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Joseph Louis de Lagrange - Œuvres, Tome 7.djvu/461
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TABLE III.
pour déterminer les valeurs de
μ
ψ
,
λ
ψ
,
ψ
{\displaystyle \mu \psi ,\lambda \psi ,\psi }
étant supposé
=
0.
{\displaystyle =0.}
Arg. V,
pour
μ
ψ
=
arg
.
I pour
μ
ψ
−
θ
.
Arg. VI, pour
μ
ψ
=
XII signes
−
arg
.
III pour
μ
ψ
−
2
A
.
Arg. V,
pour
λ
ψ
=
III signes
−
arg
.
V pour
μ
ψ
.
Arg. VI, pour
λ
ψ
=
III signes
−
arg
.
VI pour
μ
ψ
.
{\displaystyle {\begin{array}{|clc|}\hline \qquad \qquad \quad \ \,&\scriptstyle {\text{Arg. V, }}\ {\text{pour }}\mu \psi =\arg .{\text{ I pour }}\mu \psi -\theta .&\qquad \qquad \quad \ \ \,\\&\scriptstyle {\text{Arg. VI, pour }}\,\mu \psi ={\text{XII signes}}-\arg .\ {\text{III pour }}\mu \psi -2\mathrm {A} .\\&\scriptstyle {\text{Arg. V, }}\ {\text{pour }}\,\lambda \psi ={\text{III signes}}-\arg .\ {\text{V pour }}\mu \psi .\\&\scriptstyle {\text{Arg. VI, pour }}\ \lambda \psi ={\text{III signes}}-\arg .{\text{ VI pour }}\mu \psi .\\\hline \end{array}}}
S
.
O
+
I
+
II
+
S
.
S
.
VI
−
VII
−
VIII
−
S
.
¯
⏞
⏞
⏞
¯
{\displaystyle {\begin{array}{|c|c|c|c|c|}{\text{S}}.&\quad \ \,{\text{O}}\quad +\quad &\quad \ \ {\text{I}}\ \ \quad +\quad &\quad \ \ {\text{II}}\ \ \quad +\quad &{\text{S}}.\\{\text{S}}.&\quad {\text{VI}}\quad -\quad &\quad {\text{VII}}\quad -\quad &\quad {\text{VIII}}\quad -\quad &{\text{S}}.\\{\overline {\quad }}&\overbrace {\quad \ \ \qquad \qquad \qquad } &\overbrace {\quad \ \ \,\qquad \qquad \qquad } &\overbrace {\quad \ \ \ \qquad \qquad \qquad } &{\overline {\quad \ }}\end{array}}}
0
∘
0
.
′
0
,
″
0
Diff.
Cor.
0
.
′
37
,
″
2
Diff.
Cor.
1
.
′
4
,
″
5
Diff.
Cor.
30
∘
+
+
+
1
0.
1
,
3
1
,
″
3
0
,
″
0
0.38
,
3
1
,
″
1
0
,
″
1
1.
5
,
1
0
,
″
6
0
,
″
1
29
3
0.
2
,
6
1
,
3
0
,
0
0.39
,
4
1
,
1
0
,
1
1.
5
,
7
0
,
6
0
,
1
28
3
0.
3
,
9
1
,
3
0
,
0
0.40
,
5
1
,
1
0
,
1
1.
6
,
3
0
,
6
0
,
1
27
4
0.
5
,
2
1
,
3
0
,
0
0.41
,
6
1
,
1
0
,
1
1.
6
,
9
0
,
6
0
,
1
26
5
0.
6
,
5
1
,
3
0
,
0
0.42
,
7
1
,
1
0
,
1
1.
7
,
5
0
,
6
0
,
1
25
6
0.
7
,
8
1
,
3
0
,
0
0.43
,
8
1
,
1
0
,
1
1.
8
,
0
0
,
5
0
,
1
24
7
0.
9
,
1
1
,
3
0
,
0
0.44
,
9
1
,
1
0
,
1
1.
8
,
5
0
,
5
0
,
1
23
8
0.10
,
4
1
,
3
0
,
0
0.46
,
0
1
,
1
0
,
1
1.
9
,
0
0
,
5
0
,
1
22
9
0.11
,
7
1
,
3
0
,
0
0.46
,
9
0
,
9
0
,
1
1.
9
,
5
0
,
5
0
,
1
21
10
0.12
,
9
1
,
2
0
,
0
0.47
,
9
1
,
0
0
,
1
1.10
,
0
0
,
5
0
,
1
20
11
0.14
,
2
1
,
3
0
,
0
0.48
,
9
1
,
0
0
,
1
1.10
,
4
0
,
4
0
,
1
19
12
0.15
,
5
1
,
3
0
,
0
0.49
,
8
0
,
9
0
,
1
1.10
,
8
0
,
4
0
,
1
18
13
0.16
,
8
1
,
3
0
,
0
0.50
,
7
0
,
9
0
,
1
1.11
,
2
0
,
4
0
,
1
17
14
0.18
,
0
1
,
2
0
,
0
0.51
,
7
1
,
0
0
,
1
1.11
,
6
0
,
4
0
,
1
16
15
0.19
,
3
1
,
3
0
,
0
0.52
,
6
0
,
9
0
,
1
1.11
,
9
0
,
3
0
,
1
15
16
0.20
,
5
1
,
2
0
,
0
0.53
,
5
0
,
9
0
,
1
1.12
,
2
0
,
3
0
,
1
14
17
0.21
,
8
1
,
3
0
,
0
0.54
,
4
0
,
9
0
,
1
1.12
,
5
0
,
3
0
,
1
13
18
0.23
,
0
1
,
2
0
,
0
0.55
,
3
0
,
9
0
,
1
1.12
,
8
0
,
3
0
,
1
12
19
0.24
,
3
1
,
3
0
,
0
0.56
,
2
0
,
9
0
,
1
1.13
,
1
0
,
3
0
,
1
11
20
0.25
,
5
1
,
2
0
,
0
0.57
,
0
0
,
8
0
,
1
1.13
,
3
0
,
2
0
,
1
10
21
0.26
,
7
1
,
2
0
,
0
0.57
,
8
0
,
8
0
,
1
1.13
,
5
0
,
2
0
,
1
9
22
0.27
,
9
1
,
2
0
,
0
0.58
,
6
0
,
8
0
,
1
1.13
,
6
0
,
1
0
,
1
8
23
0.29
,
1
1
,
2
0
,
0
0.59
,
5
0
,
9
0
,
1
1.13
,
8
0
,
2
0
,
1
7
24
0.30
,
3
1
,
2
0
,
0
1.
0
,
3
0
,
8
0
,
1
1.14
,
0
0
,
2
0
,
1
6
25
0.31
,
5
1
,
2
0
,
0
1.
1
,
0
0
,
7
0
,
1
1.14
,
2
0
,
2
0
,
1
5
26
0.32
,
6
1
,
1
0
,
0
1.
1
,
7
0
,
7
0
,
1
1.14
,
3
0
,
1
0
,
1
4
27
0.33
,
8
1
,
2
0
,
0
1.
2
,
4
0
,
7
0
,
1
1.14
,
4
0
,
1
0
,
1
3
28
0.34
,
9
1
,
1
0
,
0
1.
3
,
2
0
,
8
0
,
1
1.14
,
4
0
,
0
0
,
1
2
29
0.36
,
1
1
,
2
0
,
0
1.
3
,
8
0
,
6
0
,
1
1.14
,
4
0
,
0
0
,
1
1
30
0.37
,
2
1
,
1
0
,
0
1.
4
,
5
0
,
7
0
,
1
1.14
,
4
0
,
0
0
,
1
0
{\displaystyle {\begin{array}{|r|c|c|c|c|c|c|c|c|c|c|}0{\overset {^{\circ }}{\,}}&0{\overset {'}{.}}\ \ 0{\overset {''}{,}}0&\scriptstyle {\text{Diff.}}&\scriptstyle {\text{Cor.}}&0{\overset {'}{.}}37{\overset {''}{,}}2&\scriptstyle {\text{Diff.}}&\scriptstyle {\text{Cor.}}&1{\overset {'}{.}}4{\overset {''}{,}}5&\scriptstyle {\text{Diff.}}&\scriptstyle {\text{Cor.}}&30{\overset {^{\circ }}{\,}}\\&&&+&&&+&&&+\\1&0.\ \ 1,3&1{\overset {''}{,}}3&0{\overset {''}{,}}0&0.38,3&1{\overset {''}{,}}1&0{\overset {''}{,}}1&1.\ \ 5,1&0{\overset {''}{,}}6&0{\overset {''}{,}}1&29\\3&0.\ \ 2,6&1,3&0,0&0.39,4&1,1&0,1&1.\ \ 5,7&0,6&0,1&28\\3&0.\ \ 3,9&1,3&0,0&0.40,5&1,1&0,1&1.\ \ 6,3&0,6&0,1&27\\4&0.\ \ 5,2&1,3&0,0&0.41,6&1,1&0,1&1.\ \ 6,9&0,6&0,1&26\\5&0.\ \ 6,5&1,3&0,0&0.42,7&1,1&0,1&1.\ \ 7,5&0,6&0,1&25\\6&0.\ \ 7,8&1,3&0,0&0.43,8&1,1&0,1&1.\ \ 8,0&0,5&0,1&24\\\\7&0.\ \ 9,1&1,3&0,0&0.44,9&1,1&0,1&1.\ \ 8,5&0,5&0,1&23\\8&0.10,4&1,3&0,0&0.46,0&1,1&0,1&1.\ \ 9,0&0,5&0,1&22\\9&0.11,7&1,3&0,0&0.46,9&0,9&0,1&1.\ \ 9,5&0,5&0,1&21\\10&0.12,9&1,2&0,0&0.47,9&1,0&0,1&1.10,0&0,5&0,1&20\\11&0.14,2&1,3&0,0&0.48,9&1,0&0,1&1.10,4&0,4&0,1&19\\12&0.15,5&1,3&0,0&0.49,8&0,9&0,1&1.10,8&0,4&0,1&18\\\\13&0.16,8&1,3&0,0&0.50,7&0,9&0,1&1.11,2&0,4&0,1&17\\14&0.18,0&1,2&0,0&0.51,7&1,0&0,1&1.11,6&0,4&0,1&16\\15&0.19,3&1,3&0,0&0.52,6&0,9&0,1&1.11,9&0,3&0,1&15\\16&0.20,5&1,2&0,0&0.53,5&0,9&0,1&1.12,2&0,3&0,1&14\\17&0.21,8&1,3&0,0&0.54,4&0,9&0,1&1.12,5&0,3&0,1&13\\18&0.23,0&1,2&0,0&0.55,3&0,9&0,1&1.12,8&0,3&0,1&12\\\\19&0.24,3&1,3&0,0&0.56,2&0,9&0,1&1.13,1&0,3&0,1&11\\20&0.25,5&1,2&0,0&0.57,0&0,8&0,1&1.13,3&0,2&0,1&10\\21&0.26,7&1,2&0,0&0.57,8&0,8&0,1&1.13,5&0,2&0,1&\ \ 9\\22&0.27,9&1,2&0,0&0.58,6&0,8&0,1&1.13,6&0,1&0,1&\ \ 8\\23&0.29,1&1,2&0,0&0.59,5&0,9&0,1&1.13,8&0,2&0,1&\ \ 7\\24&0.30,3&1,2&0,0&1.\ \ 0,3&0,8&0,1&1.14,0&0,2&0,1&\ \ 6\\\\25&0.31,5&1,2&0,0&1.\ \ 1,0&0,7&0,1&1.14,2&0,2&0,1&\ \ 5\\26&0.32,6&1,1&0,0&1.\ \ 1,7&0,7&0,1&1.14,3&0,1&0,1&\ \ 4\\27&0.33,8&1,2&0,0&1.\ \ 2,4&0,7&0,1&1.14,4&0,1&0,1&\ \ 3\\28&0.34,9&1,1&0,0&1.\ \ 3,2&0,8&0,1&1.14,4&0,0&0,1&\ \ 2\\29&0.36,1&1,2&0,0&1.\ \ 3,8&0,6&0,1&1.14,4&0,0&0,1&\ \ 1\\30&0.37,2&1,1&0,0&1.\ \ 4,5&0,7&0,1&1.14,4&0,0&0,1&\ \ 0\end{array}}}
_
⏟
⏟
⏟
_
S
.
XI
−
X
−
IX
−
S
.
S
.
V
+
IV
+
III
+
S
.
{\displaystyle {\begin{array}{|c|c|c|c|c|}{\underline {\quad }}&\underbrace {\quad \ \ \ \qquad \qquad \qquad } &\underbrace {\quad \ \ \ \qquad \qquad \qquad } &\underbrace {\quad \ \ \,\qquad \qquad \qquad } &{\underline {\quad \ \,}}\\{\text{S}}.&\quad {\text{XI}}\ \ \ -\quad &\quad \ {\text{X}}\ \quad -\quad &\quad {\text{IX}}\quad -\quad &{\text{S}}.\\{\text{S}}.&\quad {\text{V}}\quad +\quad &\quad {\text{IV}}\quad +\quad &\quad {\text{III}}\quad +\quad &{\text{S}}.\\\hline \end{array}}}