1. - " - , - . - . - , , , ". . . 1, VI : ? - - ? - - . - , - . , -, . . , -, - . - - - (-) (

2. ). 1/2. (), - . : , -. - : , -, , - (, ). -. ( ) . ; ( ), ( ). -, (-) , , -. - . . -: - 1:2 - () ; - - ;2 3. - ( - ); - () - , () , -, ; - () - , - , , , (); - , - - . - (, , , ) . - . , -. - . . . , . . - . . 3 4. - -. - , , - ( ) , . . - , - , . ( -), - (-. ). -. : 1. - ( ). 2. ( - . "" - -; - ; ). 3. -, - , ( , 4 5. . 7 ). , , , . , , , . , -, , . - - . , , , , - , , -. - . , , , , , . - - . , -. , - , , , . 5 6. - " - , , . - , - " . . VII,.3. . , - , , - . , , , . , , , - -, - , - . ? - , - . 6 7. () () - (.1). 1 I II III IV V VI VII VIII 1 +2 +3 +4 +5 +6 + 7 + 8 = 36 1 + 2 + 3 + 4 + 5 + 6 + 7 + 0 = 282 + 4 + 6 + 8 + 10 +12+ 14 + 8 = 64 1 + 22 + 32 + 42 + 52 +62 + 72 + 80 =140+80. - - . - - . - - . () 8 - ( 0) (- 1) 2=16: 1 1 02 d = 16 d = 16 = 8 , 0 2 (1) d - . 7 8. - - . - , , - , - - (.1):12 + 2 2 + 3 2 + 4 2 + 5 2 + 6 2 + 7 2 140== 5.(2)1+ 2 + 3 + 4 + 5 + 6 + 728 , - -: 5 / - ; (, , , - , ); (, , , ); -, , , - , - 6 (.2). - 6 , 21 (.2): +21 21= 6+5+4+3+2+1.(3) -6 - 21 (.2).012345 - , 42 = 21-(-21), --21 42 .2 , - . 8 9. , 21 - -:+2 +2 5 7(9+0), (4)-2 -2 5+7+(9+0)=21 - , (2+2)-(-2)-(-2)=8- . [2] - -, [4]: 1 234 567 0 - I II III IV V (5) 1 2 3 4 5 6 78"" 0 7: 7 2 d = 72 = 49, (6) 0 [1]. 7 8 :82 d = 64 - 49 = 15 1+2+3+4+5, (7)79 10. 15 - (-), . , 15, - . 15 . - -. , - - , . . - , ." , , . , , , , - . , , , - , ". . . III , .3. () . . . , - , - 6 (.2).10 11. "" , -, . 3,5 -, 2,5 6:6 = 3,5 + 2,5 = (3,5)2 - (2,5)2 = 7/2 + 5/2.(8) , , : 7/2, , - - 5/2 [8]. -, - :107/2 d + 5/2 d = 7/4 - 5/4.(9)01 , - () (q), - (*) (q*). 7/4 , "":7/4 = /q = */q*. (10) "" - - , , . 11 12. - - (.2). 2. ( )7/4 7/2 7 14 28 56112I II III IV V VIVII -- - - - - - - - - - . 80 40 20 10 5 5/2 5/4 -, - , - (Const) (.2): Const = (7/4)80 = (7/2)40 = 720 = 1410 = 285 = 565/2 = 1125/4 = 140.(11) - 3,5 2,5 56: 140 / 3,5 = 40 140 / 2,5 = 56.(12) (5) , .12 13. , -. , (11) - 7 3 : (7 - 3) 140 = 560. (13) -. , - : ", , , , , , - ". . . VIII, .4. , , , " , , -, -. , , - ." . . IX, .1 - .13 14. -- =4. - . - . - . , , . - " " [1]. , - -, , , , , . , (+=4+4= 8), - - 16 . , - , , , , -. , - -.14 15. , () - , , . , -. .. -, - 1020 . - . - : 2 = 16 - 28 . , - , . - - , - (.3). 3 ( ) () -- - - - - == q=* =* = q* =2810 -201410-20 1610-20 2810 +201410 +201610+20 - 15 16. 2 -, ; , , ., - :112 = 7 qq * = 8 * = 4 * , (14) "", -, (10). , , , : (.4). 4 - -- - 1 = 2 =3 = 4 = 5 = 10-2410-11012 1014 10+1 Const = lg 12345=2 - 1 2 3 4 =1. 5 (.4) : - , - , . 16 17. (1) : 1 Const d = 21/2 = +1 0 0Const d = 2(-1/2) = -1. (15) 1 +1 -1 . ,, . , - . , , - , , () - . (.4). (R) - , , , -. (.3). - : 17 18. H = 8 Sin / 4 = 8 Cos / 4 =82-1/4 = 27/4.(16)H L (.3) :aR a2 V=1/3a2H = 1/3827/4, (17)r .3 (.5): Sc /4 = Csc /4 = 2 . 5n 2 , n = 1,2,3,4,5,6,7 (.3) - - -- - - - . To2 - r R a2R2a =a2L 2345 6 78 2222 2 222 1+2+3+4+5+6+728 2 = 2 . , - , : - - , : H2 = r = 2 8 = 27/2.(18) : 2222 H2 = -r = 8 - 2 = 64 - 2 = 62,(19) 7/2 8 (62 : 2 8). , , , - , .18 19. -, . " " , - . - - - . : " , ". ? . . "42. . .43. . - , , -, - , " . . X,42 I,43, , - : -, , . 19 20. , , -, . - , . - , - . . . . . . , - , , , : " ". - - ; . . : .20 21. - . . . - . , - , - , . . : . , , - - . , , - . . - -, (.6). 21 22. 6 -() ()() () ()- - - - -- - = = q= * = * =q* = 1610-20 1610+202810-20 1410-20 2810+20 1410 +20 72*72M = =1020 = * =1020 q2 q*2 72 - M Const = 2 = 72 ,2 72 - "", [1]. , , . -: - (.7). 7 - , - - (.6)() () -2,5 3,5 Conct 72 / 3,5 = 3,5 / 2,5 = 1,4 = 72. 14= * . 22 23. (.7) , , " ". , - . - . - () (); - - (1) (1): =+=(72/2)10-20 =1+1=(72/2)10+20 . (20) - (.8): 8- (20) (.6)() ()==1=1= + ++1+1=11=74/44 472(10-20+1020) 2 = 7. (.8) Sc /4 =Csc /4 = 2 (.3,.5). - . . - . - .23 24. - (.4, .6). k1 M=72/210-20 M=72/210-20k2 k9 k11 k12 k10 :k7 k8k6 k5 k1=k2=k3=k4=1, k4 . 220=7 /210 =72/21020 k3 : .4 k6=k8=k10=k12=10-40, : k5=k7=k9=k11=1040, 1040 1/1040. , , , - : k1k2k3k4k5k6k7k8k9k10k11k12 = 1, (21) 12 - . - : 132-122=52=42+32 132-()2=52=To2+2. (22) = 3 - . 24 25. " . . , , Oeaohoo ". . . III, .5 - : - , . . -, -. , . , . , . , . ( ), . - - . - , , - . 25 26. "" : () , () , , - .- - (D) (Q) (Dmc), (Q=), (.5). B -Do m c D, Q = D2 - Do - Q o E : A.5. -D,= Q = 1/ (23) - mc = E = 1/, Qo=Do2=(1/)2=1/. - , - () (-, , ) . (mc), (E) : - (); - = , - , - .26 27. , , , - , - , , - - . - : (mcc = 1), (Ec = 1). mc E -, , - : mcc 1/c = 1 c = (24) Elc 1/c = 1 c = . () ( ) - ( ), = (.5), . (.9). 9 ( = 3,14592654) - I II III IV VVI VII VIII IX ()0,1+ 0,04 +510-3 +910-4 +210-5 +610-6 +510-7 +410-8 ==3,14592654: 3,00+ :0,1+ 0,04 +510-3 +910-4 +210-5 +610-6 +510-7 +0==3,1459265.3,00+27 28. (.9) - ., (Ec = 1), (mcc = 1) - (ooc2 = 1) :Ec + mcc +ooc2 = 1+1+1 = 3,(25) 72 -7 o = 10 /4c / o = 410 / - - . (1+1=2 2+1=3 3+1=4 ) (.9). - ( ), - (). " - ", . - . . , n (n+1) , - , - . ( -) n n+1: 28 29. n +1 dn= 1/2[(n+1)2 - n2]. (26), , - Const = 2 , 15: n +1=8 2 2 Const= d =21/2(8 -7 ) = 15 = 1+2+3+4+5.n =7 (27) (31,.2). : n +8=36 ( ) Const= d =21/2(36 -28 ) = 512 = 2 2 2 9 Const(9+0). (28) n = 28 ( ) - - . (9+0) . . - E = 1/ (.5). - , , , . , -, - . 29 30. , , - Lo - (.5). Lo - (.5). , ( Lo) - ( Lo ) (.5). - - (no = 1/4) (.5). , - (.10). 10 (.5) - - - - ( )-o= 2noo=jo=cono=1/4 To=4o = /2= /2o/o=1= /2 . , , -, :1 = 1/4 . (29) , , (.5), , - - = 4:30 31. 1 =1/4 E/To mc/To = 1/Toc So, (30) So - (.5, .11). 11 (.5) - - Vo = Lo = So = (Do/2)2Qo = 1/ 1/6 (Do/2)2 =Do = 1 =1/4 1/6 (.11) - () - -So So = 1/4 (.6). Qo Qo = 1/ (.11, .6). -.6 (So = 1/4) (.11) Qo = 1/ (.6) :| QoSo | | 1/1/4 | | 4/ 1/ | | 4 1 |. (31) (31) - (o = 1/4) - . 4/ 1/ - =4/, - , 16/2 = . 31 32. 4/ /4 :14//4(4/)arcSin (1/ 2 )(4/)arcCos (1/ 2 ), (32) 1/ 2 +1/ 2 = 2 = Sc /4 = Csc /4 = ....(33) ( 2 )n - (.3, .5). , - , . , - , . , - : . , , - (13, .3) -, (V = 4/3R3) : V111= 8 27 / 4 /(2 / ) = 8 27 / 4 ( R = 2) 3 H mc + E 366 V = V H (mc + E ) ,(34)7/4 = 2 - = 4 + = 4+3 = 7, (.4): = 27/4 Const (To+)/To.(35) 32 33. - , . () = 43 = 12, , - ., - , , - . - - : , , , -. - , , , - , . (/Q = 4) (/m = 4) -- L= 2R = 4 S = R2 = 4 - R= 2:4 = 2(R=2) = (R=2)2 (36) . 33 34. - . , , (.3) () 2 (36, .3). , . , (.5), , , - . ( ) - 4 1 (31). - = 4 : + 1 = 5 - 1 = 3. -, 3, 4 5. Too/c =(4/2)/ = 2 To/o=8. - . - 6, - 12, 3 (.12).34 35. 12 ( ) - -18 88: d d = -0 2 1 d Const d 22 3= 6 = 12 -1 d 3 6 12 = 1/2216 = 108. 0 -, 108 - ( 108 ). (.5) : 81 d / = 6/3 = 2. (37) 2 (.5). - , - , -. 35 36. , - :lg 24 = lg 10-11014 = 13,(38) -:lg 13 = lg 10-241012 = -12.(39) -- (38, 39):13 2 d = (132-122) = 25. (40)12 - - - :132 - 122 = 52 = 42 + 32; (41)(+1)2-To22 = 52 = To2 + 2. (""), ("") . - . Oeaohoo. : O+e+a+oh+oo, -, , , - . 36 37. "5. - - .6. , , , - . , " " , ; - " " - ; ; - . ". . . III , .5 .6 .. - . , .. " " [2,3]. , - , , - [8]. , -- , .37 38. , . "1. , , , - - ! : , -, ( 1), - - ( )" . IV,.1. 1 = 10 - - : 105 d = 101/2 = 5 -5 = 10(-1/2)= 1 d , (42) 01 - , . (42) , , - (.2), , " ". - , - -, - -. : " , - , - " [8]. -, 10+0 = 5+0, -, - . , , , , , , -, , - . .38 39. (.5) , , , 5 (42), . (.5) - , , - . -. , . - -, :1 05 d + 5 d = 5+(-5) = 0. (43)0 1 - . . . - :1 05 d - 5 d = 5-(-5) = 10 1. (44)0 1 , .39 40. (.5) - .- . . - :(+5)(-5) = -25; -5+5 = - 3125; +5-5 = 3,210-4, (45) : +5-5 (-5+5) = -1 i2.(46) 1 - n+1-n = 1. , , . - . . - . -, , , . - (45):Const (+5)(-5) 2(-25) = -50. (47) , - : 50. , . , . 40 41. , , , - [6]. , - (46, .7). 1, -, , -1 = -555-5 +1 = (-555-5)2, " " (.7). +1-1+1 -+1-1+1 - +1+1 . -1 -1-1 -1 - +1+1 (.7).+1-1+1 - +1 -1 +1 , - -.7 - - - +1 ( )-1 (.7). , " " . . - , . +1 -1 (.7) - 2:1 -(-1) = 2. (48)41 42. -. - - ( ). - , - -. - , o = /2, , -, - , - . - (.8). (.8) 4 4 4 4 - - : - .8 . , (- ) (), (.3,.5, .9)., -=22 - , , R=2 . r= 2a2=8 - - ..9 42 43. , .7, 8 9, - , . , qc, - o (.10). qc -o o=/2Const, -, - -.10 - - - Const (.10). - (.13). 13 - - mcEmc+E qq *c qq *c 2 92/ 12,521/2= * 0 * 02 1/2 = 2/ = 9= 12,5 = 18= 12,5. - . (- ) - ( ) (9+0) :43 44. 1 018 d = (9+0) 18 d = -(9+0).(49) 0 1 , 6 (.5), -, 36: 18Const = 182 = 36.(50)"6. , , - , , . ; , , ". . . III, .6. , - . - 3,5 . - :1 (+) d = 71/2 = 3,5. (51)0 (51, .13): 12,5 : 3,5 = 5. (52) 44 45. , - , 2,5 : 15 d = 2,5.(53)0 - , 6 (.5):6 = 3,5+2,5 = 3,52 - 2,52 = 3 - (-3). (54) 6 - :1 06 d - 6 d = 3 -(-3),(55)0 1 ."5. , , , -". . . IV, .5. ooc2=1mcc=Ec=1 mcc=Ec=1 ooc2=1 - - .11 - 45 46. , - - , - , (.11):mcc + Ec + ooc2 = 1 + 1 + 1 = 3. (56) , , , (.11). (.11) - - : Tom0c E c 0 0c 2 = 13 3 = m0c + E c + 0 0c 2- 3 . (57)m0c + E c + 0 0c 2 = 3To1 = m0c E c 0 0c 2 , , (57) ( = 4), 5=10, " ", ( - -). , - - , - , -, , - (.12).46 47. , , - - (.12). -.12 - - [6], - "," ( [6]). - . ( ) . : -. , - -, - , - - 5040 . , , , (.14). 47 48. 14- 12 3 4 56 7 - 2 6 24120 720 5040 , 1!=1 2!=2 3!=6 4!=24 5!=120 6!=720 7!=5040 ! - , 12..n=n!() 1 + 2 + 3 + 4 + 5 + 6 + 7 = 28 7! 1 2 3 4 5 6 7 == 180 180 0 .28 1 + 2 + 3 + 4 + 5 + 6 + 7 - 180 , (180) . , - - (.14). To+ = 4+3 =7. - : 12 + 2 2 + 32 + 4 2 + 5 2 + 6 2 + 7 2 + 8 2 + 9 2 + 10 20 + = 7 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10385 ( )=.(58)55 ( )48 49. "4. . () ; , . - , , , - - () , , ". . . (58), - ( ) - . , - - - ., - : , - . - 6 = 3 - (-3) (55) 6 (.5) (.13). 2 - (1/2Qo=1/2) - Lo=Do=1 - (.12) "" (Qo = 1/), , . - (.12) - Lo=Do=1 - (1/2Qo=1/2) 2.13 - (.5) 49 50. , .13, - , . (To = 43 = 12) - (To+ = 4+3 = 7) :5 To - (To+) = 12 - 7.(59) , () (.13). , "" . (.13), - , - - , - . - - (.15). 15 (.13) "" mo = -mo = -Sc /4(Qo/2)1To2o= sc /4(-Qo/2)1To2o= 2 (1/210)16/2=- 2 (1/2)1016/2= 40 2-40 2 --[mo - (-mo)] = (-80 2) mo(-mo) = (+40 2 )(-40 2 ) = -3200 3200= 40= 85 = ( 2 ) 5 = 5 65 2 .( )( 80 2 ) 22 250 51. - Sc /4 = Csc /4 = 2 , - (.13). To/o=8 Too/c=2, - . (.13). , (.12) - - , . (.16). 16 : 6 (To/o=8):(Too/c=2) (To/o=8)-(Too/c=2) : =4= 6. Too/c=26-4 " " (.13) - (.14). - (.12) : "" -, "-" - -. 51 52. 2 "-" ""61/2Qo1 , 5 2 (.15).4 3 - 1/2Qo 6 - " - 2" - ( ), .14 (.13) - ( )(.15). 6 - 6 "" "" - , - 1, 2,.15 3, 4 5, : n C6 + C62 + C 6 + C64 + C6 = 1 35 6! 6! 6! 6! 6!++++ =(6 1)! (6 2)! (6 3)! (6 4)! (6 5)! 6+36+120+360+1080 = 1596, (60) n - ( ), ! - - . " ; - ; " ( 49, 49 - "" [1]). III .5. . 52 53. - 1596 - . "" : - , : " ?" ? , ? - , - (.16). , I II III IV V VI VII VIII , 1 0 1 2 3 4 5 6 7 -2 8 9 10 11 12 13 1415 3 16 17 18 19 20 21 2223 2 , -4 24 25 26 9 6 29 3031 5 32 33 34 6 9 37 3839 (.3, .5).6 40 41 42 43 44 45 46477 48 49 50 51 52 53 5455 - -8 56 57 58 59 60 61 6263 r= 2.16 - , (.5). -7 L = 2 = 8 2 (.5). , , , :"6. .53 54. " - ", ( r = 2 ) - , " - ( L = 8 2 ), . . . . ". . . VII, .6. , - - 63 (.16) d: L8 2 d = d = 1/2 [(8 2 )2-( 2 )2] = 63. (61) r 2 (61) - (.15) , , , - , (.3,.5). , - -. -- -: 112 = 7 qq * = 8 * = 4 * , (62) (.17).54 55. 17 , () - - - - - - -7600 6200 5820 57505500 5100 4800 4500 7600 6200582057505500 51004800450040004000 - = = = = = = = 1400 380 = 70 = 250 400300 3005003600 1 = 28004800=800 - 2800 / 800 = 3,5; 2800 / 1120 = 2,5. - - - 4800 (.17).- - 2800 800 (.17). 3,5 (.17). (62) 5 = 10(.17):2800= 2,5 . (63) 112 10 () . - 7/2 = 3,5. , 5/2 = 2,5.55 56. , , . - , -- (62), 112. , - , 112 - -: 1 + 112N = 112 = 6328 .(64)2 , :7N + * = 3600 + 28 = 6300 + 28 = 6328 . (65)q4 , , -, (65) 6300/28 = 152 = (1+2+3+4+5)2,(66) (.5).56 57. - - () () = . -. - - , 1 (.7). = 1 - (-1) = 2 (.7). - (F = m1m2/r2) (F = q1q2/r2), - (F) m1m2 ( q1q2) (r2). ( -) , = 2 (.7). , , , .7, +1, , -, +1/ = 1/2. -1 - -1/ = -1/2. , - - : + 1 ( 1) i 6 1 1 1 0F = 2 = = d d , (67) 2 2 0 1i6 i6 F, (68)2 2457 58. i6 - , - 4 2 : , (.14, .17).+z-" ( i) ( -- + 2 )". +-z. III, .6. .17 - -, (.7). - - . . 0 +1+1(-1) -1+1 ,+1 -1 0 +1 0, , - - mcc2 = c mcc = 1 -1 0 +1+1 (.18). 0 mcc = 1mcc2 = c - , -.18 - (.18). 58 59. . - , , , f(x,y), - , f(x,y). - f(x,y) = (=2)(=2), - f(x,y)=4. 4, - () 2 - . , ( = 27/4) - - - . - , - (mcc=1), (c)- (.18):() mcc mcc mcc2 (). (69) 1 - () (.7,.18). () - (47) , - (.18).59 60. 18 - , - - . III III IV lg 12 lg 34/5 lg 24 lg 32== = 13= 12 13 12-25 +25 d =25 d = -25.13 12 25 , (.19). - (28-27 = 3,5-2,5 = 1) - - 283,5 5252, - : 28-27=1 3,5--1=-555-5, (70) 5272,5 2,5= -5 - 1, 5-5=1/55 - - , , -.19. : , , . : -, -, , , - , 60 61. *49 * = 10 20 , -, -q*2 . , , (.18), , -. - . - - , -. , -, , - . -- . , - - (.19):- 5 -5 5-5 2 (-1-5 5 )+1=(-5 5 )-1 (70) -61 62. 19 - ( ) ( ) -1 = -555-5+1 = (-555-5)2-1 = -555-55-5- 5-5 -55 -55 -1+1 -1 55-5-5 - / -55 5-5 :5-5 = 3,210-4. -55 = -3125. (.19) ., , , , . (.19) " " - . , 10-4 [1]:5-5 = 1 = 3,210-410 = 3210-4A.(71) (71) - (.20): 5-51Const = 3,210-4102 = 6410-4A.(72) 62 63. -32 - (- 10-4 , - qc ( q=1610-20 =300 ./ = 31018 /) -: - 64 4800 (.17): qc 16 10 20 Acc 3 1018 / =10-4. (73)32 - (-)= 4800 .20 - (73) , 64 32 - 10-4 - 104 -1: 10-4(1/104) -1.(74) (74) . (.19), , , - -55 5-5, 42(-55) = 83125 = 25103 (75) -5 -4-4 42(5 ) = 83,210 = 25,610 , :25,610-4 = 2510-4 + 610-5. (76) (75, 76): 63 64. 25103(2510-4 + 610-5) = 62,5 + 1,5 = 64, (77) , , (77, .20). , , . "47. : , , - . .48. , , ; - .49. , , - ". . . II. , , , - - , , - (5). - , -64 65. , : - , V (5). . : - ; - I, II, III, IV . ( , : ", -". ); - V - . - V - . - V - . , -. - - , , . V , - , - . 65 66. , , -. - , , , ., , - . , - . , , - -. , - . . - , , - - . -. - . , , , , - , .66 67. -: , - (), - . , - (5)., (.), . , .- , - ,"" , - , . , - , . . ; - . : , - (.20). 67 68. 20 1/3 En = mc2 2/3 E = 1/2mc2=m02 En : E = 2 : 11/3 : 2/3 = 1 : 2 1/3En = 2/3E 1/32 = 2/31 = 1. , (.20) ( ) . - (.21). 21 ( ) - En = mc 2 -1 2 Ek = mc21 2 : = 1: 22:13 3"- 2/11/2 " 22 = 4 1 1/4 = 1/21/2 - 4+1 = 50 5/4 = 1/4 + 1- 4-1 = 3 0 -3/4 = 1/4 - 168 69. -, -, - " ", , - , -. , , (To/o = 8) - ( = 4) ( = 3). - - (.21). To/o=8 8 S3=3 7 6 V -S2=3 5 V 4 = S1=6 3 I, II, III, IV 2 1 3 2 10 -1 -2 -3.21 (S1=6) - (S2=3 S3=3) 69 70. () I, II, III IV . = 4 - S1 = 6 (.21). IV V . - (.21). S2 = 3 (.21). S2 = 3 - : = S2:S3 = 3:6 = 1:2. , - - V -, - (.21). S2 = 3 S3 = 3 , (.21)." ( ), - , - , , ". . . VII. .7. . ? ! ? ? (.22). 70 71. - -SkL , h1 1 , r - S , R 1 . : , a = mcc = Ec = ooc2 = 1., - (h) : --, .1 5 h= +1 =. -42 : , - ,2 5 R= h=. -33 :(.22):1 5ST =h=.1. S = h/224 :, - 5 1=10 Sk = R 2 = . (.12) - 9 : , -2 h/2 = 5 /4.L = 2 R = 5 .3 - 1 : " r = h . 3 " .22 (, , , -. .12) - "- ". 71 72. , - , S = h/2 2S = h (.22):F = h 2S= 5 /2,(78) - (.13, .14), . , , - , , - - (.20).2. - , - - (3, 4 5) - , 52 = ; 42 = b g = 9 (.23). (h) =25 :b=16 2 ( p q )( p b )( p q ) p =0, (79)h0 = h=0ag=9 () - (.23) 25, .23 (-)=0: a + b + g 25 + 16 + 9 p=== 25 -=25-25=0,(80)22, , h (79) . - (h = 0, .23) , , - .72 73. , 50. , - 50 [8]. , - - ( (.13, .14,.20), , (80,.23): a+b+ ga+b+ g50 p = = 25 p = = 25 . (81) 2 2 22 - . . , , (.24). - - . - , " - ", -.24 - [6, .355] , .73 74. , , , (.24). " " , - (.24). - , - (mc), (mc2) (.22). 22 (.24) - - = r= R= h= L= S = S = 5552 5 5 5 (.22)1 6323 49 555 2 5 5 5 1 632 3 49 6 52 53 54 59 5456 36 22262 5 (2 5 )2 (3 5 )2 (4 5 )2 (9 5 ) (45)6264 , , , - , (.22) : 74 75. 2 ( )2 ( ) 6 2 5 2 5 3 5 (4 5 )2 2 6264.(82)( ) 9 5 (4 5 )2 2 : (36 25 50 75 4002)(2025-4002) 66.(83) , . - , , - , . - (83): 36 25 5075 4002. (84)0 -36+25-11 -36+50=14 -36+75=39 4002. (85) 0 0 14+11=25 39+11=504002. (86) 0 0 0 50-25=25 4002. (87) " " (83, 87):(4002-25)(2025-4002) 66.(88) 75 76. (88) , - [(4002-25)+(2025-4002)=20002453] 64.(89) : 53 = 125 (6/2)4 = 81, (90) - , (9+2) - (): 125-81 = 44 (9+2)081-125=-(9+2) (91)| | | | ", !" - , , - (.24). - , -- . - , , - - - . , , - , - , - (.22) - - (.21), - (.25). 76 77. - - -- -8 8 -7 2 d = 28 . 6-6 .V -5 (). IV -4 III -3II-2I -1 6 -3 -2 -1 01 2 3 2 d = 351 -- .25 , - . , - , - . - : , - (.25). , - : (.25). - :-, , - --, , . - - .77 78. , . , -- . , . - - (.25): 8 6 (Const = 2) d d = 35-28 = 7. (92) 61 , . " " ([2], .23). 23 (.25), () 18. . I V 19. -II , - V 22. III , VI 36. ( IV ) IX 48. , -V , ; -XII 78 79. , .25 : - , - - - -. V (): "18. - ", - , , - , - , - , -, . - : , ,, , . . : - -. (.17). : -, , . - (.17), - , (To/o=8), (Too/c=2). : ( )( ) + + 0 0 / = 2 (93) . 0 / 0 = 8 + + 79 80. (93) =1400 =70 + = 1470 = 21 .(94) (94) - - 21, 6 (.2). (94, .2) 42 ( ):21 - (-21) = 42, (95) :5 7 (9+0), 5+7+(9+0) = 21, (96) . (.23), " . - " (93): + + 0 0 / = 2 0 / 0 = 8 + + (97) + 2128 + 21 ( + 21)2282 = 16. - 2 = 16, - ()2 . - (97) , (97): 80 81. ( + 21 )2 02 + 21 21 1 . (98) 00 0 (98) - - (9+0) "" (.17): = 3600 21 7 70 = 3 ;0 = 4 4 4 (9+0)100370(7/4/q*/q*).(99) (9+0) ( q) (* q*) - . "" - 2,1 ( , 99):(9+0) 370/100(7/4) 2,1(7/4/q*/q*). (100)"6. , , - , . ; , , ". . . III..6. 81 82. " ( ) . - , , - . , . , , , , -: " . , . - , , , ". 4. -, , -; : " . , . - ". , , , . , , , - . : " , , , , -, , - , ., ". . . VI , .3 .4.82 83. 10 . , , -, : - ( ) ( ). , , , - . - , , . , - , . , 10 - , -, . ( ) " ", , . , , , , . , . , , - . 83 84. - , , - ( ) , , ,40 . - () - . (-) , . , ( XII ) -. . (.24 [8]). . , - . - "" : , , . , - , . , , , - , - . .84 85. , , - : , , [9]. - , , . : ; ; - . (9+0) - :-2 -2 95+2 7 +2(9+0) d = 28 5 * , (101) 28 , 28 . * (101) = 3 : 3 * = 28 = 14 + 14 + 14 = 42 . (102)lg 1 2 3 4 5 2 -, , , 42, 42 - ( ). 85 86. , , - , -, [9]. , (7+0) (9+0) - . , 16:( 9+ 0 ) d = 2 (9 ) 12 7 2 = 16 qq * . (103)( 7 +0 ) , - , 16 . (q*) , . () () , . (), - , 24(103) -:7 Tolg 12345 = 432 = 24 = 2 d . (104)5 , , - , 24 [9]. 86 87. " - , - , (- ), , , , -, " ([9]. 1. 10). , "- ", 12, - : 7To = 43 = 12 = d . (105) 5 , , "". "" - , 2; 3; 4 [1]. 234 - (103). (103) [2, 3]. - - . 6, 1, 2, 3, 4, 5 21 (.7).87 88. . "", 21, , 21 [9]. "" , = . , , -- : , : : - - - 1 2 3 4 5 6 = 720 21 720 21 1 + 2 + 3 + 4 + 5 + 6 = 21 72021 720 (106)240 7240 7- , -72407240 240 = 64104(6 10 )4 7 2 *2 (3600 )2 . - 2*2 4q q - . -, , : , - 2, - , - - (*)2 , (qq*)2 - . - "" - .88 89. - - , : - 28 *16 qq * 24To 21(To+) - (107) - 28 721 1 7 1 = = 16 424 2 4 2 * * .q q* q q* (107) :[(28+16)-(24+21)] = (44-45) = 1. (108) 1 - , (107): 2824 d d = 264 67,2 196,5 . 16 21(109) (108) - , - , - (To=4) : 89 90. 1 196,5 196/ + d 1/ = 72+1/8.(110) 0 , - , "" 49 [1], (110) - . - :7 * * 7= . (111)4 qq * qq * 8 : 7/41 49 2 49 49 72 d = = 2 , (112) 7/82 8 16 0 - 49, 2=16. , . - . - . . . - . . . . . - . , - 90 91. , . . . - , , . -1 ( d =0,5), 0, 5 = 10:1 2 1 92 13 2 d = 23 2= 8 = 10 5 . (113)0,5 - 6 9 :99 lg 12345 d = 2 d = 45 (1+2+3+4+5), (114)66 : "! ?!", . - [9]. . - (113) : (1+2+3+4+5) (12345=120), (115) 11 (9+2) - : 11 2 d = 2 (112 12 ) = 120 1 2 3 4 5 5! .1(116) 12 - . - 91 92. , , . -. . . . . . . . . . . . . . , -. , , . , [9]. : 12 2 . ,:12 2 d = 2 (12 2 2 2 ) = 140 5 28 = 5(1 + 2 + 3 + 4 + 5 + 6 + 7 ) 1 2212+22+32+42+52+62+72. (117) . , . . - . 5 2 . :52 d = 52-22 = 21.(118)2 21 (.2), . -. . - . , , ? : " -: , , - ; , - 92 93. " [9]. - - . - . [9]. - . . 11 . (117, 118) . 24 . "" : 24 ". , - 42 . 24 42 - (.26).0 , - 22 :4 44242422 + 24 - 24- 242 (119).26 666(9+2) 18=2(9+0) 12(9+2)(9+0) ( 42) (119)( 24) (9+0) (9+2) . - . .93 94. -- . : 24 42 = 1008 = 36 28 =1,008 ,(120) 1/16 -, (119, 120) , - 24. (119) -, (9+2) (9+0) 12 . () - (9+0) 2, - :[2 (9+0)]22 (16 9)122 2304 1296 0 2304 - 1296 = 1008. (121) (121) . (9+0) (9+2) , :lg 55 = lg1010 = 10 5 .(122) , , "" (5=30) (5=40).94 95. "" - . , , - IV (). (122) -:(lg 55 = 5 ) 1 11, 10 9 (9 + 2 ), 5 , (9 + 0 ) , (123) (9+2) (9+0). (123) - . . - III (). , . , , (). - , , - . , , . : , - . -, . - , . -: - , - ! , . . - 95 96. , : - [9]. : . . . . - . - , , - , - "": - , , , - . , - , , . ( (), - - (), ""). - "" -- , , -, ., . : , , . . , -. , - . , . 96 97. - . - , - -. . - . . . , . . . , [9]. ? . [9]. ? -. " : "! !" - , ?" , - , , , . , , - . . , , , - . , , , - .97 98. , : "50 ( ) , , - . 51 , . 52 . 53 , . ." [9].1. . - ( ). () ( -() ) - 9 (.27). d = 40 1 - . ( - 40 6011 ) d = 60 (.27).1 - -2. - - - S=1200(-) (.27, .24). 40 S1=-1200(-) , 60 (.24) - .27 , . . - " -" , , - . - - . 98 99. 24 40 60 60-40 3600-400 -60+40 40 60 60 40 23 20 3200 -20 2400 32- - 1 160 -1 1 3600 9/4 - -2 161+1 0 4/9 1600 1 . - - , . "" , - ( -) (). " " [1], - [9]. 99 100. : - : " -, , " ([9], 1; 1).1. : , - , , . ( . ..). , . - . , . : " , "([9], 1; 16). ..: , :mc c 0 0 c 2 E c 13 = mc c + 0 0 c 2 + E c 3 1mc c + 0 0 c 2 + E c 3 1 = 3 . (124)mc c 0 0 c 2 + E c1 (124) , :|16 912| |14 (9+0)| |i16 (9+0)|, (125) i16 = 14 - :100 101. |logii16 (9+0)| To22|16logii (9+0)|1221008 0, (126) (121), - 103 -. , . : , , . : -. , (- 24). ..: - 144 = 122. 241 d d = 144 = 122. (127)00 2 = 18, - (127): 144= 8 0 / 0 ,(128)18 - . : " ?". ., . . [9]. 101 102. ..: " " - (.25). 25 "" +-+2 10 - - YZ x 1 243 1 24 +10 - d d 2 d d d 0 0 0 310= 0,5 288 (9+0) -4 1056. (.25): K X Y Z288 9 ( 4 )( 0.5)144 36 == 5, (90) , (129) x10561056, "" - :5,(90) 0,(10) 6 [3-(-3)] (3,5+2,5) (3,52 - 2,52). (130) , . , [9]. 102 103. ..: : 3 d 9/2. (131) 0 . ([9], 1; 4750). ..: -, (131):397 d 2 1 = 2 = 3,5 .0 (132) . : " -, " ([9], 1; 48). ..: "" - 1008, (132, .25):( = 288)7/2 = 1008 2442 3628 . (133) , 720, -, (), 360 :(=288)(7/2-1=5/2) 720 2360 22 4. (134) , : " " ([9], 1; 51). 103 104. 2. : - ; , , ( ), ( - ); - , , 46 , ; - - , , -, ([9], 2, 224). , . -, , , -, -. , - . . (2) (25) . . , -, . - , 6. . -: 32 + 2 + = 25 + 2.(135) ., ! (135), 104 105. . - -. , -, . . 46 , -: 46 = 46 365 = 5596, (6) . (136) 3 5596,(6) - . . (135): 5596 , ( 6 ) d = d 1,566107. (137) 1 -: 1,56610710-7/1,566 1,5661070,6410-7. (138) , (6410-9), 105 106. - [64 = 32-(-32)]10-9. , :(64 1 = 63; 64; 65) 10-9,(139), , - 6310-9. 3. - , - . ([9], 3; 236). - - (To22/o2=82=64) - (To6o6/c6=26=64) . - ( Too/c)) ( To/o=8). 64 () 64 () " ", , 8 () 8 () , - - (.28). -.28 [9] , (.26). :: ? ? 106 107. : (2 = 18) (.. = 24) ([9],3, 5). ..: - :. . 24 1008/2 d 1008/(2 d =252) 4 . 2 18 (140) 26 (.28) (Too/c)6 To/o Too/c (To/o)2 648=2= 6464 18640- d d d d d 8 02 21 = 1008 2442304 = 1023. 2836 120 120120 8 ( = 3) = 24 1023 1008 15 - =3, 83=24; - =12, 212=24. , (140):1008 1008 1008 1 . (141) 24 8 126 1008 0 / 0 d 18 107 108. (141) 63 -8 2 , , 88126 = 6316 63 2 .(142) : , - ([9], 3; 6).. ..: - , 63: 63 d = ( 1 2 ) 63 1 = 1984 . (143) 1 28 - 2 Sc8/4 Csc8/4, : 8 2 1 d = 2 2 0 = 128 . 16 (144) 0 (143) (144): 0 + 1 7 1 ( = 128) d = 128 = 112 (145)0 0 4 2 112 7 qq * = 8 * = 4 * . (146) : " , -" [2]. (145) - , (.28, .26, .27): 108 109. 27 112 7 qq * = 8 * = 4 * (145) ()() 112 = 8 112 = 64 m;m; = 8 112 = 64 112 1122 m82; 1122 m642;(784=7216) m1(3,0625=547210-4) m1 +7216 -1+1 -547210-4721/16; (-)m72(16+1/16) 0 2 m0. (.27) "" - 7216=722, - -: 721/16 = (7/4)2 2/q2 (*/q*)2. (147) , , (), , , -, : , ([9], 3, 8).: ? ([9], 3, 9).: - , ?([9], 3, 10). ..: , . . .109 110. - ( ) - , ([9], 3; 22).. , - ([9], 3, 23). , . " , , , -, " [9] - - . ..: - , - : =1984 (143), - 128(.28, 144): 28 ( ) (143)(142) 128 = 1984 =1984-128=1856; =1984+128=2112 2112 1856 14, (2) * + 0, (2) . 218 ( ) ( * = 14 ), :0,(2) 0, (lg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d = 14 d = 14 d = 14 d = 1 2 3 4"" 73 75 77 79 7(3+5+7+9) = 1412 * . : " , , " ([9], 4; 38), : " - , - ; - : , " ([9], 4; 36,37). , . , . , . : ([9], 4; 52). ..: - : 0 12 * = 14 = 24 ,(151) 0 +7 .113 114. 5. ([9], 5, 147). [9]. [9]. ..: , (.5): (1+2+3+4+5=15)(12345=5!=120), (152) = 120/15 = 8 = To/o. , , - (.29). - - - . .4 21 3 5 - - (.29). .29 - . ( 2001 ) (To/o=8)2. "" (.28). , , =4. : 114 115. (1+2+3+4+5) = 415 = 602(+C).(153) (153) - - - . : . , ; , .(.28): ( 0 / 0 = 8)2 [60 = 2 ( + )] (154) [60 = 2 ( + )]( 0 0 / = 2) 6 ,|642 602||642-602=496 0||3116 0|,(155) 16 = 2, 31 - [1] - . [9]. , , -. , .( : . ). , , . 115 116. "-" :", ". . . - : 6 3,5 + 2,5 3,52 - 2,52 3-(-3). (156)| | | || | | || | | |, , - (.31). 31 - : - 2,5 -3,5 1-(-2)=3 -2+(-1)=-3 6 3,5 + 2,5 6 = 3 - (-3). 3,52 - 2,52 - "": . . . . : " ? ! , !"116 117. : " , , , ? !" , , , -. : ! . : , . . 2000 . , - , . . - -. -. , , . , , : " , ; , . , - , , , ? , -; , . , . , - ? ([9], 5, 4346). , , - . , , , - .117 118. 6. - ( , - - ) - . -, (9+0) - * = 281020(. 30). - - - (9+0) (9+2) 1 1*= * *= * 2 2*=281020 *=281020 .30 - (9+0) (9+2), ( ) (.30)118 119. - , (.30). - ( ) - , 107 -, . :107 1 lg 107 lg 1 7 0, (7 0). (157) , 7 28 .(158) - * , - - 21020: * ( *) 28 ( 28) == 2 10 20 lg 1 2 3 4 5 10 20 . (159) 28 , (159) - (157):21020(7 0 -7)141020 021020 -141020 +* 021020 -*.(160) (160) * . (9+0) 119 120. - (9+0) (9+2) (.30). ( ) . - , , - . - * , - , --, * , - , --. () - , : --- (9+0) (9+02)-(9+0) +(9+0)(9 + 2 ) [(9+0)+(9+0)]=18 (161) d = 20(9 + 0 )=5 T0 = 42=182(9+0) 18 0 0 0 d = (8 2) d = 729 = (9 + 0)3 0 (9+0) 9 , - , - - (161). -. : 120 121. 0 0 : 0 0 00 0 0:0 0 0 0- 18 1818 d = d = d =(162)9 9 9 4243162431/2243- 4 243 16 243 = 128 243 1 2432 , : 20 max = 128243 = 2 35,(163) n 2 , , 128 (64 ) ( 32 ) . , , , , . - . - . - . . - . , . .. . 12 . :5 [12 d = 6(25-4) = 621]5000 = 63104.(164)2121 122. (164) .12 - = 12, - - [2].2 - - - (159, 163):2 2 10 20 2 10 20 .(165)5 - , - . - ([2], 161): 15 (5 = 10)( d = 1/2) 01 + 2 + 3 + 4 + 5 2 + 6 2 + 7 2 140 222 2 =. (166) 1+ 2 + 3 + 4 + 5 + 6 + 7285000 - -- (163):5000 5 4 3 2 ( 0 + 1) 10 24 1012 5103. 0(167) , . " " ([9] 6,10). 21, - (.5), " 122 123. " (164):621 (3,5+2,5 3,52-2,52)(1+2+3+4+5+6). (168) , 63, - 104 1/ - (164): L =8 2 d 10 A1 ,4 4 6310 (169) r= 2 r L - . , 10 , [1]. . - 25 - 30 : " ; ". : , , - - (.30,157). (9+0) (9+2) - -, - :123 124. 30 7 ToToo/clg 10 lg 12345 d 25301227(2 d =275) (24275=6600)7 253314102 (9+2) * 52 .(170) (170) - , (Too/c=2), (lg 12345=2), - (lg 107 lg 4 = 7 ). 25 - 30 - - : (-25lg 12=lg 10-2410-1lg 10-25) (-30= lg 12/lg 105 lg 10-30) 30 d =(-30) -(-25) =30 -25 =275(9+2)5 . 2 2 2 22 2(171) 25 - 6600 (170). , , - , - , 660 [1]. - , - (9+2) (.30, 170, 171). - : , - , .124 125. - (170) :33 14 10 2= 28 25 2 33 = 1400 33 5 * 33 , 2 (172) * = 28 33 - 33=(9+2). . " , , ; , , - ; - , - ; , -: " ([9].6; 56-58) , ( ) - , . , - . , , , , , , . , - , -, , , , . . "" - , . -- , - 125 126. -. , : " !"( " ").7. " , - , " ([9], 7; 1)." ( , . ..), : , , . - , " ([9], 7; 3, 4)." : , " ([9], 7; 6).( .. - ; - ). - . . . : ? ? , -. ([9], 7; 16) : , - . : " ( , ), -. , - ? ([9], 7; 22, 23). 10 , , , 126 127. . , , . : - , - , - - , (.31).y 0 [9] 3---------------------------------------3 4---------------------------------------4 5---------------------------------------5A B- 6---------------0 ---------------- ---6 (, ) 5---------------------------------------5 4---------------------------------------4 3---------------------------------------30 , , -y , [9] .31 , , , - (.31). , , 6. - - 6 ( ),(.31). - - , , ., - , , , (.31). 127 128. , , -. - 42 ( -). 6 - (.31). (.31). - ( ),(.31), , - 3, 4 5 ( - ) - (.32). 32 (.31)- - -, 0, - -, 0, + -, 0, -, 0, + , 3+4+5=12 3+4+5=12 3+4+5=12 3+4+5=12 ,48 6/-6 6(-6) -6/6 6/-6 6(-6) -6/6(- 36+36=72) -1 36 -1 -1 36 -1 (.32) - :72 : 48 = 1,5 3 : 2 : lg 12345, (173) - : : 1+3/2=5/2; : 1+5/2=7/2; (174) -, - 128 129. . , 48 - - 4800 (22):48 4800(22 = 10-2) 480010-2.(175) 10-4 . 10-4 , 600 4200: : 10-4 300 . (176) -q=1610-20 J=qc/4800/ = 4800 / = 10-4 31018/ - =1410-20 J=c/4200 31018/ 4200/ = 10-4 (176) , : 4800 - 600 = 4200,(177) (.32):72 423 7 3 12 = 36 2 * = 14 , (178)248 72212 . - : , (.31, .32) 129 130. 02 - : +1 +1 4(3 -1 4 -1 5) [4(3+4+5=12)=48] + (179)4[1+1+(-1) + (-1)] = 16 02 qq * , 48+16=64 2 4816/6412 . (.31) - (.32): () -3,5 +3,52(-1-36-1) 2(-36-1-1 = -38) = 76 + +3,5 -3,5 (180)2(35-(-35)-(-35)+35=140) = 280 () (Const = 140) 280 528. (178180) - , , , . (- . ..). , -, . , -, . , , . , 130 131. , -, , - . ,. . , -. , - - . - . .8. , -. : ? : , . , . . . ; . , , - . , ; - , ([9], 8; 37). , ? ([9], 8,44) , , , - . - , - - . , -131 132. -, , , , , . , , .9. . -. . -, : ", !" . . . : , , - ([9], 9; 24). : ! ([9],9; 15). : , , . ([9],9; 39). : ? , , . -. - - - - . 132 133. --1/41/4, - 1/4 1/4 , --1=2-7/4 -1=V1/ V . - - =2 7/4 - 44 -, - 44 - ,.32 - - (.32): 1=V V-1. (181) (176) - - , , (V), - , . , , -, , (.32). 10-4 - - (104 1/), - . lg 10-4 = -4lg 104 = 4(182) 01 2 (To=-4) d =8=2 (To=4) d =8=10 (.32):133 134. -4lg 1/10 =-(-4)=4lg 1/104=-(+4)=-4(183) 1 0To(4) d = 8 = 2 To(-4) d =8=2 0 1 - , . , , , - , . , - , - - . -.P.S. : - - , - . , 58 , - 42, - 10. : ( ) (184) -28+14+16=58 58-16=4242=28+14 * + * + qq* 314 * * + * 134 135. (181) 108 , , - : * * qq * 28 14 16== 108,137 K . (185) * + * + qq * 28 + 14 + 16 , - . : (.32) , (186) qq + + ***qq + *** + qq** * + qq *** =16+14+28 =16+14-28=28+14-16=28+16-14= 58=2 = 26 = 30 , . 10. , : , , ; ([9], 10, 1). . - . : - . , . , , .135 136. : , ? ([9], 10; 32). .11. . ([9], 11; 157). , : 15 , , -([9], 11; 18); 2 , - ([9], 11; 6).; ? , , , , , ([9], 11; 9); ([9], 11;17). 12 ([9], 11; 9); - , .28 (.26):-15=( -1023)-( 1008) = -(1+2+3+4+5). (187) (187) -: (-15)12 = -180 -180 - -c, (188) 180 180 , , , , - . 136 137. , . - 2 :/2 o2(r = 1) - . (189) , - /4 arcSin (1/2) , - 4: /44 ,(190) 4 2 (R=2) (R=2)2 - - - 2, . , , , 4 , (190):[(/4 4 )4 ] (41664). (191) "" . - :121226(64 2 )+[(32+32) = 2 ] = 2 .(192) (191) - (192): 26281+2+3+4+5+6+72 2 = 2 2. (193) - . 137 138. -, -, . - -. . . . , , , , , ([9], 11; 51).12. , . - . . (400 ) , - ( ) ([9], 12; 3). : 300 , ( ) ([9], 12;5). :- - -6400- 6400 - (194)=2400- -3006300 6- =1800138 139. - :6 400 300 72 10 4 12 7 = = 10 2 10 2 ;6(400 + 300 ) 42 10 2712 122104 72. (195) "" ( =12)2 (104 1041/) .20 : , , , ; , ([9], 12;24). - : (- ) , (, ) ([9], 12; 50).13. - , - , - - , (.33). (.33), - . , 6400= 2400 6300 = 1800 (194) 13 14. 2 = 18, 10-4: 6300 = 1800 (2 = 18)10-4 (194). 139 140. d c : 2 d = /2 = o = jo = 2 0 (- [9] [2]: 1210-4). ( ) , -. , , 1/1210+41/ ()-1 - 1/1210+4 ( ): -12-1 = 11 (9+2), , To1041210+4 .33 13 [9] , "" . , .33, ( ) , 10-4. ( - - ) (.34). 140 141. 2o=c , -o , , , "", - o ( - ) . . - (mo) o2o=c m. .34 . mo - - -:mo- (mo) = 2 mo= 2m/2= m mc. (196) : (mc) (mc = mc) - . . - . . (- "" ) "-" . (.33): d =2 (1 2) 02 = 2 2 = = 0 22 R=2 . (197)0 , , - , (- : ). 141 142. : 2M H 2O d = 18 (9 + 0 ) 2 . (198)02 (194) (195). , -, , (Tolg 12345 =432=24)10-4.(199) (199) , ( , , - , ) "-" , 1 3+1=4; (3+0) 3-1=2, [1]. , , (199) :1 2410-4 d = 1210-4 To10-4A.(200)0 (.33). 21 (200) - (200): 142 143. 217 * 4 1 4 = 10 4 1 10 = 1 .(201)12 10 4 q* q - , "" "" -. - ("") :1 1T0 3 1 = 12 10 4 A 10 4(202) 12 A 12 2 A 108 .(203) - ( ) . (122=144) , . . - - . , (12 10-4A) : 12 1 =1(10-4A)(10-4A)-1=1. (204) , -, :(10-4A)-1(10-4) = 1, (205) - : 143 144. (10-4A)+1(104)-1 =1. (206) , , , -, , : . . . - (). - " " - . (345 =lg 10121014101 = 27). "" ( - ). . ( ). , , - , , 12 :12 - 1 = 11 = (9+2) - ,(207) :1 1/121041/.(208) 13 [9]. , . , , . : , , ([9], 13; 12, 14). 144 145. , , . ([9], 13; 4)., , - . - - . . ; , . : - ([9], 13;18). , -. . , - : ", : , "(.33, [9], 13; 38). (+= 4+3=7). 1210-4 . : 3( 0 + ) = 7 = 7 104 1 10 41 * 4 1 10 . (209) 412 10 4q A q* A . - - . , - 145 146. , .14. ; , . . , : . , , , . , , . ([9], 14; 14). , - , , - .33. -, . (-), , - (). (, ) - , . - . - . : " ", - . - - (.33, .33). 146 147. 33 (.33) (III)10-20 1020(IIIIV) - 12 - - 1/12104,1/ 12104, 1/12104,1/ 12104, 1/12104121041/1210412104=1 1 1 k1 = 12 10 4 12 10 4 = k 2 12 10 12 10 4 42(1 12 10 ) 28 1 12 1082- k1 k 2 = = 12 10 46 10 4 k1 + k2 = 0/(12104)- lg 0/(12104) = [()-4-lg 12] - : , . . , ([9], 14; 7, 9), (.32). 1/(12104) 12104 1/122 104 10-4122.(210) - - (210) -, -, - , 14 [9]. 147 148. 15. , - . , - , ; , , , . , .([9], 15; 13). , : ( ) , , -, Oeahoo () [2]. (Oeahoo) -( ) - (- [2]) (210). , , 12 , - , -, (210):Oeahoo Oeahoo -12 (211)122 10410-41/122104 122 10-4 1/122 "7 , (), (- -), - , , (, ). Oeahoo . , -,. (-). . . III. - - 148 149. -, - , - : , ([9], 15; 12); , , ([9], 15; 16); , , ([9], 15; 18); ; ([9], 15; 20). , , , , ; ([9], 15; 26, 27).16. , . ; , , , - . ([9], 16; 1 2). , , , . -, . ([9], 16; 13). - (1=10-24) (3=1012) , . (211):| 104 1/A 10-4 A | | 10To 1/10To |. (212)149 150. , , (212): | 1/102To 10To | | 1103To 1012 3 |. (213) , - , (212): |(1/10To) ToTo||10-43 10+43||10-241 1|.(214) -: 13225 = 10-24102410-110+1=1.(215) - : 32 5 1 11 lg d = lg 1050 d = = 52 .(216) 1 2 0 2 0 - : 32 5 2lg= lg 1050 1014 = 36 2 = 3600 . (217) 1 2 4 : , . ; : ([9], 16; 33).150 151. , - , , .17. : ! , , , , , , . ([9], 17; 1 2). , , - -, , , . ([9], 17; 12). 17 - . ( VII) . - - . , : - . (.34). "2. . . , -, , ." . . VII. 151 152. 34 - - lg 12lg 52/22 (+)lg 22/52 lg 34/5= -75= 36= -28 = 100 I 0+111 +47+175 0 0 -64+64 IIIII0 0 0 1282 ( 02 = 16 ) 8 = 02V 1281 141 -3 3 18. . (.34) (218) -15 36 -28 100, ([9], 18; 1). ([9], 18; 24). : ? : . : . . (218):0 111 47175 +2, (219) +1+1 152 153. : ? (219): 0 112 48 176,(220)112 8 * qq * * , (221) ([9], 18;10). (221) , - , (- ). . . -: ? . - (220): 0 0 48-112 = -64 174-112 = 64. (222) : " ?" . - (222): 0 0 064+64.(223) [9]. , 128 . - - -.153 154. 19. , -: "" . - . - , - -, . : . . , . :5 652 6 2 36-25=(9+2). (224)6 5 , ( 62) ( 52). (9+2), [2]. , - -. , , ., , - , : ! . : , ! . ([9], 19; 25-27). . - . - "-" ( 102 ).154 155. . . 100 . , - , , .20. ( ) : , ([9], 20;1, 2). . . . . , - , , , , - , . ([9], 20; 11, 12). : ! ? ([9], 20; 13).: !, . . : , ([9], 20;17). , (223), , - , - (.35, .35). (-) ( )2150 ( )-21 (-).35 . "" 155 156. 35 (.35) (223) 0 0 0 64+64 64 3 32-32 21-21 50 - - - (.35, .35): 64 [21 ( 21)] 25 21 (225)32 ( 32 ) 21 25 , (225): 252/212 1,4 0,1 * . (226) (226) , - - , , , - . , 2004 , :" , " ([9], 20;30) , , , -. 156 157. 21. , . . . : ? . : - . . . . , ([9], 21; 125). : - , . , 21 : 200 ([9], 21; 8); 153 ([9], 21; 11); - ([9], 21; 14). - : 153 1012 1014 = 51 lg 3 4 = lg 24= lg 1051 . (227) 3 1 2 10 10 1 " , ". , 200 - (227) : 157 158. 3 4 200 200 0 lg T0 lg 3 4 lg 5 1 2 51 2 4(lg 1051-lg101) = 4(51-1) = 450. (228) , : ? - : . . 200 3 : 200 3 =600(=300)+(=300), (229) - . , . , . -: ? - - . - . - . -, - . ! . !158 159. , , - . . " ". .. , . , , , , , , , , . , , , . . .1995-1998 ., , - , . : . - . . "- " . -, 1995 - 1998 - .159 160. - , - - , , 1998 . - . , , , , - . - -, , , . : - "" - ; . - . 1913 ( ) "" - . , 1913 , - . - - , - . , . 160 161. :" ", - , , . : " -". , - - . , - , - .( , ). - . , . - -; -; -; -; -; -. , , - -, , - . : , , . 161 162. , - , -. : - . - : . . , - . -. . . , . : , . ? ? ? ?.. .1995-1998 . , , , -, . .: , ? - . - , - - - 162 163. () . , - . -, . - . ( , , ) - , . , . , . .: -, , , - . - . . , -. ( ) () . - : , , ,, -. - .163 164. - . - . , - , -- . - : . - - . - . (), . - - . : (-) -- ( ). - (), . . ( ) - , , , - . . , , - . . -, , 164 165. . - , - -. -, . - , , , ., - , " ". , - , -. , . , , - . - (-), , . -, - - . , - - -, , . () () , , - , - .165 166. , , , , , . , , . - . ? , , . . .: , , , , , , , , , . , , , . , , , - . .: . -. . , - . 166 167. 1. ... . . . "". . 2000 .2. ... . 1,2... "", . 1993 .3. ... ."-". "", 1994 .4. ... . , . . "". . 2000 .5. ... . " " - . . "". . 2003 .6. .. , , - . . .-. 1994 .7. ... . ."". "". 1990 . 8. ... . " " 1, . 1985 .9. . - .10. Copyright Alexey Chernyxh. E-mail:abochehotmal.ru www:http:/www.abch.notmail.ru/Date:06 mar 2000.11. Rudolf Steiner.Aus der Akascha-Forschung. DasFnfte Evangelium. 1913.167 168. I. , , 1. . . . , , - , - ([1], .397). - - , . -: , , -, ([1], .395). , - [2,3],, , - - - . ", , .., - , , , . - " ([1], .397). . , , () -. ; - " -" . , , - , , - , 168 169. . - "", - , " ". , " " : -. , 56 - : , , .2. . - - ; - . - - , , , -. -, , . ; , - ; . , ! ,, , , -. - . , , , : , , [4], - [3]. 169 170. II. 3. . - . , . : , - . , - . , - . - . , - , - . , , - [3]; ; , - . [7] "". , , . , - , . - ; -: , , , - , , . 170 171. [7] "-". , 1, 1/3 1. 4. - . -- , 1: - : - (1)1 =n+1-En=3-2=2-1 =1/1=2/2=3/3=En/En. : - () (), . , , - 1, :- : (2)0 =n-En=2-2=1-1 =loga1lg 1ln 1. - - . - , , . , - , , , , ( ), - 171 172. - - . (2) - . , , - [2]: () - ( ) --- - - 1 =2 = 3 = 4 =5 =10-24 10-1 1012 1014 10 (3) - , - - , : - 1= 1 2 3 45 - - 2 = lg 12345 = lg 10-251027. - : - (3):(4) En+1 + En+1 = 2En+1 En + En = 2En ,: 2 lg 12345.172 173. 5. - (3) (T00/c = 2) [2, 3, 4, 5]. (, ) : (2+2) = 4 () 22 = 22 = 4 (). (5) (5) , - T0 c /0 =8. -, "" . - (2) , - : : (6) logx1 = loga1 = lg1 = = ln1 = 0,: 10 - . , - () : : (7) = loga0 = loga loga1, loga = loga loga0 = loga loga loga1. 173 174. (7) -, :" , , - " [1].6. , - : : (8) lg lg 10100 = lg 102lg 10 = 2lg10lg10 = 2 lg 12345, : 10100 - , . : 10100 . , . 1053. , - [2]: [4] :2/3 :1/3 "", , K1=2 "", , (), (), , , K2=1/2(9) - ------ * - * q*q * = * =q* = = = q=281020141020 161020 2810-20 1410-20 1610-20. (9) ( ) () , 174 175. , "" - , 7/4: * = 28 10 20 728 10 20 = = " " =. (10)q* = 16 10 20416 10 20 = q "" - (9) - : * 10 40 = * = 10 40 . (11) * (9) - 1 + 2 = 5/2, - 1 + 1 + 2 = 7/2, 7/2 - , - 7/2, 5/2 - , 5/2 [9]. 7/2 5/2 - , - . III. , 7. - (1, 2) [12]. (-) - , 175 176. , - - , 10 [6, 7]. 1 0 1 1 d =02 1 = -1 d = 2(12)101 2 = -1 11 d = 2 d = 20 1 111 1 ( ) = 1 e 2 i 1 + 1 = 2 = R ( ) = 1 e 2 i . 222 2 . , - , R = 2 (12) (-) (2) . , - ( ) (0 = 4). -:Sin /4 = Cos /4 = 2-1/2 Sc /4 = Csc /4 = 21/2.(13) - (.1). :1. - : 176 177. 1/ 2 + 1/ 2 = 2 2 + 2 =2 2, (14) (.1 1).) Sin /4 Cos /4 1/ 21/21/ 2 11+= 2221/ 2 1/2 1/ 2) S /4Cs /4 2 22 2 + 2 =2 2 22 2) -H L R ra .1 "" [2-5]2. - (.1 1): 1/ 2 1/ 2 = 1/2 2= 2 2,(15) 177 178. , - , : 1 d = 1/2 2 lg 12345, (16) 0 , - 3, 4 5: 1 4; 0 4-1 = 3; 04+1 = 5. (17)8. , - . (.1): (.1) r R a T0 2a a2 L T02 log 2 2 36 = 36 (18) - 21 22 23 24 2 5 2 6 2 7 2 8 log28 2 2 = 28. , - , -, 12 . , - , - - (T0c /0 = 8), (9+0) (9+2): 178 179. - - - 36=8+7+6+5+4+3+2+1 , : 28=0+1+2+3+4+5+6+7 "-8+8+8+8+8+8+8+8 = 64 "- 36= 8+7+6+5+4+3+2 +1 1(19)- d 28= 1+2+3+4+5+6+7 +0 0 (9+0); - .9+9+9+9+9+9+9 = 63 - 36=0+0 +8+7+6+5+4 +3+2+1- 28=1+2 +3+4+5+6+7 +0+0+0 (9+2)3 11+11+11+11+11 6. T0c /0 = 8 - , . "-" , 64 . - - , - 32 . - "": . 9. (19) - (9+0) , - : - . ((19), .2). [6] : 179 180. - "6. -I II III IV V VI VIIVIII . " - " - ,1 0 1 2 3 4 5 6 72 8 9 10 11 12 13 14 15 " - , 316 17 18 19 20 21 22 23 . -424 25 26 6 9 29 30 31 . 532 33 34 9 6 37 38 39 . 640 41 42 43 44 45 46 47 .748 49 50 51 52 53 54 55 " (856 57 58 59 60 61 62 63 VIII). - (r = 2 ) (L=8 2 ) (.1):L8 21 2 2 d = d = 2 (82 2 ) = 64 1 = 63. (20)2r210.- (9+2) (3+69+0), (19), - , 511=55 , , , -: 12 + 2 2 + 32 + 4 2 + 5 2 + 6 2 + 7 2 1405= =1+ 2 + 3 + 4 + 5 + 6 + 7 28(21)-2+2 12 + 2 2 + 3 2 + 4 2 + 5 2 + 6 2 + 7 2 + 8 2 + 9 2 + 10 2 3857=1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10=55-2+212 + 2 2 + 32 + 4 2 + 5 2 + 6 2 + 7 2 + 8 2 + 9 2 + 10 2 + 112 + 12 2 + 13 2 819 . == 9+0 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12 + 1391180 181. (19) - , , 6 1+2+3+4+5=15 (.3), (.3) (21), -:" - 6+15=21 42 = 21 - (-21)6 . . 6+15=-21 . " ( )..3 - , - -- (3628=1008) , - 24: 36 28 = 42 24 = 1008 103 (=1,008), (22): - . 181 182. IV. 11. () (-) , - (, q) (*, * q*). -, - , , - . . - : "8. - , , -, , , , - ; - , " ([7], 1, I). -(k1) (2) - , T0c /0 = 8 (k2) (.4). - (1) T00/c = 2 (.4)..4 (- -: - (.4): ) (T00/c = 2)6 = 64 = (T0c /0 = 8)2(23) - , (.4) : 182 183. (.4):k1 K 2 T0 c / 0 (T0 0 / c) 6 8 64 4===4 2 ; (24)k 2 K1 T0 0 / c (T0 c / 0 ) 2 2 64k1K2 - 4k2K1 = 0 12. (24) , -, , - -1 -1/2 -Sin /4=2-1/22 =Cos /42 - (.5); , -K10 K12 . -K7 K8 K4 K 5 3 (.5):K11 K9- :1=2=3=4=1; 1/241/2- : Sc /4=22 =Csc /4 5=7=9=11=1/2;3- : .5 6=8=10=12=2. 13. (), , , :183 184. (.5)K6 K8 K10 K121 (K + K2 + K3 + K4 ) K5 K7 K9 K11 1T02 (K1 + K2 + K3 + K4 ) K5 K7 K9 K11= 16 = 116K6 K8 K10 K12 = T0(25) . 14. ( , ) " - " (.4). . , ( ), - ( -, .4), - - : xk1K1=86483 k2(K2-x)2(64-x)(26) : (k1K1=8 )=[k2(K2-x)=2(64-x)] -x=682(7/2+5/2)82. 3 6 - , (7/2+5/2=6) - , .184 185. 15. - . , . -, (.4, (24)): (.3):k1K1 - k2K2 = 882 - 282 = 6 (27)" " () 10 I: "1. - - (, .5), -, - ( k1>k2, ), - " (T0+=4+3=7) [1]. (1=2=64), - (27). (T0+=7) 42 (.3, (22)). : " " (28)6(T0+) = 67 = 42 21 - (-21) . 16. , , , . . . - , - - . :185 186. "1. ., , -; - ; , , , . - ; , . , , , (); - -" ( VII, [7], 1). : -10 d - d =1/2 - (-1/2) = 1, -01 ; ;1 0 d + d =1/2 + (-1/2) = 0 01 , - 73 1(29) d =3; d =4; 5 = 5 d 11 0, ,3 453+5+ 7; 3+ 4+5 35 73 4 535 7 == 35.(3 + 4 + 5)(3 + 5 + 7) , , - , K5 = 7/210 = 35 =57 ( ), , (- ). , , . , , -. ,, , - , -. , - (, - ) " ". , - . , (26). 186 187. V. - 17., 02 0-2(25), , . - -, -. , , , , - ., , 0 =/2 [2]: - - x+ yxy 2 (30) ; 01 0 = yxyx+ y 2 -: x-y = 0 001 (021)/0 (0+i2)(0-i2)/0. - , - [3, 4].18. (m0) , 2 2m0 = m / 1 v 2 / c 2 . v /c - (j = c2R) - (j = -v2/R) , .187 188. : ? -, , - , , , . . : , , . -? : , , . - - - - . , - - - , - , . , (-), - . - n: n, n0. , [10]: : m0 e (31) lim (1+1/n) = e = 2,718 = lim (1+n)1/nn n n0 19. , , - , , ,, , - 188 189. : = , ci = i 1 , - lg 12345=2. : , , , [10]: - .(32)- - Sin2+Cos2 = ch2 - sh2= 1 e2i , "", - : (32)1 02i0=ln 1 ln e 2i(ln e = 1 d - d ), (33)0 1 ln e = 1 - , (29). 20. - 2i ri = i. (33). - () (.1 .6).189 190. 2i , - - ri=i, -2i Qi=4(ri2=i2)2 = -4H=27/4 Qi=4i2 Vi = 4/3(ri=i)3 = - 4/3 i. , - - R=2 .6 -, - (.6, (34)):(Qi) (.6) (.6) (34) Si=2iH = Vk=i2H=Qi=4i2 =Vi=4/3i3 = 21/4i -27/4-4 -4/3 i 3/4 3 Si/Vi = -32 -3(Qi/Vs) Qi/Vk = 21/4 Sc / 4 Csc / 4 . (34) , 2, 3 4 [3, 8]: 2 3 4 V 1 11 V =T0 k = 8 4 21 / 4 = 8 27 / 4 = a 2 H , (35)2 + 3 + 4 Qi 3 33 , - .190 191. 21. , - , -: " , ". , :H2=r (.1, (18)), : (.1, (18)), : H2 = r = ra2 = aR = rR3 = = L = 27/2. (35) , - : , . - - (, ), (, -). , , - (-), (.1 .6): : R = 2 = lg 12345(34) .(36)2LR=2R=4SR=R =4Qi=4ri=4i2=-4+1+1 -1 191 192. (36) 1:2, () () (36) " " ([7], .1). 22. . -- () (), , (18): (LR, Lr) (SR, Sr) (R=2)(r= 2 )-- (37) LR=2RSR=R2a2 Lr=2r Sr=r2= 4= 4 =8=2 2= 2 (.1): LRSR = (a=2 2 )LrSr. (37) , - , - () (37). , (-) :192 193. (VR, Vr) e (QR, Qr) (R=2) - (r= 2 ) . - -(38)QR=1/22R VR=1/3R2HV=Vr=1/3r2H Qr=1/22rL=2H2= 4/3H1/3a2H=2/3H =H2 (24) (25): QRVR = 4QrVr rToQrVr = T0QrVr. 23. (37, 38) - ( ) , , . . . -: " - !" . -: - , , -, - , "" - , - , - 10-3 ; - , - , : "" (mc=E=1/, [2]): (39) LRmc=LRE=2R1/=2R 2R/mc=2R/E=2R=LR193 194. , , ? -: " ", : ",, ? , ! , , !" , , , , . [5]. VI. 24. -. - - . , , , , - : 0/0 = 8. , , , - . -: T00/c = 2. - , - - 82: () + 8 2 8+ 2 ;; .(40)+ 8+ 2 8282 5 2 82 " " [7] ( ) 194 195. 25. - - (40) . - (.4). -, , - -, ( d) 64 (.4): -: 64 d 63 1008 .(41) 8 64= 42 = = 2 152 15215 d 2 (41) 02 0-2 (25), 63 (.2), : (41): 3(42)1008 42 24 = 28 36 10 (=1,008), = 1,008 - .26. - [4]: 10-201020- - - - .(43) = 28 = 14 q = 1628=* 14=*16=q*195 196. , - (25) - -, - 1020 ( ..). - . 02 = 16 0(0+) = 28 - . (43). "" -: 7/4 = /q. .27. , q, - ( d) , -: : 281 d = d 10 = 2(28 16 ) 10 = 26410 24 (9 + 2) 10 .(44)402 2 4040 40 q 16 ( 24), (9+2) . , , - , . - .28. . -. () - ( ). - . -196 197. . : */q* = 7/4 (43). (*) (q*) - , - , ( d): :*28.(45)1 2* d = 16 d 10 = 2(28 16 ) 10 = 264 10 24 (9 + 2) 10 40 2 404040q (*) . - (44) 1040 (45): (44, 45)* .(46) d24 ( 9 + 2 ) 1020 20 24 ( 9 + 2 ) 10 dq* == 10 40 10 40 == q*24 ( 9 + 2 ) 10 20 24 ( 9 + 2 ) 10 20q d q* d, , : " ? ?" , - , , , , , - , , , "-".29. , . . 152 (41): 197 198. (41) .(47)1 1 152 =(q+) d =10-201515=1020=(q*+*) d0 0 - 15+15=30. -- : - :" " (47)15215 + 15(48) 4152 15 + 1515 2 15(30)(30) 4 , - = (1400-500) = 900; = 300300. , "" , - : (48)15215 + 15 (152+152) 152 (49) 15 + 15152 2(15+15)=60 , 602 = 6 7/2 + 5/2 - . , (48), (49), , , -: 198 199. (48) (49)2 (50) (15 4) (15 4) 0 221 (9+2) 0. (50) , (.3), - , 21 (.3): 0221 - (9+2) = 2100. (51)30. -. - , . , - - . , , - . . - , -. [25].Sc /4= 2 =Csc /4 -1/2 E( Sc /4 L0 Csc /4 (.7, .1, (18)). , - (mc=1/), - mc S0 , - 1/2 E( - (.7). .7 - - - : - , (- , = 1/), , - (.7). - 199 200. - -: (.4) - [2, 3, 4, 5]-- - .(52) () () - mc=1/ E=1/2-R0=D0/2L0=D0 S0=R02 T02S0 = D0 (-1/2) =1/2 =1 1/4 4/ (52) - : - "" ( ), - - (). (52) - L0, - - . - T02S0 = 4/ = T0mc. - " " , , - . () - . - . S0=1/4 (52). , - () - (.7). , 02 (25), - : 200 201. , (.7)(53) T02S0 = 161/4 = 4/ (4/)2 = ( ). : , - , - , . -, , . : (54)Sin /4+Cos /4 +16=Sc /4=Csc /4 mcS0 T02S0 4/ArcSc( 2 )ArcCsc( 2 ). = 21/424/2 , . 31., , , - , - 1008 (42). -. mc=0,008 - H = 1 125mc. -: (55)lg 12345 = 250mc = 2=2.201 202. -- (0 = 16 2000mc) (AN = AN - 0,008 =14,008 - 0,008 = 14): A2=2 AN=14AO=16 No2=2 NN=7 No=8 (56)2/mc=250 14/mc=1750 16/mc=2000 2/mc=250 7/mc=875 8/mc=10001250 = 2000-1750 250 d =1251000-875.0 , , - : , . . , - , . -, ; - . . : - , , . : - - ; - (1/2), (56). , : ? ? , . 202 203. VII. "" , 32. "" , . 27 28 - 6 9 - , 35 36 [2], 9 6 , - 27, 28, 35 36 (.8).8 27,28,35,36, 6, 9, 6, 9 - - - (.2). - , (.8) 6, 9, 6, 9 (.2) - : - k1=k2= k3=k 4=.(57) 35-2736-28 35273628 =8 =8= 1563= 1663 k5 = k6= k7=k 8= 9-66-9 9669 =3 = -3 = 54 = 54 (57) , - k4 = 1663 = 1008. - k4-k3 =63 (.2).203 204. (9+0) - - -: - (9+0) (57)(58) - -k4-k3-(k8=k7) = 63-54=(9+0) (k8=k7) - k4 - k3 = -(9+0). , - (9+0) , 2 = L = 27/2 (.1., (18)). (18) - ( ) ( ) ( ) , - (.1, (57)): (57) (59) V=(k1/k2)H=1/38H1/3a2H-V=(k2/k6)H=-1/38H-1/3a2H. -, ,, :k4 - k3 = 633163 = k4+k3,(60) , -, 31, [4, 8].33. , ( - 204 205. ), , - (.3, .8, (57)): () (.8) 28 35 27 + 36 . 28 + 35 27 36 :128 35 27 361 d = 240 = 120 = 1 2 3 4 5 = 5!(28 + 35)(27 + 36) 0 2(61) : 1+2+3+4+5 = 15. :120/15 = 8 0/0. 34. - 10 (29). - - " ": - " " (29) - k = 3535 6464.(62) == 5 1020 1 * d7 1020 d d = 60 0,1 ( 2 8 + ) 0 -, .205 206. 35. , , - . - , , - , 7/4. - : ky = /q = 7/4, : k-y = */* = 7/4; - : kz = k-z =Kx = k-x =(63)7/27/27/2 7/2log 2(Csc /4) log 2(Sc /4) log 1/ 2(Sin /4) log 1/ 2 Cos /4)= 7/4 = 7/4 = 7/4= 7/4. - (.7), - 9 (63).kz (.9) k-x k-y/q kz k-z, k-y */q* k k- (.9). kx (.9) k-z .9 - - , :206 207. - :k z kz k y k x + kx + k y(7 / 4) 3 37 / 4 (64) k z + kz + k y k x kx k y 37 / 4 (7 / 4) 373 361 = 4(12)2 = . (64) - , , - . 36. () - . . - ( ), , , "-" ( ) .- 20 *=2810 - . 28K*=3510 20 35 , 36 .(35+1)1020 -27 :(28-1)1020 -- (.2, .8). .10 , , (10), 28, 27, 35, 36 (.8), "" - .9 .7. 207 208. , , (.10). - : (.10) (65) 28 35 27 + 36 28 35 27 36== 16 15 = 24028 + 35 27 36(28 + 35)(27 + 36) . , "" - , - 6 (.3). - : "" (65)(66) 240 12345(lg 12345=2) = 1202 . - - , (.11). - - -.11 : 1 + 2 + 3 + 4 + 5 = 15. (67)208 209. - , 162, - (25):- "" (66), (67) (68) 240 15 2 (2402) = 16 2 qq* .1524015 (68) - . . , - (.9). , -, - -- , (.10). , -6 n1 2 (.9)14 -, -5 3 (.12). ( ), .12 - ( ), :209 210. - (.12). - : .(69), - n , 6! ! - :C6n =(6 n)! ( ) (70) 6 62 63 64 65 66 1 630120 360 720 6!/0 1236=6+30+120+360+720, 1236 , 6!/0 - .VIII. - . 37. : - - [7]. - . , , - : "5. , -,; " ([7], 1, 76],.13). [7] (.9, .13), -210 211. - , - , - .z 7/4 7/4 -x -y 7/47/4 1 -y (.13), -x 7/4 , - (- -z7/4 (7/4)6, .13) - .13 - ( ( 1) 67/4, .13) - ( [7], - (m0=e) - [1]). : ( 7 / 4) 6m0 = 2,7355... (71) 6 7 / 4 (71) - :K1 = m0T00/clg 34 = e226; (72) : k2 = m01lg 5 = m01lg10 = m0,(73) - : k3 = m0T0c/0lg 12 = m08(-25).(74) 211 212. (.13): . - (75)(72)(73) (74) k1 = 52m0 k2 = m0k3 = -200mc k1/k3 k3/k1. , - : (75):k 2( 200) 2 (76) 3=2= 14,79... 14 + 0,8 * + 1T0 c / 0 .k1 522 . -, , - 21: (.3, .13) 7 7 6 lg 1 2 3 4 5 = 6 2 = 21 214 4. (77)42 ( )-21 (77) (, ) - (, ), - .212 213. 38."6. , . " 9[7], II, 1,.16). , , , - , , - . - , - ( ), "" - : - : : : : (78) (mc) (E) : mc E(E) (mc) - * 7 4 - - = = q* 4 7 q * q* q -- - - () () ()(). - - [11]. -, - (78). 213 214. , - - (78). -, (.13), -: (78). , - -. -, - "" , [7]. , , - . , , . - [11]. - , 1,0201,040 [11]. :1. , - , ;2. , , -;3. , - , [11]. () 4105. . R0 = (1,71,3)10-13, 1,7-1,3 = 0,4 [12]. 214 215. - : (25) [2]: (79)- [25][11] [2] [12]2 60 = 160 = 4 410 410-14 . "" [2]."" - : , , , . (..). (80): (80)4 106 = 10201 / 1020 . 4 1014 39. - - . . . - 215 216. - [11]. - , - . - 21 35 , - 3 7 . - - , 37=21, - , 35-21=14. -, - , : - 35-21 = 14;(81) 35+21 = 56 37 = 21; 56/21 = 2,(6) 56-14 = 4242:21= 2 14/21 = 0,(6),: 42lg 12345 6=7/2+5/2. ( ) . 40. . "" , . 216 217. . - . - 28 , - : : (82) 28 * 28 1020 28 1020 . [11]:- ( , , );- ( -, );- ( );- ( , ,, ). 3 - 2 - 1 , 1 1 0 2 3 4 3 4 , - 5 9 8 7 "", 6 5 4 6 7 8 5 6 , "- 7 " - -.14 (.14). 217 218. (.14) 1 3 4 56 7 89.(83)1 2 3 4 5 6 7 8 0 1 2 34 5 672 15125424 (83) - . 3, 4 5 (83). 12, - (.14,(83)):7+8+9 12 = 3 + 4 + 5 .(84)0 +1+1 12 (84), - - (83). - - : : (85)(85)54 15 54 15 ;54 + 101 54 / 150 -152 - ( * + q*) d ( + q) d . 542 542-152; 1 0 0 152. , , - (85) 10 [7]: 218 219. "8. ? ? , , ? , , , - , . 9. - (*+q*) - (+q), , ,- . 10. - , , (- ), , - (), , ( ) , ". 41. , - 7/2, - 5/2 [9]. -, , - - (85). .(86) k=2*/q*+2/q=7/4+7/4=7/21 - k = 1-7/2 = 5/2 , , -, - :219 220. - (86) (87) kT0c/0 = 7/2 8 = 28 kT0c/0=7/2 8 = 28 * 28 . : - , - . 42. () - () , , [7]: " VII. 1. - . , - , ". . - - - , 02=16 (25). - "" 72(.15). (.15) 7/2=5/2+1 * 7 7(88) T02 = 16 = 7 2. q* q 4 4 5/2 1 15/2 7 7 - - 7/2 .15 (.15): = 5/200/clg 34 = 5/2226 = 130 k1; (89) 220 221. () 7/2 - :=7/20 c/0lg 12=7/28(-25)= -700 = k2. (90) (89), (90) " - " - : (89), (90):k1 k2k +k 2 1 (k1 k2 ) 2 k2 k12 2k2 k1 k1 k2(91103)2 72 104-132 102(91)E, :(91103 ) 27 = 2 104 . 7 10 13 104 2 2 4 104 "" - :7 7 7 7 7 ( )= + = ,(92) 0 / 0 0 / 0 8 8 4 104 - 10-4 , - [2]. 43. - . : " , - , ". :221 222. - : = +*, (93)282 = 142 + 142. 282 : E = = 2 = lg 1 2 3 4 5 . 142 + 142 , , - . 44. . - * . - - . - (2*) - . , -, - . ( ) * k1 (89); * - k2(90), * q*: 222 223. (89) (90) * (94)( *)2 * q*=k 2 = 350 * d = 30 10 40 *k1=130* * + * 2*260-350151020(q*+*)/2. - () : () (94) 260 350 90 20 (95)K0 ==10 6 1020.15 10 201545. - - (9+0) (9+2) (.16). (.16) - - - --. - * . ** * - -(9+0) (9+2) - .16 107 , -- -7 - : 10 = 4 . 223 224. (*) -, : (9+0), . (96)4 107 1 ( 9+ 0 ) =1013 0,036 1013 . * 28 10 20 28 - (R0) [12]. 46. - (9+0) * * *. . - (9+0), --. (9+2), * - - (.16). - - (.3), , - - (.17). , -.17 - , - - , (.17). 224 225. . -- , -. , , , - - 1 63 (.2) 27, 28, 35 36 (.8) ( ) - 6, 9, 9, 6 (.8): 1 + 63 (97)N1 = 63 -(27+28+35+36)= N2=N1+(6+9+9+6) =21890 +30 = 1920 2016 - 126 = 1890N1/63=30; N2/30=64 (). (.17) (), - . (97) : N1= 30 (q + )(q * + *) (16 + 14)(16 + 14) . (98) 63 (98) - : C 0,1 300 30 30 0,1 300 . (99), , . : " ?". : "- ". -, . (97) - (99).225 226. 1. .. -, , - , , -, 1994.2. ... . . . "", , 2000.3. ... . - . -. ., 1999.4. ... . - . , -. . "", , 2000.5. ... . - " " . . "", , 2003.6. . ... . "-","", 1997.7. ... . 1 2. - "", , 1993.8. ... . - . "". "", 1990.9. ... . " ",1.1985., 43 .10. . .. . ."", , 1978., 130 .11. . "", , 1974., 127., 445 ( 3) 148149 . ( 2).12. .. ... .. "", , 1968., 807 . 226 227. I. . 1. . . . , . 2. . , . ( .). - . : - . , - , - . 1040- . 3. . , - . - 1/3 2/3 . - , . -, - , 2:1, . - - , 2:1, 1:2 ;227 228. - 1:3, , - , - - . 4. . - , , , - ( ). (-) (). -- ... -: 1020 . - . , , , 1/1020 = 10-20, 1020 . , . : 28 ( ) , 0 = 4. , , . , (), = 281020 q =021020 = 161020 . . ( - ), , (). , 228 229. ( * = 281020; q* = 161020), - , -, 7/4 . 7/4 , , . , 7/4 [7]. 5. [1,2]. III .5 - : ( ), , () , Oeaohoo . : , Oeahoo? -, . - . - - (). - (). - , . - . -. . - ( d ) : 1 : d = 1 / 2 , : 01 d = 1 / 2 .0 229 230. - , - . , : , .. - ( ). 6. Oeahoo . Oeahoo . , , , -, . . () [16] , , -, [10,11]. . - , . - . - - - . , , (Vn) [6,11]:2 3 4 () 11 Vn = 27 / 4 8 27 / 2 = a 2 H , (1)(2 + 3 + 4) 33 a - , . 230 231. II. . .7. - . - . - * = 281020 . - . (+1/2), ; (-1/2), - . . . () (). - () . , - . - 0 = 4 -: 114 10 207( * d *) : T0 = 10 20 . (2) 0 42 3,5 = 7/2 -. .8. - , , - 28. - :231 232. 1728 / 10 20 d = 16 10 20 q .(3)20 . - , . 9. . . ,, .., - .. [14]. - . . , - 7/2 ( ); - , - 5/2 ( ). - : (2 / 3) ( 1/ 3) 1 5 = 2 + = .(4) ( 1/ 3) (2 / 3)2 2 - (.1) - . - . .1 232 233. - . ( ) - . 10. , . , , : o oo = 7600 A 4000 A = 3600 A . 6( 5 = 10) , ..602 = 3600. (.2):.2 36, , 6. - -. : 233 234. 1 + 36 36 =2 36 = 666(5)1+ 6 6 =2 6 = 21 (6). 666 21. 666 , , , 21 (-21) = 42 : () 42 . . . . , 21 = 5+7+9 - (9+0), - . 11. - , , :7 / 2 + 5 / 2 = (7 / 2) 2 (5 / 2) 2 . (7) - . -, , - -. - , - . -, 2.234 235. , , , - 70: 1 23 45 6 7/4 7/2 7 14 28 56 40 20 10 5 5/2 5/4 (8) 70 70 70 70 70 70. () - :8 7 6 5 4 3 21=36()1 2 3 4 5 6 70=28 () 1(9) 9 9 9 9 9 9 9 d 64. () 0 - 63: 70 9( 2 = 10 1 ) = 63 .(10) - . 64 10, 64 d = 32 64 d = 32 01.235 236. 12. 24 - , . - - (0 = 4) (q = 3), .. - 4 3 = 12 (12 , 12 , - ..) 24: T0 q lg 1 2 3 4 5 = 4 3 2 = 24, (11) 1 2 3 4 5 - , , - . - () - : 7 * 24 4 q * = q = 42 . (12) , - , - - , .. - - , - . - , .. 42 - , .3 . q. (12)236 237. () - . , , - - (12).13. : -, (c.3), -, - . - , - , , , 36 28. , - . - - (13) 3628= 42 24 =1008 103 1,008 , 1,008 . - , -, :- - (14)(42 + 24 = 6 (36 + 28 = 64) = 2 = lg 1 2 3 4 5 64 ( (9) 66 -. , - - 660. .237 238. III. . .14. - , - (9+0) . [11]: - (15) 7 24 = = 42 (21 +5 +7 +(9 + 0) (2) 5 7 (9 + 0) .4 q - , 10. , . , 8, 2. 6 = 8 2, , 4. - - (a = =1), (b = m = 1) - ( = 002= 1) (.4) a b a b 10 (.4); c c , ( .4 ) ( 6) [13]. 238 239. 15. . () 28 27. - , 7, .. . - - . , , - : , 1040 - : * 28 10 20 (16) P=== 10 40 . 28 10 20 V :5. - . : . (.4), 5= 10, , , : :11 0(17) ( 5 = 10) d = = 5 5 = 5 d . 20 1 . (5 ()) 239 240. . , , , . ( , , , ) . - ,, : : : 77* = =q 44q* . - , 0 = 4. (18). : -, , -, -. .. 4! : C 2 =4 = 12 , -(4 2) ! .16. , , .. , .., : () , - , , . , , ; - . -; -; . . (. V).240 241. : , (.4) - . ( ). - - (.5) , , - - . - , .5 : , - 32 - .(.6). 17. - , (.4, .6). , - . , , .241 242. .6 : . - , . , -. ,.. , . -. , . - . , , , -242 243. - - . 18. : . -: - . , . - , - . , , : - -, - - (.6). , : .(.7)IIIIII123456I .II .III ..7. (.7,I), (. 7,II), - (. 7, III). - . 1 6 (C1 = 6!/ 5!= 6) ;6, , , -: 243 244. 6+50+120+360+720=1256.(19) , , 1256 . : 6!6! C6 6 = ,(20)(6 6)! 0! ( -) . - . . - (.7) - () (): - (7), (8). - . - , , , .. 72 = 49 - . . - -. 19. .. , - . , (): , - -244 245. , , - . , , -, . -, - - . , , : , , - . : - . . , .. -- () , - : (21) * K1 = d 8 3 1110 40 K1 = d 8 3 11 10 +40 . qq* 21 -, -- (1/2 = 10-80), - - (1/2 = 1080). - 245 246. . , -. 20. . -, . -, 3 10 6 , . , , , .. - -. , , . , , - . - , -, . , , , .. - - . , , -, , . . - , , .246 247. , - ., , , , - . , , . , , .IV. 21. . , , - . , -- , , . - - , -, . , , , - -, , , , . . - , - . - (q), . - . 247 248. , - - , - [1 14]: - 10 20 () 10 -20 (22) * = 28 * = 14 q*=16 = 28 = 14 q=16 72 72 * = 10 20 10 20 = . q 2 2 q -- (22) . () , - - ( ) , - () 49. , T0 + = 4 + 3 = 7 , (7/2) .22. , -- , . (.8)248 249. .8 : - . -- . - (.8) , . - , - . : , 249 250. - . : - . - , . , , , - (.8). - : , . ( ), - , , , (.8). , , - , - (.8). -, , - . , - . , - 10 40 . - . - . -.250 251. 23. (.8) , .. . , , , , , , , -, . .[1,2]. , (), , : 1. , -, . 2. , . 3. , -, . 4. . , . 5. , - , . , , . - : 1. , . - . ( ) 251 252. . - , 0 + = 4 + 3 = 7 (- ). - 12 = 4 3 0 . 2. , - . - , - . 3. - ( d), - : -* 1 0(23) d d = 7 12 44 = d d (*) = 7 12 44 = 2 2 22q* 0 q1 8 0,066(23) 5 0,066(23) 58 . (23) - ,.. * q* . (23) (*)2 . -. , - , . ! 24. , - - : , , , .. (.9). 252 253. .9 - ( ) : ( ) ( ) ( 9) - (.9) 6 () - [6] 72 , [5]: 0+ = 4+3 = 7 0 = 43= 12 (24) 7(Q6 = 6) = 42 12(Q6 = 6) = 72 [6] [5]. , 253 254. (.9), , (-) , (- ) . 25. ( ). .10 - , , , [11,13]. . -. () () ( ), - (). [11,13]254 255. . ( - ( -). : 9. , -, ? [1]. , (.10). , . ( ) -, ( = [11]) ( 0 / 2 [11]) . : T0 0 / c = 2 (.10) , : T0 c / 0 = 8 ( , .10)26. - . , - . - (.10), : () ( ) (.10)(T0 0 / c = 2) ( 7 / 2+5 / 2=6) = 64 = (T0 c / 0 = 8) 2 (25) , 2= lg 1 2 3 4 5 7/2 + 5/2 . , - - : :255 256. (.10) 64 / T0 0 / c = 64 / 2 = 32 (); 64 - (26)64 / T0 c / 0 = 64 / 8 = 8 32 + 8 = 40; 32 8 = 24. 64 - 32..11 (). - (.11). - , - *, * q* : 256 257. * 171K * d = 14 10 20 =7 2 5 2 1018 ,q* 042 (27)( ) *07 1K * d = 14 10 20 = 7 2 5 2 1018 q*14 2( ). , , ; . -. . - . 27. - . . - , - . , - -: - 1 0* * d 1 2 q d 3 4 q* 0 1(28) 7 1 7 1 14 10 20 10 24 10 1 14 10 20 1012 1014 4 2 4 27 2 5 2 10 7 K 7 2 52 10 7 , = 10 4 / 10 -7 = 10 g = 11 (9 + 2). 257 258. (9+2) - , , . ( ).28. -, -, 1( 5 d = 5) -0 : , , -, , [11,13]. , - , , , [1,3], - , , - [3]. , - , . (.9,10,11 [1,2,3],). , , -! 29. (*) ( X, Y,Z) . - , - [13]. (7) - () (). , , -. (.11) . [1,3]. . - , .. ( ), : 258 259. ( X, Y, Z) (29)* lg 1 2 3 4 5 6 = 28 10 20 2 6 = 336 10 20. ( ) - (=4) . 5. (). -. . [1, .81] , : - . ( ) : , (8)336 10 20 (30)= 112 10 20 7 q * ( ) 3 8 * ( ) 4 * ( ) . (9) , [1] , - , . - , , - ( 1 2 ) - ( 3 4 ), :259 260. : 1 2 = 10 3 4 / 5 = 101 2 / 5 3 4 = 10(31)50 58 10 1 1 101 e = 8 = 10 50 10 58 = 10 8 12 = e2 2 e4 . - 8 - 108. (m0 = ), -, 4 ln . , ; , , [14]. 30. , , - , - : (.11)-- - - (32) - - -- () (). - , , , .. - , , -. - 260 261. . . . 20 - -. . . . . . V. .31. ( d ) ( ) . - - 6 36. , 630: 361(33) d = 2 (36 2 6 2 ) = 7 9 10 = 630 .6 ( 5 = 10 ), ( 2 = 10 1 ): : (34) 5 630 = 10 630 = 6300 2 630 = 10 1 630 = 63 . = 7600 4000 = 3600 , ( 28), - 261 262. 112 6328 - [9]; 71 + 112 3600 + 28 = 6328 + 112 , (35) 4 2 - 112 - . , 63, - , 8 , , 6 9, 9 6(.12).I IIIII IV V VI VII VIII10 1 2 3456 72891011 1213 1415318171819 2021 22234242526 6929 30315323334 9637 3839640414243 4445 4647748495051 5253 5455856575859 6061 6263 .12. - :6 9 = -3 i,(36) 9 6 = 3. - -oo ( = 300 ) ( C = 300 A ),o.. 300 A . - :262 263. - (37)o o2 2 300 A (9 6) 5 = 300 300 = (6 9) 5 300 . () -, -, 3, 6 (m0= e = 2,7) , - e: () 6 9 = 54 9 + 6 = 15 () () 6 + 9 = 15 6 9 = 54 () (38) o 3 10 3 3600 3,6 2, (7) e m 0 .2 : 2. - ( - ), : , - ( ), , ( 3,6) - ( ); ( ) , ([14], VI, .15). , - , . 32. , 6 9 27 28, - 9 6 35 36(.12) 263 264. , , - (.13). , - 28 27 (.13). - (.6). -: , (.4, .5), , , . ( - ) - 35 36 (.12) - ..13 [13]. -, . 33. (.13) - 35 36, - 27 28 (.13):264 265. 28 27 28 + 27 35 36 35 + 36 28 + 27 28 27 35 + 3635 36 75655 126071(39) 55 756 711260 2 1260 71 22 [2, (15)] [2 + (0,15 + 0,015 + ...)] .756 55 (39) , -: [.4, .5]: 12 + 2 2 + 3 2 + 4 2 + 5 2 + 6 2 + 7 2 + 8 2 + 9 2 + 10 2 3857==; (40) 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 55 () (-): 2 2 1 0 [0, (15)] (q + ) 10 20 d (q * +*)10 20 d ,2 (41) 0 1 q = 1610 20, =1410 20, q* =1610 +20 * =1410 +20 , q* * - - () -, ; [2 + 0,(15)]2, - : 265 266. 2 = lg 1 2 3 4 4 , (42) , , , , - (): 214 = ( 2) ( 2) ( 2) ( 2) ( 2) ( 2) ( 2) 276 54 321 Kc=214(43) 2 21 2 2 2 3 2 4 2 5 2 6 2 7 = 2 28 K=228. , - , - , : Kc2 = (214)2 K = 228. (44) : (45) 1 10 24(10 +12 ) 32 . -, -266 267. , , , , , . , . - , - -. 34. , , : - H = 27/2 ( r = 2 ), , - (l = 8) : : 2(46) H = ( 2 7 / 4 ) 2 ( r = 2 )(l = 8) = 2 7 / 2 . -: (l2) - (H 2 + r 2), : 2(47)H = l 2 r 2 = 82 ( 2 ) 2 = 64 2 = 62 . , - , , - - : H2 62 2 7 / 2 = 31 2 5 / 2 . (48) H 2267 268. , : , . , ! . . , -. , . -, : , , - 21 31 [7]. - - . , - (.14). Lr 2 H R (2) 2 a (2) 3 r 2T0(2) 4 R 2a(2) 5 aa2 (2) 6 L (2) 7 ( 2) n n n =1, 2 , 3,.., 7 Sc Csc = 4 4 .14 268 269. , (.14) . - Sin / 4 = Cos / 4 = 1 / 2 , Sin / 4 + Cos / 4 = 2 1 / 2 = 2 = Sc / 4 = Csc / 4 . - ( 2 -5/2) :( 2)1 n =1, 2,3,.., 7 28 22 = 214 . (49) , - , . -, -, . , - , , (.12). : - : (Sc / 4 r = 2 ), , (L ( 2)7= 8 2 ), ( ). ( ). ( ). . . ([14], VII, .19). , .. - ( d ), . VII, .19[14] - - : - (.12) . - .269 270. () , - (.14) =8 2 1 2 1 ( r 2 ) = (8 2 ) 2 2 = 63 () 2 d = 2 2 (50) n= 2r= 2 , = 8 2 ().270 271. 1. . . .I. I. 15-32. .. , 19932. .. . II . .2.35-42. .. , 1993.3. . . . The Bhaktivecdanta Book Trust Interna-tional, 19944. 19865. .. - 2(7) - 19966. .. . 19907. .. . , - 20008. .. . , 20009. .. . - . . - -. 199910. .. . , 200011. .. . -: - , 200012. .. . , 200013. . ,, - ., -, 199414. .. 1 1985,4315. .. . .10-21 - 199416. . , 2003. 271 272. , , - , - . , , , " " : " " ( : , , ), " ", " ", - ( - "-" ). - - , - , . ,, " ", - , . , - . - , - : 1. , "-" -, , . : - (), (-) . - (.1), - - , -. , -272 273. : , -, - . - - . 2. , , - . 1. - - - : , - - , . , - "", " ". "-" , - : ,, ..., - , . , , , - (d), - :273 274. 0 1 1 11 d = 2 d = 2 (1 02 ) = , (1) 2 1 02 - " ", " " .., - - . , , , - , . () () : = 0 == , (2) - / ==1. - , , .3. , . , , (:" "). , , , () - () , , , , 1020 (.. " "). ;, 2=16, , 274 275. , 28 . , (), (q) - () : 28/1020=28*10-20= (2=16) / 1020=1610-20=q, (3) () - :11 = d = 28 10 20 = 14 10 20 . (4)0 2 , - - - :7q=8=4=11210-20 , (5) "", 7/4 :7 28 10 20 .(6)4 16 10 20 q 4. , , -, , , - . - , , - , 1040 . - 275 276. , , , . -. "" . : - . , , - , ( -), , , , - (.1), 1020 . , -, (.1) 1 , , ( ). 281040 =1 161020 =2 161020 =3 K1/ = 1040K2/ = 1040 K3/ = 1040 1=28104022=281040 7/4 =281040 K1 + 2 K 2 56 10 40 7 = 20 = 10 60 . q 16 10 2 , , , - -, - 7/2 (.1). 5. . -276 277. . : , , - , 56 - ( ). - , , (.2). 2 ()-2/3 1 = 1/2 1/3 - - 2 = 2 3 = 1 1020 c= =0 4 = 1 - : :: - 5 = 7/4 28102016.1020 6 = 7/4 - , , q."" : - , - (-, , ) , - (, - , , .2). - , . - , 277 278. - (.2);, ,K = r/q : :(7) "" + 2 = 2 2q. : 1( + 2 ) / d = (2810-20)2 = 11210-20, (8) 0 :7q() = (8 = 4) - = 11210-20,(9) : 7 q = 8 = 4 = 112 10 20 V == 64 = 82 , (10) /q = 7/4 (7q=8=4=11210-20)(/q=7/4) = 287 = 472. , , - ( ) - - -, " " -. 6. , - , : , , . - . , () , , , - 278 279. . , . - , . . , , , 1012, /( = 8 2=16 , 1 1( d = ). 0 2 - :1012 8 16 1 / 2 = 512 212 2 3 2 4 2 1 = 512 218 , (11) 18 12 - , - 5 2. - - - :log x 512 218 = log 5 512 + log 2 218 = 12 1 + 18 1 = 30 , (12) (12) : - (12) (11) - , - 30 (12).279 280. - , - :" , , , - !" - , - ,, , . , , ! 280 281. ...................................1 - ......................1 - .........6 , , , ...............................................13 . .............................................19 .................25 ............................................................37 ................................................64 .........................................................82 , , ..............................................................85 .......................................................................100 .............................................................159 .......................................................................................167................................................................................168 I. , , ..........................................168 II. ................170 III. , ......................175 IV. ..........................................182 V. - ..............................................................................................187 VI. ........................................194 VII. "" , ..........................203 VIII. - . ....210 .......................................................................................226 .........................................................227I. ......................................................227II. . . ............................................................ 231III. . ..................................................238IV. ........................................................247V. . .................................................................... 261 ........................................................................................271 .................................................272281