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Ω
=arcsin
Λ
1
−
Λ
2
Λ
1
+
Λ
2
,
(F.62)
Λ
2
=
(tr[C
l
G
−
l
])
2
,Λ
1
+
Λ
2
=
(tr[C
l
G
−
l
]) + 2
.
Λ
1
−
−
(F.63)
End of Corollary.
Proof.
Λ
2
)
2
and (
Λ
1
+
Λ
2
)
2
under the postulate of an equiareal
mapping
Λ
1
Λ
2
= 1, namely by means of (
F.48
).
(
Λ
1
− Λ
2
)
2
=
Λ
1
+
Λ
2
−
2
Λ
1
Λ
2
=
Λ
1
+
Λ
2
−
2= tr[C
l
G
−
l
]
−
2
,
For the proof of (
F.63
) just compute (
Λ
1
−
(F.64)
(
Λ
1
+
Λ
2
)
2
=
Λ
1
+
Λ
2
+2
Λ
1
Λ
2
=
Λ
1
+
Λ
2
+2= tr[C
l
G
−
l
]+2
.
End of Proof.
Fig. F.1.
Vertical weighted mean of the generalized Lambert projection and the generalized Sanson-Flamsteed
projection of the biaxial ellipsoid
E
2
A,B
, squared relative eccentricity
E
2
=0
.
1, weight parameters
α
=1,
β
=0
.
1
Fig. F.2.
Vertical weighted mean of the generalized Lambert projection and the generalized Sanson-Flamsteed
projection of the biaxial ellipsoid
E
2
A,B
, squared relative eccentricity
E
2
=0
.
1, weight parameters
α
=1,
β
=0
.
5
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