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Joseph Louis de Lagrange - Œuvres, Tome 6.djvu/606
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log
1,018
05
=
0,007
7692
,
log
0,981
95
=
9,992
0894
,
log
p
2
=
log
386
=
2,586
5873
_
,
log
F
=
2,594
3565
,
log
G
=
2,578
6767.
{\displaystyle {\begin{aligned}\log 1{,}01805=&0{,}0077692,\\\log 0{,}98195=&9{,}9920894,\\\log {\frac {p}{2}}=\log 386=&{\underline {2{,}5865873}},\\\log \mathrm {F} =&2{,}5943565,\\\log \mathrm {G} =&2{,}5786767.\end{aligned}}}
Donc
F
=
392
,
97
,
G
=
379
,
03.
{\displaystyle \mathrm {F} =392{,}97,\quad \mathrm {G} =379{,}03.}
Employant maintenant les valeurs trouvées d’après la seconde série, on aura
q
+
q
′
=
0,844
20
,
q
−
q
′
=
13,470
96
,
log
=
1,129
3986
,
2
log
=
2,258
7972
,
(
q
−
q
′
)
2
=
181,467
20
,
−
4
p
′
=
−
176,535
76
_
,
4,931
44
log
=
0,692
9746
,
1
2
log
=
0,346
4872
,
{\displaystyle {\begin{alignedat}{3}q+q'\quad =&\qquad \,0{,}84420,\\q-q'\quad =&\quad \ \ \ 13{,}47096,\qquad &\log =&1{,}1293986,\qquad &2\log =&2{,}2587972,\\(q-q')^{2}=&\quad \ 181{,}46720,\\-4p'=&-{\underline {176{,}53576}},\\&4{,}93144&\log =&0{,}6929746,&{\frac {1}{2}}\log =&0{,}3464872,\end{alignedat}}}
(
q
−
q
′
)
2
−
4
p
′
=
2,220
69
,
q
+
q
′
=
0,844
20
_
.
S
o
m
m
e
…
…
…
3,064
89.
D
i
f
f
e
´
r
e
n
c
e
…
…
1,376
49.
{\displaystyle {\begin{aligned}{\sqrt {(q-q')^{2}-4p'}}=&2{,}22069,\\q+q'=&{\underline {0{,}84420}}.\\\mathrm {Somme} \ldots \ldots \ldots \ \ &3{,}06489.\\\mathrm {Diff{\acute {e}}rence} \ldots \ldots \ \ &1{,}37649.\\\end{aligned}}}
Donc
ϖ
=
0,688
24
,
ρ
=
−
1,532
44.
{\displaystyle \varpi =0{,}68824,\quad \rho =-1{,}53244.}
Ensuite
log
(
q
−
q
′
)
=
1,129
3986
,
log
(
q
−
q
′
)
2
−
4
p
′
=
0,346
4873
_
.
D
i
f
f
e
´
r
e
n
c
e
…
…
0,782
9113.
N
o
m
b
r
e
c
o
r
r
.
=
6,066
12.
{\displaystyle {\begin{alignedat}{2}\log(q-q')=&1{,}1293986,\\\log {\sqrt {(q-q')^{2}-4p'}}=&{\underline {0{,}3464873}}.\\\mathrm {Diff{\acute {e}}rence} \ldots \ldots \ \ &0{,}7829113.\qquad &\mathrm {Nombre\ corr} .=6{,}06612.\end{alignedat}}}
log
5,066
12
=
0,704
6755
,
log
7,066
12
=
0,849
1800
,
log
−
p
2
=
log
82
,
5
=
1,916
4539
_
,
log
(
F
)
=
2,621
1294
,
log
(
G
)
=
2,765
6339.
{\displaystyle {\begin{aligned}\log 5{,}06612=&0{,}7046755,\\\log 7{,}06612=&0{,}8491800,\\\log -{\frac {p}{2}}=\log 82{,}5=&{\underline {1{,}9164539}},\\\log(\mathrm {F} )=&2{,}6211294,\\\log(\mathrm {G} )=&2{,}7656339.\end{aligned}}}