? ???????????? ???????: II11. ???? ? ??? ???? ????????
??????? ?????????? ?? ????? (? ??????? ??????????
????? ????????? ????? ??????? ??????? ??????), ?? ???-
?????????, ??? ????? ??? ?????? 280 ??????????. ???????-
?????????????, ??? ????????? ????? 1111 ? 250 ????????? ???.
114.???????? ?????? ??????? ????? ???????????????
??????? ????????? ???????, ? ??????:
1 337 174 : 943 = 1418;
1 343 784 : 949 = 1416;
1 200 474 : 846 = 1419;
1 202 464 : 848 = 1418.
115.???? ?????? ???????? ?????? ?????? ??????
???????:
7 375 428 413 : 125 473 = 58 781.
??? ?????????, ?????? ???????? ?????? ???? ???????
???????????? ? ???????????? ????????: «??????????????
??????», 1920 ?. ? «???????? ???», 1906 ?.
116.? ?????????? ????? ?????? ????? ?????????? ???-
???????????. ?????? ?????? ??????????? ???? ? ????? ???-
1 ?; ?????
????????????? ??????????? ?????????? ??????
1000 ?, ??????? ??
?? ?????????? ?. ?. 1 ??: ?????????
????? ????????. ???????? ??????????????: ????? ?????-
1000 ??.
117.?????
?????????? ?? ??...
??????? ?????? ??????. ? ????????? ?????????? ????-
X ??????. ??????
?????????? ??????????? ?????? X ??????
?????? ????????????? ???????, ???????????? ???? ??
??????, ???? ????? ? 1000 1? = ??. ? ??? ??? ? ??? ????-
??????? ??? ? ?????? ??? ??????, ?? ? ?????????? 1000 ??.
118.?? ???. 100 ?????, ??? (?????????? ????????? ?????
1 ?2) ???????? ??????? ???????? ??? ????????? ? ???????-
??????????????? ???????? ???????????, ??? ?????????? ????-
????????? ? ?????
???????? ?? ????????? ? ??????? ??????.
????????? ?????? ? ??????
??????, ?????? ???????? ???
????? ?, ????? ?????????:
12 000:8 = ?:0,12,
?????? ?= 180 ?.
????????
119.???? 89,4 ? ?? ???????, ?. ?. ?? ??????
?????.
150
???. 101.
???. 102.
???. 100. ???. 103.
???????? ? ??? ??????: 89,4 ? X 1000 — 89,4 ??,
? ??????
?????? ??? ????????? ??? ?????? ??????. ?????:
89,4 ?? X 1000 = 89,4 ?????, ?????? ??? ????? ? ??????
??? ?????? ??????????.
????, ??????? ??? — 89,4 ?????.
120.???? ????? ?? ???????? ?? ? ?? ? ????? ?????-
????????? 70. (??????????????? ??????? ???? ?????? ????????
? ??????? ?????? ??????????, ??????????????? ? ??????
???????.)
121.??? ??? ????? ???? ?????, ???????????? ?? ??-
??????????, ????? 78, ?? ????? ??????? ?? ????? ????????
?????? ?????????? ?????? 78 : 6, ?. ?. 13. ??? ?????????
????????? ???????, ??????? ???????? ?? ???. 101.
1221— 23. ??????? ???????? ?? ???????????
???. 102 ? 103.
124.????????? ???? ?????? ????? ???????? ???? ???-
??????? ????? ???? ?????, ?????? ??? ????? ?????? ???
????? ???????????? ????? ????????? ????????? ? ???-
?????? ?????? ????; ? ???? ??????? ????, ??? ????????? ????
? ??
?? ????????. ??? ??????, ??? ????? ??????????????,
???
??????????.
??? ?????? ??? ?????? ???????????? ?????????
??????????? ???????????? ? ??????????????? ?????????.
????????? ???? ?? ??????? ?? ????????? ??????????;
??
????????, ???????? ????? ?????? ??? ??????????
? ???, ?????
????????? ?? ????????.
125.??
?????? ?????? ????? ????????, ???? ??????-
??????????, ????? ????? ?????????? ???????. ??????? ? ?????
????????,
?????? (???. 96) ??????????, 7 ???. ??????,
????? ??????? ???? ??????? ????????? ???? ? ?* ??????
??????????. ???? ??? ??????????
? ?????????
??????? ? ?????? ?????? ??????????, ??? ????????
??????????,
9 ?. 30 ?. ???? ????? ?? ??????? ????????
372 ??????????? ???? ?????? ?????????? ??? ?
—, .
? ????????? ???? ??? ??????????
^360° ? =
152
126. ???????? ???? ????????
? 175
????? ?? ? ????????? ??????
????? R, ?????:
2??,14?(? + 175)-2??,14?
?/?-2??,14?175 = 1100 ??,
?. ?. ????? 11 ?. ??????????-
?? ????? ??, ??? ????????? ??-*
???????? ?? ??????? ?? ??-*
????? ???? ?, ?????????????,• •• ••
???????? ?? ??????????????. 104.
?????? ? ????????? ??????.
??????
127.?????????? ????? ?????????????, ????
? ????? ????????
?????????? ????? ??????????????, ???
?? ???. 104.
128.????????, ????????? ? ?????????????? ??????
?????????? ?????, ??????, ????????, ? ????????????
??? ??????
?????? ???????????? ?????? ?????????????.
?????????? ? ???????????? ??????? ?????? ????, ?? —
?????? ?????? — ?????? ?????????? ? ?????????????
?????? ? ???????, ???????????? ????? ?????? ?????-
??????????.
????? ???, ??????, ??????????, ????? ???? ??????
?????????????? ???????????, ???? ??????????????? ?????
?????????? ?????????? ????????????? ??????????? ???-
???????. ?????????, ??????? ? ???? ? ????, ??????, ???
????? ???????? ??????????, ??????????? ?? ???????,
????? ?????????, ???????????? ?? ?????????? (???. 105).
????????? ??????? ???????? ?? ?????? ??????? (???. 106),
?????, ??? ??? ?????????????? ??????? ?????? ???????-
??????????? ???????????? *). ???? ??????????? ????? ?????-
??????????????, ?? ?????? ??????? ? ??????????? ?????
??????????? ???????? ????? ???????????? (???. 107).
?????? ???????, ??? ????? ????????????? ????? ????-
????????? ?????????????? ????????????? ???????????, ???-
??????? ???????? ????? ??????? ?????. ????????-
? ??? ???
?????????????? ????????????? (???. 108), ??
??????????? ???????????? ? ????????????
???????
? ???? ??? ???????? ????? ?????????????? ???????????
???????? ???????????? ?????????.
*) ????????? ??? ???????? ? ????????? ??? ????????? «???????
153
? ???????????? ????????».
???. 105. ???. 106. ???. 107.
1%
? /?
???. 108. ???. 109.
???????? ?????? ?????????? ???? ??????? ? ???????-
???????????? ?????? ???????? ?????? (????????????, ???
????????, ?? ???? ?????????? ???? ? ????? ?????? ????-
?????????).
?????????? ????????? ???????? ?????????? ?????? ??-
?? ???
??????????; ??? ???????? ?? ???. 109 ? 110; ???
?????????? ???????? ? ????, ??? ????????? ???????
???????? ? ?????????? ??????????????? ??????.
??????
?????????: ?????????? ? ???????????? ?????
????? ?????? ????? ?????? ?????, ??????? ??????????
?? ???? ??? ???????????: ????????? ????????? ? ????-
?????????? ???????? ?????????? ?????????????? ????????
??????? *).
????, ??? ??? ?????????? ??????, ?????????????
?????. ????? ? ? ? ????? (???. 111) ????????? ??????;
*) ??? ?????? ????, ??????? ?? ????? ?? ????, ????? ???????-
????????? ???? ?????: ??? ???????? ???? — ??????????????, ??????????
?? — ??????????. ????????? ????? ?????????? ??????
???? ???????, ????????? ??? ?? ??? ???????????.
154
Jill
???. 110.
? ???????? ? ???? ?????? ??????????? ????????????? ?
??????????? ?? = ? ?. ?????????????? ???????????
? ?? ????'????? ?? ???????? OADC, ??????? ??????-
?????????? ? ????? ????? ?? ????????, ????????? ?? ???. 109
? 110.
129.????????? ?????????????? ??????????? ?? ?????-
????????? ??????: ??? ????? ????????? ????? ??????????? ???-
?????
??????????. ? ????? ????, ?????????? ????? ?? ?????
??? 27, ?? ??????? ???? ????????? ??????? ???,
????? ??????, ? ??????? ??????????? ????????? ??
????? ??????? ????? ???? ?????? ????? ??????????? ??-
??????, ??? ?? ?? ?? ???????????? ?????.
130.??????? ?????????, ?????? ????? ???? ???????-
???? ??????,
?????????? ????? ????????. ???? ?? ??????? ??
????? ??????????? ?? ??? ?????. ????????? ????????,
???? ?? ???????? ??? ?? ???, ?? ??????? 4 ?????. ????
?? ?????????? ?? ???, ??? ?????? ?????? ????????? ??
???, ?? ????? ?????? ????? ????????, ? ????? ????????
?????
??????? ?? ??????? 8 ??????. ?????????? ???????
16 ??????
?? ??????? ????? ??????? (???? ?????? ????-
????????? ??? ???????????? ????? ?????), ????? ?????? —
32 ?????. ?????? ????? ???? ???????? ?? ????? ??? ??
?????? ???????? 64 ????????? ??????????. ? ???? ?????
??????? ???????, ????? ????? ?????? ????? ????????,
?? ????? ???????????? ???????? 64 ????????? ??????-
??????????. ?????? ????? ??? ?????? ????????? ???????? ??-
??????????.
?? ?????? ???? ??? ????????, ??? ????? ????????
???????????
????? ? ???????????????? ???, ????? ??????
??
??? ????? ?????? ??????????? ?????????? ??????????
155
HI
????? ???????-
???????
???????
???. 112.
2?=64 ????????? ??????????. ??? ??? ???????? ???????:
???? ?????? ???????, ????? ????? ??????? ??????? ???
????? ??????????? ??????? ? ????? ?????? ???-
????????? ?????? ???????? ?????? ?? ?????? ???????. ??
???. 112 ???????? ?????? ??? ???????.
??????????
????? ??????. ??????? ? ?????????????
1.????? ?? ??????8
2.? ????? ?????5
3.?????? ???????? ????????
4.??? ???????6
5.??? ? ????7
6.??????????????? ??????7
7.????? ?????????8
8.????8
9.?????? ?? ????????9
10.???????? ????9
11.?????? ? ??????? ... . . .10
....11
12.?????????????? ?????10
...20
??????? ??????????? 1—12 ....
13.??????????? ????? ......19
14.???????? ?????, ?????? ?? ?????????
15.??? ??? ?????21
????? ??????. ?????????? ? ?????
??????24
16.???? ?? 28 ??????24
17.?????? ? ????? ????24
18.????? ? ??????24
19.?????24
20.???? ?????????24
21.?????????? ???????? ?? ??????25
22.?????????? ?? ??????26
???? ? 15, ??? ?????26
23.?????? ?????? ?????32
24.?????? ?????? ?????32
25.?????? ?????? ?????32
??????32
26.?????? ?????? ??? ????????????32
27.??? ? ???????33
28.?????? ?????? ??? ???????????33
29.?????? ????????? ??? ???????????? ...33
30.???????????? ????????? ,33
??????? ??????????? 163— 033
157
????? ??????. ??? ?????? ???????????
31.????????? . ...41
32.????? ? ????????.41 42
43
33.????????????? ??????42 43
43
34.?????????? ????? 42
.44
35.?????? ??????42
44
36.???? ???????42
37.????????? ???????42
??? ????????
??. ???????
???? ,. . . .
,.. .
40.????? ????????
41.????????????? ????????
42.??????? ,
??????? ??????????? 31—42,
????? ?????????. ?????? ?? ?? ????????
43.?????? ?? ?? ????????50
44.?????
??????? ??????? ? ?????, 62
????? ?????. ???????? ??????????? 56
56
45.?? ???? ?????? — ???55 56
56
46.??????55 56
56
47.???????? ?????? 57
57
48.???????? 57
58
49.??????????? ?????
63
50.????? ?????? .. .
71
51.??? ??????? .... 76
( 79
52.??????? ?? 11 ...
??? 108
53.???????? ?????? ?????????
54.???????? ???????????.,
55.??? ???????? ???????????«57
50. ?????????? ??????i
??????? ??????????? 45—56i
????? ??????. ????????????? ?????????
57.??????? , ,,
58.???
????????? ????????67
????? ???????. ???????? ? ??????-?????????
59.???????? ??????,
60.????????? ?????(
61.?????? ??????? ??????????? ....
62.???????,82
63.??????? ? ????????? ?????87
64.??????? ???????????91
65.?????????? ???? 96
66.?????????????? ?????100
67.????104
68.???????? ???????? ?????? ? ??????
158
????? ???????. ??? ?????? ???????
69.????????? ???? ??????112
?????????
70.?????
??? ?????? ?????114
71.?????????
????? ???????. ?????????????? ???????????
72.??????116
73.? ?????????????? ??????116
74.????????? ???????116
75.????? ??????117
76.?????? ???? , .118
77.?? 12 ??????118
78.?? 8 ?????? , ,118
79.???? ???? 118
80.????? ???????119
81.?????? ???????119
82.?????? ???????119
83.??????? ?????119
84.?????? ????? ..... . ... 119
120
85.???????? ??????119
142
86.???? ?????????120 159
87.????????120
88.??????? ? ??????120
89.??? ??????120
90.??? ????120
91.?????
92.?????? ????? ??????120
93.??? ????????120
94.?? ??????121
???????
??????????? 729— 4 121
????? ???????. ????????? ????? ? ?????
95.????????131
96.??????? ??????133
97.??????? ??????134
????? ????????????. ?????????? ? ????????
? ??????
98.???????? ? ?????? 137
99.??? ?? ???? ??????138
100.???????? ?? ???? ??????? 139
????? ???????????. ???????? ?????? ?????
101.????141
102.????? ? ????141
103.????, ????? ? ??????141
104.??????? ? ?????? ????141
105.???????142
106.???????? ???????142
107.??? ?????
108.????? ???????142
109.???????142
110.????? ?????????142
111.??????? ???????142
112.????????
?????????142
??. ???????? ????????? . .... 142
114.?????????? ??????? .
115.??? ?????? ???????143 142
116.??? ??????????143 144
117.? ??? ?? ????143
118.???????143
119.??????? ???????143
120.????? ?????'143
121.?????????143 144
122.?????????????? ??????
123.???????? ??????
124.????????? ????144
125.????? ?????145
126.?? ????????145
127.? ????? ?????145
128.????? ? ?????????145
129.?????? ????145
130.??? ??????146
??????? ??????????? 101—130146
The words you are searching are inside this book. To get more targeted content, please make full-text search by clicking here.
13-Перельман Я.И. Живая математика
Discover the best professional documents and content resources in AnyFlip Document Base.
Search