Тригонометрия гиперболической плоскости положительной кривизны. Ромакина Л.Н. - 44 стр.

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b
3
> 1
t + 1 2b
3
c
3
> 0.
t > 1
t + 1 > 2b
3
c
3
,
c
3
(t + 1) < 2b
3
c
2
3
, b
3
(t + 1) < 2b
2
3
c
3
,
2tb
3
c
3
(t + 1) < 2tb
3
2b
3
c
2
3
= 2b
3
(t c
2
3
) < 0,
2c
3
b
3
(t + 1) < 2c
3
2b
2
3
c
3
= 2c
3
(1 b
2
3
) < 0.
c
3
(t + 1) 2tb
3
> 0, b
3
(t + 1) 2c
3
> 0.
hhh(II)
α α R
+
β
β R
+
χ χ R
+
(b c)
(a c) (a b)
ABC A = πi α B = πi β
C = πi χ
ch A = ch α, ch B = ch β, ch C = ch χ,
sh A = sh α, sh B = sh β, sh C = sh χ.
ch
˜a
ρ
=
t + 1 2b
3
c
3
2
p
b
2
3
1
p
c
2
3
t
, ch
˜
b
ρ
=
c
3
p
c
2
3
t
, ch
˜c
ρ
=
b
3
p
b
2
3
1
.
ch A =
t + 1
2
t
, ch B =
2c
3
b
3
(t + 1)
p
(t 1)
2
4(b
3
c
3
)(c
3
tb
3
)
,
ch C =
2tb
3
c
3
(t + 1)
t
p
(t 1)
2
4(b
3
c
3
)(c
3
tb
3
)
.
sh
˜a
ρ
=
p
(t 1)
2
4(b
3
c
3
)(c
3
tb
3
)
2
p
b
2
3
1
p
c
2
3
t
,
sh
˜
b
ρ
=
t
p
c
2
3
t
, sh
˜c
ρ
=
1
p
b
2
3
1
.
sh A =
t 1
2
t
, sh B =
(t 1)
p
b
2
3
1
p
(t 1)
2
4(b
3
c
3
)(c
3
tb
3
)
,
sh C =
(t 1)
p
c
2
3
t
t
p
(t 1)
2
4(b
3
c
3
)(c
3
tb
3
)
.