4
,
0
]
λ
cos
(
φ
−
φ
IV
)
λ
IV
=
0
″
,
1261
m
[
4
,
0
]
λ
sin
(
φ
−
φ
IV
)
=
−
0
″
,
0007
m
9,100
7967
,
6,837
0840
,
[
4
,
1
]
λ
′
cos
(
φ
′
−
φ
IV
)
λ
IV
=
−
2
″
,
2446
m
′
[
4
,
1
]
λ
′
sin
(
φ
′
−
φ
IV
)
=
−
0
″
,
0308
m
′
0,351
1444
,
8,488
6625
,
[
4
,
2
]
λ
″
cos
(
φ
″
−
φ
IV
)
λ
IV
=
−
1
″
,
0372
m
″
[
4
,
2
]
λ
″
sin
(
φ
″
−
φ
IV
)
=
−
0
″
,
0032
m
″
0,015
8706
,
7,509
0316
,
[
4
,
3
]
λ
‴
cos
(
φ
‴
−
φ
IV
)
λ
IV
=
11
″
,
7487
m
‴
[
4
,
3
]
λ
‴
sin
(
φ
‴
−
φ
IV
)
=
−
0
″
,
0451
m
‴
1,069
9903
,
8,654
3635
,
[
4
,
5
]
λ
V
cos
(
φ
V
−
φ
IV
)
λ
IV
=
4
″
,
7266
m
V
[
4
,
5
]
λ
V
sin
(
φ
V
−
φ
IV
)
=
−
0
″
,
0451
m
V
0,674
5476
,
8,654
0571
,
[
5
,
0
]
λ
cos
(
φ
−
φ
V
)
λ
V
=
0
″
,
0011
m
[
5
,
0
]
λ
sin
(
φ
−
φ
V
)
=
−
0
″
,
0001
m
7,037
8060
,
5,804
1101
,
{\displaystyle {\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}}}