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Joseph Louis de Lagrange - Œuvres, Tome 7.djvu/458
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TABLE I.
(Suite)
{\displaystyle \scriptscriptstyle {\text{(Suite)}}}
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 {\qquad \,}}&\overbrace {\ \qquad \qquad \qquad } &\overbrace {\,\ \ \ \qquad \qquad \qquad } &\overbrace {\ \ \ \qquad \qquad \qquad } &{\overline {\qquad \,}}\end{array}}}
15
.
∘
0
′
3
.
′
5
,
″
5
Diff.
Cor.
8
.
′
26
,
″
8
Diff.
Cor.
11
.
′
32
,
″
4
Diff.
Cor.
15
.
∘
0
′
+
+
+
15.30
3.11
,
6
6
,
″
1
0
,
″
1
8.31
,
3
4
,
″
5
0
,
″
4
11.33
,
9
1
,
″
5
0
,
″
5
14.30
16.
0
3.17
,
6
6
,
0
0
,
1
8.35
,
7
4
,
4
0
,
4
11.35
,
5
1
,
6
0
,
5
14.
0
16.30
3.23
,
6
6
,
0
0
,
1
8.40
,
0
4
,
3
0
,
4
11.37
,
0
1
,
5
0
,
5
13.30
17.
0
3.29
,
6
6
,
0
0
,
1
8.44
,
2
4
,
2
0
,
4
11.38
,
4
1
,
4
0
,
5
13.
0
17.30
3.35
,
6
6
,
0
0
,
2
8.48
,
5
4
,
3
0
,
4
11.39
,
8
1
,
4
0
,
5
12.30
18.
0
3.41
,
5
5
,
9
0
,
2
8.52
,
7
4
,
2
0
,
4
11.41
,
1
1
,
3
0
,
5
12.
0
18.30
3.47
,
4
5
,
9
0
,
2
8.56
,
9
4
,
2
0
,
4
11.42
,
3
1
,
3
0
,
5
11.30
19.
0
3.53
,
3
5
,
9
0
,
2
9.
1
,
0
4
,
1
0
,
4
11.43
,
6
1
,
2
0
,
5
11.
0
19.30
3.59
,
2
5
,
9
0
,
2
9.
5
,
1
4
,
1
0
,
4
11.44
,
8
1
,
2
0
,
5
10.30
20.
0
4.
5
,
1
5
,
9
0
,
2
9.
9
,
1
4
,
0
0
,
4
11.45
,
9
1
,
1
0
,
5
10.
0
20.30
4.11
,
0
5
,
9
0
,
2
9.13
,
1
4
,
0
0
,
4
11.46
,
9
1
,
0
0
,
5
9.30
21.
0
4.16
,
9
5
,
9
0
,
2
9.17
,
1
4
,
0
0
,
4
11.48
,
0
1
,
1
0
,
5
9.
0
21.30
4.22
,
7
5
,
8
0
,
2
9.21
,
0
3
,
9
0
,
4
11.48
,
9
0
,
9
0
,
5
8.30
22.
0
4.28
,
5
5
,
8
0
,
2
9.24
,
9
3
,
9
0
,
4
11.49
,
8
0
,
9
0
,
5
8.
0
22.30
4.34
,
3
5
,
8
0
,
2
9.28
,
7
3
,
8
0
,
4
11.50
,
6
0
,
8
0
,
5
7.30
23.
0
4.40
,
1
5
,
8
0
,
2
9.32
,
5
3
,
8
0
,
4
11.51
,
4
0
,
8
0
,
5
7.
0
23.30
4.45
,
8
5
,
7
0
,
2
9.36
,
2
3
,
7
0
,
4
11.52
,
2
0
,
8
0
,
5
6.30
24.
0
4.51
,
6
5
,
8
0
,
2
9.39
,
9
3
,
7
0
,
4
11.52
,
8
0
,
6
0
,
5
6.
0
24.30
4.57
,
3
5
,
7
0
,
2
9.43
,
6
3
,
7
0
,
4
11.53
,
5
0
,
7
0
,
5
5.30
25.
0
5.
2
,
9
5
,
6
0
,
2
9.47
,
2
3
,
6
0
,
4
11.54
,
1
0
,
6
0
,
5
5.
0
25.30
5.
8
,
6
5
,
7
0
,
2
9.50
,
7
3
,
5
0
,
4
11.54
,
6
0
,
5
0
,
5
4.30
26.
0
5.14
,
2
5
,
6
0
,
2
9.54
,
3
3
,
6
0
,
4
11.55
,
0
0
,
4
0
,
5
4.
0
26.30
5.19
,
8
5
,
6
0
,
2
9.57
,
8
3
,
5
0
,
4
11.55
,
4
0
,
4
0
,
5
3.30
27.
0
5.25
,
4
5
,
6
0
,
2
10.
1
,
2
3
,
4
0
,
4
11.55
,
8
0
,
4
0
,
5
3.
0
27.30
5.31
,
0
5
,
6
0
,
2
10.
4
,
6
3
,
4
0
,
4
11.56
,
1
0
,
3
0
,
5
2.30
28.
0
5.36
,
5
5
,
5
0
,
2
10.
7
,
9
3
,
3
0
,
4
11.56
,
3
0
,
2
0
,
5
2.
0
28.30
5.42
,
0
5
,
5
0
,
2
10.11
,
2
3
,
3
0
,
4
11.56
,
5
0
,
2
0
,
5
1.30
29.
0
5.47
,
5
5
,
5
0
,
2
10.14
,
4
3
,
2
0
,
4
11.56
,
7
0
,
2
0
,
5
1.
0
29.30
5.53
,
0
5
,
5
0
,
2
10.17
,
6
3
,
2
0
,
4
11.56
,
8
0
,
1
0
,
5
0.30
30.
0
5.58
,
4
5
,
4
0
,
2
10.20
,
8
3
,
2
0
,
4
11.56
,
8
0
,
0
0
,
5
0.
0
{\displaystyle {\begin{array}{|c|c|c|c|c|c|c|c|c|c|c|}15{\overset {^{\circ }}{.}}\ \ 0'&3{\overset {'}{.}}\ \ 5{\overset {''}{,}}5&\scriptstyle {\text{Diff.}}&\scriptstyle {\text{Cor.}}&8{\overset {'}{.}}26{\overset {''}{,}}8&\scriptstyle {\text{Diff.}}&\scriptstyle {\text{Cor.}}&11{\overset {'}{.}}32{\overset {''}{,}}4&\scriptstyle {\text{Diff.}}&\scriptstyle {\text{Cor.}}&15{\overset {^{\circ }}{.}}\ \ 0'\\&&&+&&&+&&&+\\15.30&3.11,6&6{\overset {''}{,}}1&0{\overset {''}{,}}1&8.31,3&4{\overset {''}{,}}5&0{\overset {''}{,}}4&11.33,9&1{\overset {''}{,}}5&0{\overset {''}{,}}5&14.30\\16.\ \ 0&3.17,6&6,0&0,1&\ \ 8.35,7&4,4&0,4&11.35,5&1,6&0,5&14.\ \ 0\\16.30&3.23,6&6,0&0,1&\ \ 8.40,0&4,3&0,4&11.37,0&1,5&0,5&13.30\\17.\ \ 0&3.29,6&6,0&0,1&\ \ 8.44,2&4,2&0,4&11.38,4&1,4&0,5&13.\ \ 0\\17.30&3.35,6&6,0&0,2&\ \ 8.48,5&4,3&0,4&11.39,8&1,4&0,5&12.30\\18.\ \ 0&3.41,5&5,9&0,2&\ \ 8.52,7&4,2&0,4&11.41,1&1,3&0,5&12.\ \ 0\\\\18.30&3.47,4&5,9&0,2&\ \ 8.56,9&4,2&0,4&11.42,3&1,3&0,5&11.30\\19.\ \ 0&3.53,3&5,9&0,2&\ \ 9.\ \ 1,0&4,1&0,4&11.43,6&1,2&0,5&11.\ \ 0\\19.30&3.59,2&5,9&0,2&\ \ 9.\ \ 5,1&4,1&0,4&11.44,8&1,2&0,5&10.30\\20.\ \ 0&4.\ \ 5,1&5,9&0,2&\ \ 9.\ \ 9,1&4,0&0,4&11.45,9&1,1&0,5&10.\ \ 0\\20.30&4.11,0&5,9&0,2&\ \ 9.13,1&4,0&0,4&11.46,9&1,0&0,5&\ \ 9.30\\21.\ \ 0&4.16,9&5,9&0,2&\ \ 9.17,1&4,0&0,4&11.48,0&1,1&0,5&\ \ 9.\ \ 0\\\\21.30&4.22,7&5,8&0,2&\ \ 9.21,0&3,9&0,4&11.48,9&0,9&0,5&\ \ 8.30\\22.\ \ 0&4.28,5&5,8&0,2&\ \ 9.24,9&3,9&0,4&11.49,8&0,9&0,5&\ \ 8.\ \ 0\\22.30&4.34,3&5,8&0,2&\ \ 9.28,7&3,8&0,4&11.50,6&0,8&0,5&\ \ 7.30\\23.\ \ 0&4.40,1&5,8&0,2&\ \ 9.32,5&3,8&0,4&11.51,4&0,8&0,5&\ \ 7.\ \ 0\\23.30&4.45,8&5,7&0,2&\ \ 9.36,2&3,7&0,4&11.52,2&0,8&0,5&\ \ 6.30\\24.\ \ 0&4.51,6&5,8&0,2&\ \ 9.39,9&3,7&0,4&11.52,8&0,6&0,5&\ \ 6.\ \ 0\\\\24.30&4.57,3&5,7&0,2&\ \ 9.43,6&3,7&0,4&11.53,5&0,7&0,5&\ \ 5.30\\25.\ \ 0&5.\ \ 2,9&5,6&0,2&\ \ 9.47,2&3,6&0,4&11.54,1&0,6&0,5&\ \ 5.\ \ 0\\25.30&5.\ \ 8,6&5,7&0,2&\ \ 9.50,7&3,5&0,4&11.54,6&0,5&0,5&\ \ 4.30\\26.\ \ 0&5.14,2&5,6&0,2&\ \ 9.54,3&3,6&0,4&11.55,0&0,4&0,5&\ \ 4.\ \ 0\\26.30&5.19,8&5,6&0,2&\ \ 9.57,8&3,5&0,4&11.55,4&0,4&0,5&\ \ 3.30\\27.\ \ 0&5.25,4&5,6&0,2&10.\ \ 1,2&3,4&0,4&11.55,8&0,4&0,5&\ \ 3.\ \ 0\\\\27.30&5.31,0&5,6&0,2&10.\ \ 4,6&3,4&0,4&11.56,1&0,3&0,5&\ \ 2.30\\28.\ \ 0&5.36,5&5,5&0,2&10.\ \ 7,9&3,3&0,4&11.56,3&0,2&0,5&\ \ 2.\ \ 0\\28.30&5.42,0&5,5&0,2&10.11,2&3,3&0,4&11.56,5&0,2&0,5&\ \ 1.30\\29.\ \ 0&5.47,5&5,5&0,2&10.14,4&3,2&0,4&11.56,7&0,2&0,5&\ \ 1.\ \ 0\\29.30&5.53,0&5,5&0,2&10.17,6&3,2&0,4&11.56,8&0,1&0,5&\ \ 0.30\\30.\ \ 0&5.58,4&5,4&0,2&10.20,8&3,2&0,4&11.56,8&0,0&0,5&\ \ 0.\ \ 0\end{array}}}
_
⏟
⏟
⏟
_
S
.
XI
−
X
−
IX
−
S
.
S
.
V
+
IV
+
III
+
S
.
{\displaystyle {\begin{array}{|c|c|c|c|c|}{\underline {\qquad \,}}&\underbrace {\ \,\qquad \qquad \qquad } &\underbrace {\quad \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}}}