Тригонометрия гиперболической плоскости положительной кривизны. Ромакина Л.Н. - 52 стр.

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b ABC R
c E E
0
(1 : 1 : 1)
E ˜c AB P
1
= A
E b
(P
2
= A
E
0
b) b
R P
1
(b
3
: 0 : c
3
) P
2
(b
3
: 0 : c
3
)
λ
1
= (AC, P
1
) =
b
3
b
3
1
, λ
2
= (AC, P
2
) =
b
3
b
3
+ 1
.
λ
1
λ
2
˜a ABC πρ/2
m
b
sh B = i cth
˜c
ρ
, i sh
˜c
ρ
ch B = 1.
ABC
B = πi/2
ch
˜c
ρ
cos
˜a
ρ
= sin
˜a
ρ
sh
˜c
ρ
, cos
˜a
ρ
ch
˜c
ρ
= 1, m
b
λ
1
λ
2
= 1.
˜a = πρ/2 B = πi/2
b
2
3
= 1
ehp(II) ABC
ehp(I) ˜c ˜a
¯a ˜a ˜a
b c
¯a
ABC ¯a
˜
b ˜c ehp(II)
ehp(II)
˜a = πρ ¯a
cos
¯a
ρ
= m
b
ch
˜c
ρ
,
cos
¯a
ρ
+ ch
˜c
ρ
= i sin
¯a
ρ
sh
˜c
ρ
sh B, i sin
¯a
ρ
sh
˜c
ρ
ch B cos
¯a
ρ
ch
˜c
ρ
= 1.
B C ehp(II)