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Joseph Louis de Lagrange - Œuvres, Tome 7.djvu/460
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TABLE II.
(Suite)
{\displaystyle \scriptscriptstyle {\text{(Suite)}}}
pour déterminer les valeurs de
μ
ψ
,
λ
ψ
,
ψ
{\displaystyle \mu \psi ,\lambda \psi ,\psi }
étant supposé
=
1
∘
.
{\displaystyle =1^{\circ }.}
Arg. III, pour
μ
ψ
=
arg
.
I pour
μ
ψ
+
θ
.
Arg. IV, pour
μ
ψ
=
arg
.
II pour
μ
ψ
+
θ
−
VI signes
.
Arg. III, pour
λ
ψ
=
III signes
−
arg
.
III pour
μ
ψ
.
Arg. IV, pour
λ
ψ
=
III signes
−
arg
.
IV pour
μ
ψ
.
{\displaystyle {\begin{array}{|clc|}\hline \qquad \qquad \qquad \,&\scriptstyle {\text{Arg. III, pour }}\mu \psi =\arg .{\text{ I pour }}\mu \psi +\theta .&\qquad \qquad \qquad \,\\&\scriptstyle {\text{Arg. IV, pour }}\,\mu \psi =\arg .{\text{ II pour }}\mu \psi +\theta -{\text{VI signes}}.\\&\scriptstyle {\text{Arg. III, pour }}\,\lambda \psi ={\text{III signes}}-\arg .\ {\text{III pour }}\mu \psi .\\&\scriptstyle {\text{Arg. IV, pour }}\ \lambda \psi ={\text{III signes}}-\arg .{\text{ IV 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 {\qquad \,}}&\overbrace {\quad \,\qquad \qquad \qquad } &\overbrace {\quad \,\qquad \qquad \qquad } &\overbrace {\,\ \ \ \qquad \qquad \qquad } &{\overline {\qquad }}\end{array}}}
15
.
∘
0
′
7
.
′
26
,
″
6
Diff.
Cor.
20
.
′
20
,
″
2
Diff.
Cor.
27
.
′
46
,
″
8
Diff.
Cor.
15
.
∘
0
′
−
−
+
15.30
7.41
,
1
14
,
″
5
0
,
″
0
20.30
,
8
10
,
″
6
0
,
″
1
27.50
,
6
3
,
″
8
0
,
″
1
14.30
16.
0
7.55
,
6
14
,
5
0
,
0
20.41
,
3
10
,
5
0
,
1
27.54
,
3
3
,
7
0
,
1
14.
0
16.30
8.10
,
1
14
,
5
0
,
0
20.51
,
7
10
,
4
0
,
1
27.57
,
9
3
,
6
0
,
1
13.30
17.
0
8.24
,
5
14
,
4
0
,
0
21.
2
,
0
10
,
6
0
,
1
28.
1
,
3
3
,
4
0
,
1
13.
0
17.30
8.38
,
9
14
,
4
0
,
0
21.12
,
2
10
,
2
0
,
1
28.
4
,
6
3
,
3
0
,
1
12.30
18.
0
8.53
,
2
14
,
3
0
,
0
21.22
,
3
10
,
1
0
,
1
28.
7
,
8
3
,
2
0
,
1
12.
0
18.30
9.
7
,
5
14
,
3
0
,
0
21.32
,
4
10
,
1
0
,
1
28.10
,
9
3
,
1
0
,
1
11.30
19.
0
9.21
,
8
14
,
3
0
,
0
21.42
,
3
9
,
9
0
,
1
28.13
,
8
2
,
9
0
,
1
11.
0
19.30
9.36
,
0
14
,
2
0
,
0
21.52
,
1
9
,
8
0
,
1
28.16
,
6
2
,
8
0
,
1
10.30
20.
0
9.50
,
2
14
,
2
0
,
0
22.
1
,
8
9
,
7
0
,
1
28.19
,
3
2
,
7
0
,
1
10.
0
20.30
10.
4
,
3
14
,
1
0
,
0
22.11
,
5
9
,
7
0
,
1
28.21
,
9
2
,
6
0
,
1
9.30
21.
0
10.18
,
4
14
,
1
0
,
0
22.21
,
0
9
,
5
0
,
1
28.24
,
3
2
,
4
0
,
1
9.
0
21.30
10.32
,
4
14
,
0
0
,
0
22.30
,
4
9
,
4
0
,
1
28.26
,
6
2
,
3
0
,
1
8.30
22.
0
10.46
,
4
14
,
0
0
,
0
22.39
,
8
9
,
4
0
,
1
28.28
,
8
2
,
2
0
,
1
8.
0
22.30
11.
0
,
3
13
,
9
0
,
0
22.49
,
0
9
,
2
0
,
1
28.30
,
8
2
,
0
0
,
1
7.30
23.
0
11.14
,
2
13
,
9
0
,
0
22.58
,
1
9
,
1
0
,
1
28.32
,
7
1
,
9
0
,
1
7.
0
23.30
11.28
,
1
13
,
9
0
,
0
23.
7
,
1
9
,
0
0
,
1
28.34
,
5
1
,
8
0
,
1
6.30
24.
0
11.41
,
8
13
,
7
0
,
0
23.16
,
0
8
,
9
0
,
1
28.36
,
1
1
,
6
0
,
1
6.
0
24.30
11.55
,
6
13
,
8
0
,
0
23.24
,
8
8
,
8
0
,
1
28.37
,
6
1
,
5
0
,
1
5.30
25.
0
12.
9
,
3
13
,
7
0
,
0
23.33
,
5
8
,
7
0
,
1
28.39
,
0
1
,
4
0
,
1
5.
0
25.30
12.22
,
9
13
,
6
0
,
0
23.42
,
1
8
,
6
0
,
1
28.40
,
2
1
,
2
0
,
1
4.30
26.
0
12.36
,
4
13
,
5
0
,
0
23.50
,
6
8
,
5
0
,
1
28.41
,
3
1
,
1
0
,
1
4.
0
26.30
12.49
,
9
13
,
5
0
,
0
23.58
,
9
8
,
3
0
,
1
28.42
,
3
1
,
0
0
,
1
3.30
27.
0
13.
3
,
4
13
,
5
0
,
0
24.
7
,
2
8
,
3
0
,
1
28.43
,
2
0
,
9
0
,
1
3.
0
27.30
13.16
,
8
13
,
4
0
,
0
24.15
,
3
8
,
1
0
,
1
28.43
,
9
0
,
7
0
,
1
2.30
28.
0
13.30
,
1
13
,
3
0
,
0
24.23
,
4
8
,
1
0
,
1
28.44
,
5
0
,
6
0
,
1
2.
0
28.30
13.43
,
4
13
,
3
0
,
0
24.31
,
3
7
,
9
0
,
1
28.45
,
0
0
,
5
0
,
1
1.30
29.
0
13.56
,
6
13
,
2
0
,
0
24.39
,
1
7
,
8
0
,
1
28.45
,
3
0
,
3
0
,
1
1.
0
29.30
14.
9
,
7
13
,
1
0
,
0
24.46
,
8
7
,
7
0
,
1
28.45
,
5
0
,
2
0
,
1
0.30
30.
0
14.22
,
8
13
,
1
0
,
0
24.54
,
4
7
,
6
0
,
1
28.45
,
6
0
,
1
0
,
1
0.
0
{\displaystyle {\begin{array}{|c|c|c|c|c|c|c|c|c|c|c|}15{\overset {^{\circ }}{.}}\ \ 0'&7{\overset {'}{.}}26{\overset {''}{,}}6&\scriptstyle {\text{Diff.}}&\scriptstyle {\text{Cor.}}&20{\overset {'}{.}}20{\overset {''}{,}}2&\scriptstyle {\text{Diff.}}&\scriptstyle {\text{Cor.}}&27{\overset {'}{.}}46{\overset {''}{,}}8&\scriptstyle {\text{Diff.}}&\scriptstyle {\text{Cor.}}&15{\overset {^{\circ }}{.}}\ \ 0'\\&&&-&&&-&&&+\\15.30&7.41,1&14{\overset {''}{,}}5&0{\overset {''}{,}}0&20.30,8&10{\overset {''}{,}}6&0{\overset {''}{,}}1&27.50,6&3{\overset {''}{,}}8&0{\overset {''}{,}}1&14.30\\16.\ \ 0&\ \ 7.55,6&14,5&0,0&20.41,3&10,5&0,1&27.54,3&3,7&0,1&14.\ \ 0\\16.30&\ \ 8.10,1&14,5&0,0&20.51,7&10,4&0,1&27.57,9&3,6&0,1&13.30\\17.\ \ 0&\ \ 8.24,5&14,4&0,0&21.\ \ 2,0&10,6&0,1&28.\ \ 1,3&3,4&0,1&13.\ \ 0\\17.30&\ \ 8.38,9&14,4&0,0&21.12,2&10,2&0,1&28.\ \ 4,6&3,3&0,1&12.30\\18.\ \ 0&\ \ 8.53,2&14,3&0,0&21.22,3&10,1&0,1&28.\ \ 7,8&3,2&0,1&12.\ \ 0\\\\18.30&\ \ 9.\ \ 7,5&14,3&0,0&21.32,4&10,1&0,1&28.10,9&3,1&0,1&11.30\\19.\ \ 0&\ \ 9.21,8&14,3&0,0&21.42,3&\ \ 9,9&0,1&28.13,8&2,9&0,1&11.\ \ 0\\19.30&\ \ 9.36,0&14,2&0,0&21.52,1&\ \ 9,8&0,1&28.16,6&2,8&0,1&10.30\\20.\ \ 0&\ \ 9.50,2&14,2&0,0&22.\ \ 1,8&\ \ 9,7&0,1&28.19,3&2,7&0,1&10.\ \ 0\\20.30&10.\ \ 4,3&14,1&0,0&22.11,5&\ \ 9,7&0,1&28.21,9&2,6&0,1&\ \ 9.30\\21.\ \ 0&10.18,4&14,1&0,0&22.21,0&\ \ 9,5&0,1&28.24,3&2,4&0,1&\ \ 9.\ \ 0\\\\21.30&10.32,4&14,0&0,0&22.30,4&\ \ 9,4&0,1&28.26,6&2,3&0,1&\ \ 8.30\\22.\ \ 0&10.46,4&14,0&0,0&22.39,8&\ \ 9,4&0,1&28.28,8&2,2&0,1&\ \ 8.\ \ 0\\22.30&11.\ \ 0,3&13,9&0,0&22.49,0&\ \ 9,2&0,1&28.30,8&2,0&0,1&\ \ 7.30\\23.\ \ 0&11.14,2&13,9&0,0&22.58,1&\ \ 9,1&0,1&28.32,7&1,9&0,1&\ \ 7.\ \ 0\\23.30&11.28,1&13,9&0,0&23.\ \ 7,1&\ \ 9,0&0,1&28.34,5&1,8&0,1&\ \ 6.30\\24.\ \ 0&11.41,8&13,7&0,0&23.16,0&\ \ 8,9&0,1&28.36,1&1,6&0,1&\ \ 6.\ \ 0\\\\24.30&11.55,6&13,8&0,0&23.24,8&\ \ 8,8&0,1&28.37,6&1,5&0,1&\ \ 5.30\\25.\ \ 0&12.\ \ 9,3&13,7&0,0&23.33,5&\ \ 8,7&0,1&28.39,0&1,4&0,1&\ \ 5.\ \ 0\\25.30&12.22,9&13,6&0,0&23.42,1&\ \ 8,6&0,1&28.40,2&1,2&0,1&\ \ 4.30\\26.\ \ 0&12.36,4&13,5&0,0&23.50,6&\ \ 8,5&0,1&28.41,3&1,1&0,1&\ \ 4.\ \ 0\\26.30&12.49,9&13,5&0,0&23.58,9&\ \ 8,3&0,1&28.42,3&1,0&0,1&\ \ 3.30\\27.\ \ 0&13.\ \ 3,4&13,5&0,0&24.\ \ 7,2&\ \ 8,3&0,1&28.43,2&0,9&0,1&\ \ 3.\ \ 0\\\\27.30&13.16,8&13,4&0,0&24.15,3&\ \ 8,1&0,1&28.43,9&0,7&0,1&\ \ 2.30\\28.\ \ 0&13.30,1&13,3&0,0&24.23,4&\ \ 8,1&0,1&28.44,5&0,6&0,1&\ \ 2.\ \ 0\\28.30&13.43,4&13,3&0,0&24.31,3&\ \ 7,9&0,1&28.45,0&0,5&0,1&\ \ 1.30\\29.\ \ 0&13.56,6&13,2&0,0&24.39,1&\ \ 7,8&0,1&28.45,3&0,3&0,1&\ \ 1.\ \ 0\\29.30&14.\ \ 9,7&13,1&0,0&24.46,8&\ \ 7,7&0,1&28.45,5&0,2&0,1&\ \ 0.30\\30.\ \ 0&14.22,8&13,1&0,0&24.54,4&\ \ 7,6&0,1&28.45,6&0,1&0,1&\ \ 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 {\quad \ \,\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}}}