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Joseph Louis de Lagrange - Œuvres, Tome 7.djvu/457
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TABLE I.
pour déterminer les valeurs de
μ
ψ
,
λ
ψ
,
ν
ψ
,
ψ
{\displaystyle \mu \psi ,\lambda \psi ,\nu \psi ,\psi }
étant supposé
=
1
∘
.
{\displaystyle =1^{\circ }.}
Arg. I, pour
μ
ψ
=
φ
−
A
.
Arg. II, pour
μ
ψ
=
VI signes
−
(
φ
+
A
)
.
Arg. I, pour
λ
ψ
=
III signes
−
arg
.
I pour
μ
ψ
.
Arg. II, pour
λ
ψ
=
III signes
−
arg
.
II pour
μ
ψ
.
Arg. I, pour
ν
ψ
=
arg
.
V pour
ν
ψ
+
A
.
Arg. II, pour
ν
ψ
=
VI signes
+
arg
.
III pour
μ
ψ
+
A
.
{\displaystyle {\begin{array}{|clc|}\hline \qquad \qquad \quad \ &\scriptstyle {\text{Arg. I, pour }}\,\mu \psi =\varphi -\mathrm {A} .&\qquad \qquad \quad \ \\&\scriptstyle {\text{Arg. II, pour }}\mu \psi ={\text{VI signes}}-(\varphi +\mathrm {A} ).&\\&\scriptstyle {\text{Arg. I, pour }}\,\lambda \psi ={\text{III signes}}-\arg .\ {\text{I pour }}\mu \psi .&\\&\scriptstyle {\text{Arg. II, pour }}\lambda \psi ={\text{III signes}}-\arg .{\text{II pour }}\mu \psi .&\\&\scriptstyle {\text{Arg. I, pour }}\,\nu \psi =\arg .{\text{V pour }}\nu \psi +\mathrm {A} .&\\&\scriptstyle {\text{Arg. II, pour }}\nu \psi ={\text{VI signes}}+\arg .{\text{III pour }}\mu \psi +\mathrm {A} .&\\\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 {\ \,\qquad \qquad \qquad } &\overbrace {\ \,\qquad \qquad \qquad } &\overbrace {\ \ \ \qquad \qquad \qquad } &{\overline {\qquad \,}}\end{array}}}
0
.
∘
0
′
0
.
′
0
,
″
0
Diff.
Cor.
5
.
′
58
,
″
4
Diff.
Cor.
10
.
′
20
,
″
8
Diff.
Cor.
30
.
∘
0
′
+
+
+
0.30
0.
6
,
3
6
,
″
3
0
,
″
0
6.
3
,
8
5
,
″
4
0
,
″
3
10.23
,
9
3
,
″
1
0
,
″
4
29.30
1.
0
0.12
,
5
6
,
2
0
,
0
6.
9
,
2
5
,
4
0
,
3
10.26
,
9
3
,
0
0
,
4
29.
0
1.30
0.18
,
8
6
,
3
0
,
0
6.14
,
5
5
,
3
0
,
3
10.29
,
9
3
,
0
0
,
4
28.30
2.
0
0.25
,
1
6
,
3
0
,
0
6.19
,
9
5
,
4
0
,
3
10.32
,
9
3
,
0
0
,
4
28.
0
2.30
0.31
,
3
6
,
2
0
,
0
6.25
,
2
5
,
3
0
,
3
10.35
,
8
2
,
9
0
,
4
27.30
3.
0
0.37
,
6
6
,
3
0
,
0
6.30
,
4
5
,
2
0
,
3
10.38
,
7
2
,
9
0
,
4
27.
0
3.30
0.43
,
8
6
,
2
0
,
0
6.35
,
6
5
,
2
0
,
3
10.41
,
5
2
,
8
0
,
4
26.30
4.
0
0.50
,
0
6
,
2
0
,
0
6.40
,
8
5
,
2
0
,
3
10.44
,
3
2
,
8
0
,
4
26.
0
4.30
0.56
,
3
6
,
3
0
,
0
6.46
,
0
5
,
2
0
,
3
10.47
,
0
2
,
7
0
,
5
25.30
5.
0
1.
2
,
5
6
,
2
0
,
0
6.51
,
1
5
,
1
0
,
3
10.49
,
6
2
,
6
0
,
5
25.
0
5.30
1.
8
,
7
6
,
2
0
,
1
6.56
,
2
5
,
1
0
,
3
10.52
,
2
2
,
6
0
,
5
24.30
6.
0
1.15
,
0
6
,
3
0
,
1
7.
1
,
3
5
,
1
0
,
3
10.54
,
8
2
,
6
0
,
5
24.
0
6.30
1.21
,
2
6
,
2
0
,
1
7.
6
,
4
5
,
1
0
,
3
10.57
,
3
2
,
5
0
,
5
23.30
7.
0
1.27
,
4
6
,
2
0
,
1
7.11
,
4
5
,
0
0
,
3
10.59
,
8
2
,
5
0
,
5
23.
0
7.30
1.33
,
6
6
,
2
0
,
1
7.16
,
4
5
,
0
0
,
3
11.
2
,
2
2
,
4
0
,
5
22.30
8.
0
1.39
,
8
6
,
2
0
,
1
7.21
,
3
4
,
9
0
,
3
11.
4
,
6
2
,
4
0
,
5
22.
0
8.30
1.46
,
0
6
,
2
0
,
1
7.26
,
2
4
,
9
0
,
3
11.
6
,
9
2
,
3
0
,
5
21.30
9.
0
1.52
,
2
6
,
2
0
,
1
7.31
,
1
4
,
9
0
,
3
11.
9
,
2
2
,
3
0
,
5
21.
0
9.30
1.58
,
3
6
,
1
0
,
1
7.35
,
9
4
,
8
0
,
3
11.11
,
4
2
,
2
0
,
5
20.30
10.
0
2.
4
,
5
6
,
2
0
,
1
7.40
,
7
4
,
8
0
,
3
11.13
,
6
2
,
2
0
,
5
20.
0
10.30
2.10
,
6
6
,
1
0
,
1
7.45
,
5
4
,
8
0
,
3
11.15
,
7
2
,
1
0
,
5
19.30
11.
0
2.16
,
8
6
,
2
0
,
1
7.50
,
3
4
,
8
0
,
3
11.17
,
7
2
,
0
0
,
5
19.
0
11.30
2.22
,
9
6
,
1
0
,
1
7.55
,
0
4
,
7
0
,
3
11.19
,
7
2
,
0
0
,
5
18.30
12.
0
2.29
,
1
6
,
2
0
,
1
7.59
,
6
4
,
6
0
,
3
11.21
,
7
2
,
0
0
,
5
18.
0
12.30
2.35
,
2
6
,
1
0
,
1
8.
4
,
3
4
,
7
0
,
3
11.23
,
6
1
,
9
0
,
5
17.30
13.
0
2.41
,
3
6
,
1
0
,
1
8.
8
,
9
4
,
6
0
,
3
11.25
,
5
1
,
9
0
,
5
17.
0
13.30
2.47
,
4
6
,
1
0
,
1
8.13
,
4
4
,
5
0
,
3
11.27
,
3
1
,
8
0
,
5
16.30
14.
0
2.53
,
4
6
,
0
0
,
1
8.17
,
9
4
,
5
0
,
3
11.29
,
0
1
,
7
0
,
5
16.
0
14.30
2.59
,
5
6
,
1
0
,
1
8.22
,
4
4
,
5
0
,
4
11.30
,
7
1
,
6
0
,
5
15.30
15.
0
3.
5
,
5
6
,
0
0
,
1
8.26
,
8
4
,
4
0
,
4
11.32
,
4
1
,
7
0
,
5
15.
0
{\displaystyle {\begin{array}{|c|c|c|c|c|c|c|c|c|c|c|}0{\overset {^{\circ }}{.}}\ \ 0'&0{\overset {'}{.}}\ \ 0{\overset {''}{,}}0&\scriptstyle {\text{Diff.}}&\scriptstyle {\text{Cor.}}&5{\overset {'}{.}}58{\overset {''}{,}}4&\scriptstyle {\text{Diff.}}&\scriptstyle {\text{Cor.}}&10{\overset {'}{.}}20{\overset {''}{,}}8&\scriptstyle {\text{Diff.}}&\scriptstyle {\text{Cor.}}&30{\overset {^{\circ }}{.}}\ \ 0'\\&&&+&&&+&&&+\\0.30&0.\ \ 6,3&6{\overset {''}{,}}3&0{\overset {''}{,}}0&6.\ \ 3,8&5{\overset {''}{,}}4&0{\overset {''}{,}}3&10.23,9&3{\overset {''}{,}}1&0{\overset {''}{,}}4&29.30\\1.\ \ 0&0.12,5&6,2&0,0&6.\ \ 9,2&5,4&0,3&10.26,9&3,0&0,4&29.\ \ 0\\1.30&0.18,8&6,3&0,0&6.14,5&5,3&0,3&10.29,9&3,0&0,4&28.30\\2.\ \ 0&0.25,1&6,3&0,0&6.19,9&5,4&0,3&10.32,9&3,0&0,4&28.\ \ 0\\2.30&0.31,3&6,2&0,0&6.25,2&5,3&0,3&10.35,8&2,9&0,4&27.30\\3.\ \ 0&0.37,6&6,3&0,0&6.30,4&5,2&0,3&10.38,7&2,9&0,4&27.\ \ 0\\\\3.30&0.43,8&6,2&0,0&6.35,6&5,2&0,3&10.41,5&2,8&0,4&26.30\\4.\ \ 0&0.50,0&6,2&0,0&6.40,8&5,2&0,3&10.44,3&2,8&0,4&26.\ \ 0\\4.30&0.56,3&6,3&0,0&6.46,0&5,2&0,3&10.47,0&2,7&0,5&25.30\\5.\ \ 0&1.\ \ 2,5&6,2&0,0&6.51,1&5,1&0,3&10.49,6&2,6&0,5&25.\ \ 0\\5.30&1.\ \ 8,7&6,2&0,1&6.56,2&5,1&0,3&10.52,2&2,6&0,5&24.30\\6.\ \ 0&1.15,0&6,3&0,1&7.\ \ 1,3&5,1&0,3&10.54,8&2,6&0,5&24.\ \ 0\\\\6.30&1.21,2&6,2&0,1&7.\ \ 6,4&5,1&0,3&10.57,3&2,5&0,5&23.30\\7.\ \ 0&1.27,4&6,2&0,1&7.11,4&5,0&0,3&10.59,8&2,5&0,5&23.\ \ 0\\7.30&1.33,6&6,2&0,1&7.16,4&5,0&0,3&11.\ \ 2,2&2,4&0,5&22.30\\8.\ \ 0&1.39,8&6,2&0,1&7.21,3&4,9&0,3&11.\ \ 4,6&2,4&0,5&22.\ \ 0\\8.30&1.46,0&6,2&0,1&7.26,2&4,9&0,3&11.\ \ 6,9&2,3&0,5&21.30\\9.\ \ 0&1.52,2&6,2&0,1&7.31,1&4,9&0,3&11.\ \ 9,2&2,3&0,5&21.\ \ 0\\\\9.30&1.58,3&6,1&0,1&7.35,9&4,8&0,3&11.11,4&2,2&0,5&20.30\\10.\ \ 0&2.\ \ 4,5&6,2&0,1&7.40,7&4,8&0,3&11.13,6&2,2&0,5&20.\ \ 0\\10.30&2.10,6&6,1&0,1&7.45,5&4,8&0,3&11.15,7&2,1&0,5&19.30\\11.\ \ 0&2.16,8&6,2&0,1&7.50,3&4,8&0,3&11.17,7&2,0&0,5&19.\ \ 0\\11.30&2.22,9&6,1&0,1&7.55,0&4,7&0,3&11.19,7&2,0&0,5&18.30\\12.\ \ 0&2.29,1&6,2&0,1&7.59,6&4,6&0,3&11.21,7&2,0&0,5&18.\ \ 0\\\\12.30&2.35,2&6,1&0,1&8.\ \ 4,3&4,7&0,3&11.23,6&1,9&0,5&17.30\\13.\ \ 0&2.41,3&6,1&0,1&8.\ \ 8,9&4,6&0,3&11.25,5&1,9&0,5&17.\ \ 0\\13.30&2.47,4&6,1&0,1&8.13,4&4,5&0,3&11.27,3&1,8&0,5&16.30\\14.\ \ 0&2.53,4&6,0&0,1&8.17,9&4,5&0,3&11.29,0&1,7&0,5&16.\ \ 0\\14.30&2.59,5&6,1&0,1&8.22,4&4,5&0,4&11.30,7&1,6&0,5&15.30\\15.\ \ 0&3.\ \ 5,5&6,0&0,1&8.26,8&4,4&0,4&11.32,4&1,7&0,5&15.\ \ 0\end{array}}}
_
⏟
⏟
⏟
_
S
.
XI
−
X
−
IX
−
S
.
S
.
V
+
IV
+
III
+
S
.
{\displaystyle {\begin{array}{|c|c|c|c|c|}{\underline {\quad \ \ \ \,}}&\underbrace {\ \,\qquad \qquad \qquad } &\underbrace {\ \ \qquad \qquad \qquad } &\underbrace {\ \ \ \,\qquad \qquad \qquad } &{\underline {\qquad }}\\{\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}}}