Accueil
Au hasard
Se connecter
Configuration
Faire un don
À propos de Wikisource
Avertissements
Rechercher
Page
:
Joseph Louis de Lagrange - Œuvres, Tome 7.djvu/459
Langue
Suivre
Modifier
Le texte de cette page a été
corrigé
et est conforme au fac-similé.
TABLE II.
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 \quad \ \ \ \,&\scriptstyle {\text{Arg. III, pour }}\mu \psi =\arg .{\text{ I pour }}\mu \psi +\theta .&\qquad \qquad \quad \ \ \ \,\\&\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 {\quad \ \ \ }}&\overbrace {\ \ \ \,\qquad \qquad \qquad } &\overbrace {\quad \,\qquad \qquad \qquad } &\overbrace {\ \ \ \qquad \qquad \qquad } &{\overline {\qquad \,}}\end{array}}}
0
.
∘
0
′
0
.
′
0
,
″
0
Diff.
Cor.
14
.
′
22
,
″
8
Diff.
Cor.
24
.
′
54
,
″
4
Diff.
Cor.
30
.
∘
0
′
−
−
−
0.30
0.15
,
1
15
,
″
1
0
,
″
0
14.35
,
8
13
,
″
0
0
,
″
1
25.
1
,
8
7
,
″
4
0
,
″
1
29.30
1.
0
0.30
,
1
15
,
0
0
,
0
14.48
,
7
12
,
9
0
,
1
25.
9
,
2
7
,
4
0
,
1
29.
0
1.30
0.45
,
2
15
,
1
0
,
0
15.
1
,
6
12
,
9
0
,
1
25.16
,
4
7
,
2
0
,
1
28.30
2.
0
1.
0
,
2
15
,
0
0
,
0
15.14
,
4
12
,
8
0
,
1
25.23
,
6
7
,
2
0
,
1
28.
0
2.30
1.15
,
3
15
,
1
0
,
0
15.27
,
1
12
,
7
0
,
1
25.30
,
6
7
,
0
0
,
1
27.30
3.
0
1.30
,
3
15
,
0
0
,
0
15.39
,
8
12
,
7
0
,
1
25.37
,
4
6
,
8
0
,
1
27.
0
3.30
1.45
,
3
15
,
0
0
,
0
15.52
,
4
12
,
6
0
,
1
25.44
,
2
6
,
8
0
,
1
26.30
4.
0
2.
0
,
4
15
,
1
0
,
0
16.
4
,
9
12
,
5
0
,
1
25.50
,
9
6
,
7
0
,
1
26.
0
4.30
2.15
,
4
15
,
0
0
,
0
16.17
,
4
12
,
5
0
,
1
25.57
,
5
6
,
6
0
,
1
25.30
5.
0
2.30
,
4
15
,
0
0
,
0
16.29
,
7
12
,
3
0
,
1
26.
3
,
9
6
,
4
0
,
1
25.
0
5.30
2.45
,
4
15
,
0
0
,
0
16.42
,
0
12
,
3
0
,
1
26.10
,
5
6
,
3
0
,
1
24.30
6.
0
3.
0
,
4
15
,
0
0
,
0
16.54
,
3
12
,
3
0
,
1
26.16
,
4
6
,
2
0
,
1
24.
0
6.30
3.15
,
3
14
,
9
0
,
0
17.
6
,
4
12
,
1
0
,
1
26.22
,
4
6
,
0
0
,
1
23.30
7.
0
3.30
,
3
15
,
0
0
,
0
17.18
,
5
12
,
1
0
,
1
26.28
,
4
6
,
0
0
,
1
23.
0
7.30
3.45
,
2
14
,
9
0
,
0
17.30
,
4
11
,
9
0
,
1
26.34
,
2
5
,
8
0
,
1
22.30
8.
0
4.
0
,
2
15
,
0
0
,
0
17.42
,
4
12
,
0
0
,
1
26.39
,
9
5
,
7
0
,
1
22.
0
8.30
4.15
,
1
14
,
9
0
,
0
17.54
,
2
11
,
8
0
,
1
26.45
,
5
5
,
6
0
,
1
21.30
9.
0
4.29
,
9
14
,
8
0
,
0
18.
5
,
9
11
,
7
0
,
1
26.50
,
9
5
,
4
0
,
1
21.
0
9.30
4.44
,
8
14
,
9
0
,
0
18.17
,
6
11
,
7
0
,
1
26.56
,
3
5
,
4
0
,
1
20.30
10.
0
4.59
,
6
14
,
8
0
,
0
18.29
,
2
11
,
6
0
,
1
27.
1
,
5
5
,
2
0
,
1
20.
0
10.30
5.14
,
5
14
,
9
0
,
0
18.40
,
7
11
,
5
0
,
1
27.
6
,
6
5
,
1
0
,
1
19.30
11.
0
5.29
,
3
14
,
8
0
,
0
18.52
,
1
11
,
4
0
,
1
27.11
,
6
5
,
0
0
,
1
19.
0
11.30
5.44
,
0
14
,
7
0
,
0
19.
3
,
4
11
,
3
0
,
1
27.16
,
4
4
,
8
0
,
1
18.30
12.
0
5.58
,
8
14
,
8
0
,
0
19.14
,
6
11
,
2
0
,
1
27.21
,
1
4
,
7
0
,
1
18.
0
12.30
6.13
,
5
14
,
7
0
,
0
19.25
,
8
11
,
2
0
,
1
27.25
,
7
4
,
6
0
,
1
17.30
13.
0
6.28
,
2
14
,
7
0
,
0
19.36
,
8
11
,
0
0
,
1
27.30
,
2
4
,
5
0
,
1
17.
0
13.30
6.42
,
8
14
,
6
0
,
0
19.47
,
8
11
,
0
0
,
1
27.34
,
5
4
,
3
0
,
1
16.30
14.
0
6.57
,
4
14
,
6
0
,
0
19.58
,
7
10
,
9
0
,
1
27.38
,
7
4
,
2
0
,
1
16.
0
14.30
7.12
,
0
14
,
6
0
,
0
20.
9
,
5
10
,
8
0
,
1
27.42
,
8
4
,
1
0
,
1
15.30
15.
0
7.26
,
6
14
,
6
0
,
0
20.20
,
2
10
,
7
0
,
1
27.46
,
8
4
,
0
0
,
1
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.}}&14{\overset {'}{.}}22{\overset {''}{,}}8&\scriptstyle {\text{Diff.}}&\scriptstyle {\text{Cor.}}&24{\overset {'}{.}}54{\overset {''}{,}}4&\scriptstyle {\text{Diff.}}&\scriptstyle {\text{Cor.}}&30{\overset {^{\circ }}{.}}\ \ 0'\\&&&-&&&-&&&-\\\ \ 0.30&0.15,1&15{\overset {''}{,}}1&0{\overset {''}{,}}0&14.35,8&13{\overset {''}{,}}0&0{\overset {''}{,}}1&25.\ \ 1,8&7{\overset {''}{,}}4&0{\overset {''}{,}}1&29.30\\\ \ 1.\ \ 0&0.30,1&15,0&0,0&14.48,7&12,9&0,1&25.\ \ 9,2&7,4&0,1&29.\ \ 0\\\ \ 1.30&0.45,2&15,1&0,0&15.\ \ 1,6&12,9&0,1&25.16,4&7,2&0,1&28.30\\\ \ 2.\ \ 0&1.\ \ 0,2&15,0&0,0&15.14,4&12,8&0,1&25.23,6&7,2&0,1&28.\ \ 0\\\ \ 2.30&1.15,3&15,1&0,0&15.27,1&12,7&0,1&25.30,6&7,0&0,1&27.30\\\ \ 3.\ \ 0&1.30,3&15,0&0,0&15.39,8&12,7&0,1&25.37,4&6,8&0,1&27.\ \ 0\\\\\ \ 3.30&1.45,3&15,0&0,0&15.52,4&12,6&0,1&25.44,2&6,8&0,1&26.30\\\ \ 4.\ \ 0&2.\ \ 0,4&15,1&0,0&16.\ \ 4,9&12,5&0,1&25.50,9&6,7&0,1&26.\ \ 0\\\ \ 4.30&2.15,4&15,0&0,0&16.17,4&12,5&0,1&25.57,5&6,6&0,1&25.30\\\ \ 5.\ \ 0&2.30,4&15,0&0,0&16.29,7&12,3&0,1&26.\ \ 3,9&6,4&0,1&25.\ \ 0\\\ \ 5.30&2.45,4&15,0&0,0&16.42,0&12,3&0,1&26.10,5&6,3&0,1&24.30\\\ \ 6.\ \ 0&3.\ \ 0,4&15,0&0,0&16.54,3&12,3&0,1&26.16,4&6,2&0,1&24.\ \ 0\\\\\ \ 6.30&3.15,3&14,9&0,0&17.\ \ 6,4&12,1&0,1&26.22,4&6,0&0,1&23.30\\\ \ 7.\ \ 0&3.30,3&15,0&0,0&17.18,5&12,1&0,1&26.28,4&6,0&0,1&23.\ \ 0\\\ \ 7.30&3.45,2&14,9&0,0&17.30,4&11,9&0,1&26.34,2&5,8&0,1&22.30\\\ \ 8.\ \ 0&4.\ \ 0,2&15,0&0,0&17.42,4&12,0&0,1&26.39,9&5,7&0,1&22.\ \ 0\\\ \ 8.30&4.15,1&14,9&0,0&17.54,2&11,8&0,1&26.45,5&5,6&0,1&21.30\\\ \ 9.\ \ 0&4.29,9&14,8&0,0&18.\ \ 5,9&11,7&0,1&26.50,9&5,4&0,1&21.\ \ 0\\\\\ \ 9.30&4.44,8&14,9&0,0&18.17,6&11,7&0,1&26.56,3&5,4&0,1&20.30\\10.\ \ 0&4.59,6&14,8&0,0&18.29,2&11,6&0,1&27.\ \ 1,5&5,2&0,1&20.\ \ 0\\10.30&5.14,5&14,9&0,0&18.40,7&11,5&0,1&27.\ \ 6,6&5,1&0,1&19.30\\11.\ \ 0&5.29,3&14,8&0,0&18.52,1&11,4&0,1&27.11,6&5,0&0,1&19.\ \ 0\\11.30&5.44,0&14,7&0,0&19.\ \ 3,4&11,3&0,1&27.16,4&4,8&0,1&18.30\\12.\ \ 0&5.58,8&14,8&0,0&19.14,6&11,2&0,1&27.21,1&4,7&0,1&18.\ \ 0\\\\12.30&6.13,5&14,7&0,0&19.25,8&11,2&0,1&27.25,7&4,6&0,1&17.30\\13.\ \ 0&6.28,2&14,7&0,0&19.36,8&11,0&0,1&27.30,2&4,5&0,1&17.\ \ 0\\13.30&6.42,8&14,6&0,0&19.47,8&11,0&0,1&27.34,5&4,3&0,1&16.30\\14.\ \ 0&6.57,4&14,6&0,0&19.58,7&10,9&0,1&27.38,7&4,2&0,1&16.\ \ 0\\14.30&7.12,0&14,6&0,0&20.\ \ 9,5&10,8&0,1&27.42,8&4,1&0,1&15.30\\15.\ \ 0&7.26,6&14,6&0,0&20.20,2&10,7&0,1&27.46,8&4,0&0,1&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 {\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}}}