Geography Reference
In-Depth Information
Proof ((
16.48
):
l
1
).
Ω
)=
A
2
tan(
L
−
A
1
cos
i
tan
α,
(16.60)
d
α
=
A
2
dtan(
L
−
Ω
)
1
cos
2
(
L
d
L
cos
i
cos
2
α
,
=
A
1
d
α
−
Ω
)
1
1+tan
2
(
L
1
cos
2
(
L
−
Ω
)=
Ω
)
=
−
1+
A
2
cos
2
i
A
1
tan
2
α
⇒
d
α
=
A
2
d
L
cos
i
cos
2
α
=
1
=
(16.61)
A
1
1+
A
2
cos
2
i
A
1
tan
2
α
A
1
A
2
cos
i
A
1
cos
2
α
+
A
2
cos
2
i
sin
2
α
⇒
l
1
:=
d
L
=
d
α
(
α
0
)
.
End of Proof.
Proof ((
16.47
):
b
2
).
d
2
B
d
α
2
=
A
2
A
1
(1
E
2
)sin
i
−
×
sin
α
[
A
1
(1
E
2
)
2
+
E
2
A
2
sin
2
i
sin
2
α
]
−
1
[
A
1
+(
A
2
cos
2
i − A
1
)sin
2
α
]
−
1
/
2
×
−
−
−
2
E
2
A
2
sin
2
i
sin
α
cos
2
α
−
×
E
2
)
2
+
E
2
A
2
sin
2
i
sin
2
α
]
−
2
[
A
1
+(
A
2
cos
2
i
A
1
)sin
2
α
]
−
1
/
2
[
A
1
(1
×
−
−
−
(16.62)
(
A
2
cos
2
i
A
1
)sin
α
cos
2
α
−
−
×
A
1
)sin
2
α
]
−
3
/
2
[
A
1
(1
E
2
)
2
+
E
2
A
2
sin
2
i
sin
2
α
]
−
1
[
A
1
+(
A
2
cos
2
i
×
−
−
⇒
2
b
2
:=
d
2
B
d
α
2
(
α
0
)
.
End of Proof.
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