lukeiou mathimatika kateuthinsis kefalaio 1 - theoria-askiseis

Upload: elisavet-makri

Post on 16-Jul-2015

100 views

Category:

Documents


0 download

TRANSCRIPT

- :[ -:,,-,.,,,,,- .[ , -.[ .[ , .[ .[ .[ .[ - .[ , .[ .[ .10. - : - - AB JJJG JJJG . AB A JJJG JJJG JJJG JJJG JJJG JJJG JJJG JJJG , , GG G , R :: // G GG G R , 0 G G // GG G G, G , R +GG G.G- G G. : 2+

JJJG JJJGJJJJG()A B 1. ++G GG G2.( ) ( ) + ++ +G GG G G G3. 0 + GG G4. ( ) 0 + GG G5. ++ G GG G G G6. x x 0 + GG G G G7. x 0 x +GG G G G8.( )( )( ) + +G GG G9. AB B AJJJG JJJG JJJG10. + +G G GG G G : ++G G GG G G +G G GG G G11.0 0 GG , 0 0 G G12.( ) ++G GG G13.( ) ++GG G14.( ) ( ) G G15. 1 G G16. 0 0 GG 0 GG17.( ) ( ) ( ) GG G G18.( ) G GG G19.( ) G G G20. GG 0 GG21. G G 0 GG 11. - xy G , ( )1 1 x , y G 1 1x , y - 1 1 x i y j + G GG.1. ( ) ( )1 1 2 2 x , y , x, yGG 1 2 x x GG 1 2y y 2. ( ) ( )1 1 2 2 x , y , x, yGG ( )1 2 1 2 x x, y yGG++ +3. R ( )1 1 x , y G ( )1 1 x , y G4. ( ) ( )1 1 2 2x , y , x, y : ( )2 1 2 1 x x , y y JJJG ( ) ( )2 22 1 2 1 x x y y + JJJG (x,y) : 1 2x xx2+

, 1 2y yy2+

5. ( ) ( )1 1 2 2 x , y , x, yGG : 1 11 2 2 12 2x y || 0 x y xy 0x y GG 11yx

G, 22yx

G 1x 0 , 2x 0 || G GGG, , G G ( )n , , (, 0). A 0 0, 0 G G G G G G G G G GG G G G G G ( ) ( )1 1 2 2 x , y , x, yGG :( )1 2 1 21 2 1 22 2 2 21 1 2 2 x x y yx x y y , x y x y + + + + GGGGGGGG 1. G GG G2.( )( ) ( ) G G GG G G3. ( ) + + G GG G G G G4. 22 G G G G. .5. G G GG G G6. G G GG G G7. 0 G GG G8. 1 2 1 2 x x y y 0 + GG9. 1 G GGGG , G10.1 G G G G( 1 GG G)12. 11 GaGE . GDGE . . o OAG o AMG . c O o A OG c c o M AG c c .o o A O OAG c co o M A AMG c c,o oA A O O cc o oM M A A cc . ,o oM M O O cc , o oM O OM c c.aoaoEoEoaoOcEo Mco o ao o a -, o : 13. 1 A o OAG o OBG , GGD E -O0 O$ 2% .2 -.(1) aGG GG( )(2) ) ( ) ( GGG GG ( )(1) :o o oOM AM OA GGo o oOM BM OB GG.GG GGD E E D.(2) :o o o o o o* * * O B OB B AB OA ) ( ) (GGGo o o o o o. ) ( ) ( * * * O A OA B AB OA GGG ( ) ( )GGG GGGD E J E Ja .3 . :ao ao o EaoaoEoEoEoao ao o EaoaoEoEoEoao o oE JE Jo o

ao o EaoJoEo14. 1 . . - AO , . . AB OB AB OA = + AB= OB- OA .4 oG |G| | | | | | | | | |GGGGGGo | o | o | s + s +, - :) ( ) ( ) ( | ) ( ) ( | AB OA OB AB OA + s s | | | | | | | | | |GGGGGGo | o | o | s + s +5 | oGG, , 0G G= | , | oGG// | oGG= , R e . oG |G, 0G G= | , | oGG= , .(Oaa + |a||15. 1 ). . , oG |G 0G G= | , :| oGG = . ko|=| || |GG , | | | | | k oGG= :- | oGG||, | k oGG= .- | oGG|!, = GG.- 0GG= o , | oGG = 0 . , , | oGG = .6 OM : AB - .OM : AM OA OM + = (1) BM OB OM + =(2) ,(1) (2) : OB OA BM OB AM OA OM + = + + + = 2 . 2OB OAOM+= .OA OBOM2 +=16. 17 , DG , - -iG jG .Oxy DG. -o OAG . 1A 2A x xc c yy,:o o o2 1OA OA OA(1) y x, A , :o x OAG

1oj y OAG

2. (1) j y i xG GGD (2) DG iG jG. x y . DG iG jG. , DG :: j y i xG GGccD(3) (2) (3) : j y i x j y i xG G G Gccj y y i x xG G) ( ) (cc x x c z , 0 z cx x , G Giy yx xj c c , , G Gi j / / , , iG jG . x x c, y y c.aoaoiojoA1 y x A217. 1 8 oG |G, GG+ , G, R e - G G oG |G. ) , (1 1y x = oG) , (2 2y x = |G, :-GGG G G G G Go | + = + + + = + + + ( ) ( ) ( ) ( ) xi y j xi y j x x i y y j1 1 2 2 1 2 1 2- j y i x j y i xG G G GG) ( ) ( ) (1 1 1 1 o + = + =GGo | + = + + ( , ) x x y y1 2 1 2o G= ( , ) x y1 1 ) , ( ) , ( ) , (2 1 2 1 2 2 1 1y y x x y x y x + + = +) , ( ) , (1 1 1 1y x y x =, o |GG+ :) , ( ) , ( ) , (2 1 2 1 2 2 1 1y y x x y x y x | o + + = + = +GG.9 ) , (1 1y x A ) , (2 2y x B - ) , ( y x - . 22 1x xx+= 22 1y yy+= . ) , (1 1y x A ) , (2 2y x B ) , ( y x . : y x A(x1,y1)B(x2,y2)(x,y)18. 1 ) (21OB OA OM + = , ) , ( y x OM= ,) , (1 1y x OA= ,) , (2 2y x OB= , )] , ( ) , [(21) , (2 2 1 1y x y x y x + = |.|

\| + +=2,22 1 2 1y y x x22 1x xx+= 22 1y yy+= .10 ) , ( y x - ) , (1 1y x A ) , (2 2y x B - : 1 2x x x = 1 2y y y = . ) , (1 1y x A ) , (2 2y x B ) , ( y x - AB., OA OB AB = ,) , ( y x AB= ,) , (2 2y x OB= , ) , (1 1y x OA= ,:) , ( ) , ( ) , ( ) , (1 2 1 2 1 1 2 2y y x x y x y x y x = =: ) , ( y x ) , (1 1y x A ) , (2 2y x B 1 2x x x = 1 2y y y = .11 ) , ( y x = oG . :2 2| | y x + = oG. y x A(x1,y1)B(x2,y2)19. 1 ) , ( y x = oG- - OAG= . 1A2A x x' y y' . x y , - | | ) (1x = OA | | ) (2y = OA . 1 :2 2 2 2 222121212 2| | | | ) ( ) ( ) ( ) ( ) ( | | y x y x + = + = + = + = = OA OA A A OA OA oG.:2 2| | y x + = oG12 A( , ) x y1 1) , (2 2y x B 21 221 2) ( ) ( ) ( y y x x + = AB . A( , ) x y1 1) , (2 2y x B . ) (AB ) , (1 2 1 2y y x x AB = , :2 22 1 2 1( ) AB ( x x ) ( y y ) = = + JJJG : A( , ) x y1 1) , (2 2y x B 21 221 2) ( ) ( ) ( y y x x + = AB .a A1 y x A(x,y)2y x A(x1,y1)B(x2,y2)20. 113 | oGG, ,Go = ( , ) x y1 1G| = ( , ) x y2 2 - 1 2 :2 1// = GG Go = ( , ) x y1 1G| = ( , ) x y2 2 1 2 , : 2 122111 2 2 12 21 10 // xyxyy x y xy xy x = = = = GG.14 Go = ( , ) x y1 1G| = ( , ) x y2 2 . OAG= OBG= . - . + = OB A OB OA OB OA AB ) )( ( 2 ) ( ) ( ) (2 2 2 ,, . ( ) ( ) ( ) AB22 122 12= + x x y y ,( ) OA21212= + x y ( ) OB22222= + x y ., :a | y x (x1,y1)(x2,y2)21. 1 B O A OB OA. + + + = + ) )( ( 2 ) ( ) (2222212121 221 2y x y x y y x xB O A OB OA. + + + = + + + ) )( ( 2 2 222222121 2 12221 2 12221y x y x y y y y x x x x GG =.B O A OB OA ) )( ( , :GGo |= + xx yy1 2 1 215 : - R ), ( ) ( e== GG GGG- G GGG GGG += +) (- 1 2 = -1GG, G=1 G=2,( y y ' // ,GG)Go = ( , ) x y1 1,G| = ( , ) x y2 2G = ( , ) x y3 3, :( ) ( , )( , ) ( ) ( ) ( ) ( ) o | o |GGGG = = + = + =x y x y x x y y xx yy1 1 2 2 1 2 1 2 1 2 1 2GGGGo | o |= = + = + =( ) ( , )( , ) ( ) ( ) ( ) ( ) x y x y x x y y xx yy1 1 2 2 1 2 1 2 1 2 1 2.,( ) ( ) ( ) o | o | o |GGGGGG == GGGo | + = + + = + + + ( ) ( , )( , ) ( ) ( ) x y x x y y x x x y y y1 1 2 3 2 3 1 2 3 1 2 3= + + + = + + + ( ) ( ) ( ) ( ) xx xx yy yy xx yy xx yy1 2 1 3 1 2 1 3 1 2 1 2 1 3 1 3=+ GGG Go | o .1 1 0 02 122112 1 2 1 2 1 2 1 = = = = + = xyxyx x y y y y x x GGGG16Go = ( , ) x y1 1G| = ( , ) x y2 2 - .A222221212 1 2 1y x y xy y x x+++= .22. 1GGGGD E D E VXQT | | | | | | | |

GGGG. GGD E xx yy1 2 1 2, | |GD x y1212 | |GE x y2222.,222221212 1 2 1y x y xy y x x

17 v G G, 0GGz . G G G GG .o OAG o OMG . oOA 1M . o1OM G G GG : o

1OM GG .(H G G ). G G:o o o o o OM M M OM M M OM v G G G G G G G1 1 1 1 1) ( GG: G G G GG ao M1MAvo23. 2. 2003. 1.3 : 6, 7, 9: 5, 6, 8 1.4 : 3, 5, 6, 8: 2, 3, 5 1.5 : 6, 7, 12, 13: 2, 4, 5: 1, 3. 1:: 3, 5 : 7, 112:: 3 : 1, 5, 63:: 1, 3, 5, 7, 8, 12 : 3, 4, 524. 31.x:1A AB3

JJJG JJJG, 1A A5

JJJG JJJG, JJJG JJJGi.JJJG JJJG AB JJJG G A JJJG G,,.ii.JJJGJJJGGG .:: 1 1A AB 3 3 JJJG JJJG G 1 1A A 5 5 JJJG JJJG G AB AB A +JJJG JJJG JJJG JJJG JJJG JJJG G Gi. 2 5 B 2A 3 3 + JJJG JJJG JJJG JJJG JJJG G G G G G ( ) 11 1 1 5 1 A 5 3 5 3 5j \ + , (( ,JJJG JJJG JJJG JJJG JJJG G G JJJG GG JJJG JJJG& , , .ii. 1 A 5 +JJJG JJJG JJJG G G 1 A A A 3 +JJJG JJJG JJJG JJJG JJJG G G 1 1 5 3j \j \ , (, (( ,( ,JJJG JJJG G G G G25. 3 2 2 2 21 1 1 16 1 1 15 5 3 15 5 3 + GG G G GG GG G Gx: 20x 602G G G G.( ) xGG 22 216 x 1 1 x x 015 2 5 3 JJJG JJJG. BE 2.(6,-1),(1,3),(1,2),(-1,-1)(1,-1).i. JJJJG JJJJG, 1 .ii.,.iii., JJJG JJJG, JJJG JJJG JJJJG JJJJG, 1 .:i. (x,y).( )( ) ( )( )( )x 1 6 x x 1, y 3 6 x, 1 yy 3 1 y JJJJG JJJJG : 1 6x1 +

+ ( )3 y 11

+ii. ( ) x 1, y 2 JJJG ( ) M x 1, y 1+ +JJJJGx 1 y 2 M 0x 1 y 1 + +JJJG JJJJG& 3x 2y 1 0 + (1) :1 6 3 23 2 1 0 1 1 21+ + + +iii. ( ) ( ) k 2, 0 k 7, 0 JJJG JJJG27 ( ) ( )10,1 0, 33 JJJG JJJG105 84 10 8 21 , , 23 23 23 23 2j \ j \ , ( , (( , ( ,JJJJG JJJJG26. 3:2 1 2117 3 2j \j \ , (, (( ,( ,3.i. (3,2) (-1,4). ii. A (,5) , .:i. (x,y) . :( )3 x1 3 x 2 x 52 A 5, 62 y4 2 y 8 y 62+ + + + ii. , A, :( )A det A, A 0 JJJJG JJJG JJJJGJJJG& (1) ( ) 8, 4 JJJJG ( ) 3, 3 JJJG (1) :8 40 24 4 12 0 4 12 3 3 3 + 4. , 0 G GG . ( ) +GG G& ( ) +GG G& :( ) + GG G& .: ( ) +GG G& R : (1) + GG G ( ) +GG G& R : ( ) 2 + GG G (1) (2) : + G GG G G G( ) ( ) ( ) 1 1 3 ++ ++G G GG G G 1 + 1+ , 1 0 + 27. 3 (3) : ( ) 1 . 1 +

+G GG G& , .: 1 0 1 + 1 0 1 + , (1): ( )( ) . + + +G G GG G G G G G&5.(x1,y1)(x2,y2)(x3,y3):2 1 3 2x - x = x - x .1,2,3, , JJJG JJJG JJJG,:1 2 3 2 + :( )2 12 1 2 1 12 1y y x x , y y , x x JJJG,( )3 23 2 3 2 23 2y yx x, y y ,x x JJJG,( )3 13 1 3 1 33 1y yA x x , y y ,x x JJJG( ) ( )3 2 2 1 3 2 2 11 2 2 1 3 22 1 3 2 2 1y y y y y y y y x x x x 1x x x x x x + ++ :1 32 1 3 2 2 1 3 2x xx x x x 2x x x x2+ + (2) (1) (2) :3 11 21 31y yx xx2+ +3 1 3 133 13 1y y y y2 2x xx x2 6. , ( ) 2,1 G ( ) 3,1 Gxx,: 4+ .:11 2 21 3 28. 3( )1 1 5 5 2 3 6 6 1 1 1 1 51 41 12 3 6 6+++ 4+.7., , GG G: 1 GG G, GG, m( ), 6

G Gm( ),3

GG,3 2 + GG GGG G.:( )2 22 2 23 2 3 2 3 4 2 3 4 3 4 + + + + + G G G G GG G G G G G G G G G( )( )2 2 23 4 4 3 , 4 , + + G GG G G G G G3 131 1 41 4 31 1 41 1 8 6 2 02 2 + + . 3 2 0 + GG G 3 13 2 0 2 2+ +G G GG G G G.8., , x, yGG G G,, GG& .. x y G G G G x y G GG G,;i.x yG G& ii.x y G Giii.x y G G. 1 G,:( )22 G GG:. ( ) x y x y 0 x y 0 G G G G G G G G G G G 0 GG x y G G ( ) x y G G G29. 3 ( ) x y x y 0 x y 0 G G G G GG G G G G G 0 G G x y G G ( ) x y GG G. 0 G 0 G , GG ( ) x y G G G ( ) x y GG G GG& .x y G G.. ( )22 G GG m( )22 2 2 , G G G G GG G Gm( )2 12 22 ,

G G GG Gm( )2, 1 GGm( )m( )2 , 1 , 1 G GG G GG& . ( )22 G GG9.GG.-,: + GG GG(1) + GGG G(2): GG.:(1): . + GG GG G G G( )22 + + G G GG G G G G(3) (2) : . + GG G G GG G( )22 + + G G G G GG G G(4) (3) (4) : 22 G GG G.10., GG m( ),3

GG +GG G..: 2 GGG.. GG.30. 3:. :2 1 12. . , . 2 2 G G GG G G GG G G( )2 2 221 1 1 2 2 2 + + G G G G G G G GG G Gm( )2 21 , 2+G G G GG G 1GG: 1 1 11 1 1 1 13 2 2 2 + + . 1 : GG Gm( )( )( )2 , 1

G G G G GG G GGGG G GG G G: 22 1 1 1 1 13 2 2 G G G GG G( )2 2 22 22 21 2 2 2 + +G G G G GG G G G G G1 1 1 1 1 +G (1) :m( )112, 1 1 2GG, : m( ) 2, 3 3 GG11. G, GG:( ) 1, 2GG ( ) 2,1 GGi.GG.ii. G.:i.( )* R || 1, 2G GG GG G G( )* R || 2,1 G GG GG G G: ( )( ) 1, 2 2,1 G G 0 12 2 1 0 + G G G G, 0 0 GGGG G G G31. 3 ii. 1 GJJG G 2 GJJG G G G :( ) ( ) ( ) ( )1 2 1, 2 2,1 1 2, 2 1 1, 3+ + + + JJG JJG G12.,,,,-.i.: ( )2 2 2 2 AB A B B A + + + + JJJG JJJG JJG JJJG JJJG JJGii. JJG JJG,:( ) ( )2 2 2 2 1 1 + + :i.( )2 22 2 22 2 A AB A 2AAB AB + JJG JJG JJG JJJG JJG JJG JJJG JJJG2 22 2 2B B 2B + +JJG JJG JJJG JJJG JJG JJJG:2 2 2 2B +JJG JJJG, 2 2 22 + JJJG JJG (1) :2 2 22A + JJJG JJG (2) 2 2 22B + JJJG JJG (3) . (1), (2) (3) :2 2BBA 2AB + + JJJG JJG JJG JJJG JJJG JJG2 2 2 2 2 2 2 2 2 + + + + + ( )2 2 22 + + + +JJJG JJG JJG JJJG JJJG JJG.ii. ( ) ( )2 2 22 B B B ++ JJJG JJJG JJJG JJJG JJG2 22 22 2 2 2 + + + JJJG JJJG JJG JJG JJJG JJJG JJG JJG2 2 2 2 +JJJG JJG 2 2 22A + JJJG JJG( (2) i.) -:( )2 2 2 2 2 2 2 2 2 2 2 2 2A + + + + =( ) ( )2 2 2 1 1 + + .32. 41. // GG R GG G 2 3+G GG.........................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................2. , , GG G.( ) // GG G( ) // GG G + GG G.............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................3., JJJG G JJJG G 2 JJJG JJJG., JJJG,JJJG JJJJG -GG. 2 JJJG JJJJG.....................................................................................................................................................................................................................................................................................................................................................................................33. 4 ........................................................................................................................................................................................................................................................4. = JJJG JJJG, = JJJGG = JJJGG :i. =JJJG;. +G G.( ) +G G. G G. G Gii. = ;JJJG. ( )1 2+G G. 1 2+G G. 1 2+G G.( )1 2 +G G........................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................5.1( ) 3, 5 x+G2- ( ) 12, x 4G, x : 1 2 2 3 +.............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................6.(2,1),(6,4)(5,5).....................................................................................................................................................................................................................................................................................................................................................................................34. 4........................................................................................................................................................................................................................................................7.(2,5)( ) 6, 4 JJJG:.(6,4) .(8,9) .(4,9) .(8,1)............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................8. 2+JJJG GG 2 JJJG GG. JJJG JJJG,( )2 22 3G GG G. 4 G 5 G( m( ) , GG).........................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................9. (,) (,) . 0 , n( ), JJJGJJJG.........................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................35. 4 10.( ) 1, 3G , GG 2 GG 1 G G. 2 3 +G GG G G.............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................11. , GG i 2 j+G GG 1 G m( ),6

GG.u, G Gu 2 3+GG G 2GG G.....................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................12. , GG : 2 2 GG, 2 8 + GG n( ) 2, 23+ G GG G. G G.........................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................36. 413. R ( ) 3, 4 1 G( ) 3 9, 3 + G.........................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................14. , B JJJG G JJJG G JJJG G,: 3G G, 7 G, 2 3 0 + G G G G.,,.., , GG GG GG m( ) ,GG..xG ( )x G G G& ( ) ( )x + +G G G G:i.N:( )21x 4 G G Gii. xG........................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................15. AB 2 +JJJG GG, 3JJJG G G,G 1GG m( )2, 3GG .:37. 4 .:i.GGii. GG 4 2 +GG. AMJJJJG, BJJJGG,G AMB JJJJG JJJG AMJJJJG BJJJG.................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................16.(0,3),(2,1) ( )2 3,1 .:i. JJJG JJJGii. iii.JJJJG................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................17. . G,G 2 GGGGGG. ( ) v 1, 2 G( ) u 3, 4G.. ()=, ()=.: ( ) ( ) 0 + JJJG JJJG G38. 4................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................18., 0 G GG 2 GGG,3 8

GGG..:2 23 2 8G GG G.:3 4

GG. m( ) , GG..v +G GGw GG G R .........................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................39. 5 1.1. i , jG Gxxyy( ) x, y G xi yj+G GG. G iG jG .........................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................(5)2.( )2 , 3 2 +G i , jG G.( ) i j + :. 2 . 1 2 . 3 . ........................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................(8).:1. ( ) 1, 2,( ) 2, 3( ) 6, :40. 5. 1. 0 2 . 0 23 . 7 ............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................(7)2. () () -. , GG:.// G GG G. G GG G G G. G G GG G G. G GG G . G GG G........................................................................................................................................................................................................................................................( 5) 20 , GG ( ) 2 4 3, 2 + GG ( ) 4 9, 4 GG.. ( ) 4, 2 G 5 1 ,4 2j \ , (( ,G...........................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................(7)41. 5 . 8 +GG 4 +GG -...........................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................(8). G G...........................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................(10) 30. , GG GG G. ( ) 2 G GG............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................(10). , ( ) 3 9 JJJG JJJG. JJJG JJJG.....................................................................................................................................................................................................................................................................................................................................................................................42. 5........................................................................................................................................................................................................................................................(15) 40 ( ) 3, 5G, ( ) 2,1G ( ) 3, 1G. G G G.......................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................(25)