.
, IIα I .
IIαα IIα 50 . . 100 . . , IIαα IIα 100 50 . . 550 450 . ., . . .
, αα () 200 C α400 I .
2) -. : M (, αα + α ) = V (b, ßß + ß ).
, b) ) ; , .
. , ), , , I a. , I b .
, 2)?
, , {, I: V = M (. 191 *)}, ½ , ½ 1/10 , 9 / 10 .
I ) , a I b) .
, :
I ) ( + I b) ( )
)
C α280 + V α70 + α70 b 120 + Vb 30 + Mb 30
IIαα) αα280 + V αα70 + αα70 + IIßß) C ßß120 + V ßß30 + ßß30
IIα) C α280 + V α70 + M α70 + IIß) C ß120 + V ß30 + M ß30.
, , . 272. .
.
300 ( 3 × 70 = 210 V (, αα, α) 3 × 30 = 90 V (b, ββ, β), 210 + + 90 = 300 . ., ).
Ι α) 70 . . 1/10 [× 70], 70 7 = 63 . ., 1/10 I b).
Ι α) 2 × 63 . . = 126 . . IIαα IIα 81 . . I b, IIββ, ΙΙβ. ( ditto 1/10 .)
, Ι α) 63 . . + 126 . . + + 81 . . = 270 . . (= 300 1/10× 300).
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270 . . Ι α 63 . . , : ()
ΙΙαα) C αα280 + V αα70 + M αα70 + ΙΙββ) ββ120 + V ββ30 + ββ30
ΙΙα) C α280 + V α70 + M α70+ IIβ) C β120 + V β30 + M β30.
, , I b. , I b) I, ΙΙ αα ΙΙ α. 21 . . (3 × V 7 ) I b 3 × 3 = 9 (= 3 V 3). 30 . .
, , I b, :
IIαα) C αα280 + V αα70 + M αα70+IIββ) ββ120 + V ββ30 + ββ30
ΙΙα) α280 + V α70 + M α70 + IIβ) C β120 + V β30 + M β30
, I 300 1/10 × × (300) = 270 , , , I b Vb 30, 1/6 I b, 180, 6 × 30 = 180 . . (1/6 180/6= 180/6 = = 30 . c.), 1/10 (300/10 = 30 . .).
, , , α70 in natura. , α35, .
.
, I , ½ , 300/2 = 150 . . 150 . . I 35 . .
, I 150 35 = 115 . . , , Ι α, 73 + + 7 + 35 = 115 . .
, :
ΙΙαα) C αα280 + V αα70 + M αα70+ IIββ) Cββ120 + V ββ30 + ββ30
ΙΙα) α280 + V α70 + M α70 + IIβ) Cβ120 + V β30 + β30
207 . . Ι α IIαα. , V αα70+ αα70= 140 . . 140 207, 67, αα280. 280 67 = 213 ΙΙαα. ΙΙαα V αα70, IIα 70 + + 67 = 137. Vα70 + Μ α67, :
IIα 70 . . . 35 Ι α) 35 I b). 67 . , 35 . . Ι α 32 . . 1 b).
. 293 |
: |
35 . . Ια 35 [. .] [] αα. αα 213 αα 178+ αα 35 () + . . ΙΙαα 3 . . IIα. :
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ΙΙαα) αα 178+ 3 ( α ) + αα 32() + αα 67 ( α ) + αα 70 ( α ) + Vαα 70
()
αα 140 ( α ) + 140 (T αα) + Vαα 70() + { 38 ( α ) + αα 32()} IIα) : α 280 + Vα 70() + α 3().
, :
IIα) α 280 + Vα 70 ()+ΙΙβ) C β120 + V β30 + M β30. |
[199] IIα 3 . . I b, ;
.
ΙΙαα 32 . . Ια, Ια 32 . . ΙΙαα. ΙΙαα 3 . , 32 . . 3 . , Ια 29 . . [] I b. :
ΙΙα) α280+ V α70() + IIβ) β120 + V β30 + M β30.
I b Ι α 15 . . , ( ).
:
IIαα) αα280 + V αα70 () + M αα (Τ) 6 + IIββ) C ββ120 + V ββ30 + M ββ30
ΙΙα) α280 + V α70 () + ΙΙβ) C β120 + V β30 + M β30.
IIα) α280 + V α70()+ ΙΙβ) C β120 + V β30 + M β30. |
11 . . Ι α) 6 . . [] αα 5 . . |] I b. Ditto IIαα 6 . . I b, II . . I b, :
198- ,
.
60 . . I b) IIββ. 30 . . V ββ30, 30 . . IIβ, V β30. . :
75 (Tb) ΙΙββ 60 [. .], 15 . . I b. , 7½. .,
I b) = Cb(T) 60 + Cb( [ T ]ββ ) 60 + Vb 30 ()+ (7½ . . -
).
, ββ30+ + β30 15 . ., 30 [. .], ΙΙββ 15 . . 15 . . I b. IIβ 15 . . I b.
:
I b) b 30 () + b 30 (b) + b 60 ( [ ]ββ ) + Vb 30().
I b 30 . . ββ, : I b) b 30 ( [ ]ββ) + b 30 (Tb) + Cb 60 ( [ T ]ββ ) + Vb 30().
, ΙΙββ : ΙΙββ) ββ90 + ββ30() +V ββ30() + ββ30( ΙΙβ).
ΙΙββ 30 . . ΙΙβ : ΙΙββ) ββ90 + ββ30( β) + Vββ30 () + Mββ30 ([] β).
Ditto ΙΙβ) Cβ1 20 + V β1 20 () + Μ 30 ().
.
[200] :
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IIβ 15 . . [] Ι α), Ι α) 15 . . [] I b), I b) 15 . . IIββ.
:
ΙΙα) α280 + V α70()
ΙΙββ 15 . . [] Ια), Ια) 15 . . [] I b), I b) 15 . . ΙΙββ, 15 . . ΙΙββ. :
. 299 |
( + αα + α) = 70 × 3 = 210 . . V (b + ββ + β) = 30 × 3 = 90 . . |
, Μ ( + αα + α) I b) . . |
(= 90) 105 90 = 15 . . .
Ια) = 280 + V 70+ 70= 420 . . ( I a) = V 70 + 70+
+ V 70 + M 70 + V 70+ M 70.
Ι α, ΙΙαα, ΙΙα [] Ια:
1) 3 × V 67= V 189(a, αα, α); , 3 ×
× V 7 = V 21(a, αα, α).
:
2) 3 × M 35= 105(a, αα, α); ,
3 × Μ 35 = Μ 105 (a, αα, α).
:
I b)= Cb 120 + Vb 30 + Mb 30= Vb 30 + Mb 30 + V ββ30+ ββ30+ V β30+ + M β30.
I b), IIββ, IIβ I b):
1) 3 × V 3= V 9(b,ββ, β). , : 3 ×
× V27 = V 81 (b, ββ, β).
:
2) 3 × 15= 45 (b, ββ, β); , :
45(b, ββ, β).
, :
I a) = V 21(a, αα, α) (T Ι a) + 105 (a, αα, α) (T Ι a) + + 1 b) = V 81(b, ββ, β) (T Ι b) + 45 (b, ββ, β) (T Ι b).
, Ι a) Μ 105 (a, αα, α) = M 81 (a, αα, α) + + Μ 24 (a, αα, α).
:
.
I a, I b, , , 2 :
I a) M 81 (a, αα, α) = I b) V 81(b, ßß, ß), .
I a) M 81 , V 81(b, ßß, ß), I b) V 81(b, ßß, ß) , I a) M 81.
, -, I b . ., I a, 24 (b, ßß, ß), 105 [. .] (, αα, α) V 81(b, ßß, ß), M 24 (a, αα, α).
, I b, IIßß, IIß, M 21(b, ßß, ß), V (a, αα, α), I b, V 21(, αα, α).
I a, IIαα, IIα 70 × 3 = 210, M 210(a, αα, α).
Ib, IIßß, IIß 30 × 3 = 90, V 90 (b, ßß, ß).
, M 210 (a, αα, α) M 105 (a, αα, α) ( I a . .) 24 (b, ßß, ß) ( I a) = V 90 (b, ßß, ß) V 9 (b, ßß, ß), I b.
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M 210(a, αα, α) M 105 (a, αα, α) M 24 (b, ßß, ß) = M 81(a, αα, α), V 90 (b, ßß, ß) V 9 (b, ßß, ß) ditto V 81(b, ßß, ß).
[201] , 24 (b, ßß, ß) = M 45 (b, ßß, ß)
M 21(b, ßß, ß) = V 21 (a, αα, α), :
M 210(a, αα, α) M 105 (a, αα, α) { M 45 (b, ßß, ß)
M 21(b, ßß, ß) = V 21 (a, αα, α)} = V 90 (b, ßß, ß) V 9 (b, ßß, ß), M 21(a, αα, α) = V 81 (b, ßß, ß).
, I a, IIαα, IIα M 210(a, αα, α) , -, , I { 105(a, αα, α)} , -, I a, IIαα, IIα, I b, IIßß, IIß, I ( I b, IIßß, IIß , V (a, αα, α), , I a), M (a, αα, α) V (b, ßß, ß) V (b, ßß, ß)4 I b.
. 301
, I b)= b 120 + Vb 30 + b 30 Vb 30+ + Mb 30 + V ßß30 + M ßß30 + V ß30 + M ß30.
V M, I , V' . ., a , I b, V" . .,
1) Vb + Mb + V ßß + M ßß + Vß + M ß = V'b + M'b + M'b +
+ ''b + V' ßß + V' ßß + M' ßß + M' ßß + V 'ß + M' ß + M'' ß.
,
2) I b = V''a + V"aa + V''a + M"a + M''aa + M"a + V ''b + V '' ßß +
+ V"ß + M"b + M" ßß + M 'ß.
:
3) V"a + V " aa + V"a + M"a + M"aa + M"a + [ V " b ] + [ V "ßß]+ + [ V" ß] + [ M"b ] + [ M "ßß] + [ M "ß]= V'b + [ V"b ] + M'b +
+ [ M"b ] + V'ßß + [ V" ßß] + M" ßß + [ M" ßß] + V' ß + [ V' ß] +
+ M' ß + [ M" ßß] *.
V" (b, ßß, ß) M" (b, ßß, ß), :
4) V " (, αα, α) + " (, αα, α) = V (b, ßß, ß) + M' (b, ßß, ß).
, -:
V " (, αα, α) < " (, αα, α) V (b, ßß, ß) > M ' (b, ßß, ß).
: V " (a, αα, α) < M' (b, ßß, ß).
V " (a, αα, α) = M' (b, ßß, ß),
M" (a, αα, α) = V (b, ßß, ß).