Читаем онлайн «Бог создал целые числа»
- 123 . . . последняя (13) »
БОГ СОЗДАЛ
ЦЕЛЫЕ ЧИСЛА
МАТЕМАТИЧЕСКИЕ ОТКРЫТИЯ,
ИЗМЕНИВШИЕ ИСТОРИЮ
ИЗДАТЕЛЬСТВО АСТ
МОСКВА
ɍȾɄ
ȻȻɄ
51(091)
ɝ
ɏ
ɉɟɪɟɜɨɞɨɪɢɝɢɧɚɥɶɧɨɝɨɢɡɞɚɧɢɹ
Stephen Hawking
GOD CREATED THE INTEGERS
The Mathematical Breakthroughs that Changed History
ɉɟɱɚɬɚɟɬɫɹɫɪɚɡɪɟɲɟɧɢɹɢɡɞɚɬɟɥɶɫɬɜɚ5XQQLQJ3UHVV$GXOW
DQLPSULQWRI3HUVHXV%RRNV//&DVXEVLGLDU\RI+DFKHWWH%RRNV1HZɤɨɬɨɪɚɹ ɧɚɡɵɜɚɟɬɫɹ ɨɤɪɭɠɧɨɫɬɶɸ@ ɧɚ ɤɨɬɨɪɭɸ ɜɫɟ
ɢɡ ɨɞɧɨɣ ɬɨɱɤɢ ɜɧɭɬɪɢ ɮɢɝɭɪɵ ɩɚɞɚɸɳɢɟ >ɧɚ ɨɤɪɭɠɧɨɫɬɶ
ɤɪɭɝɚ@ɩɪɹɦɵɟɪɚɜɧɵɦɟɠɞɭɫɨɛɨɣ
ɐɟɧɬɪɨɦɠɟɤɪɭɝɚɧɚɡɵɜɚɟɬɫɹɷɬɚɬɨɱɤɚ
Ⱦɢɚɦɟɬɪ ɠɟ ɤɪɭɝɚ ɟɫɬɶ ɤɚɤɚɹ ɭɝɨɞɧɨ ɩɪɹɦɚɹ ɩɪɨɜɟɞɟɧɧɚɹ
ɱɟɪɟɡɰɟɧɬɪɢɨɝɪɚɧɢɱɢɜɚɟɦɚɹɫɨɛɟɢɯɫɬɨɪɨɧɨɤɪɭɠɧɨɫɬɶɸ
ɤɪɭɝɚɨɧɚɠɟɢɪɚɫɫɟɤɚɟɬɤɪɭɝɩɨɩɨɥɚɦ
ɉɨɥɭɤɪɭɝɠɟɟɫɬɶɮɢɝɭɪɚɫɨɞɟɪɠɚɳɚɹɫɹɦɟɠɞɭɞɢɚɦɟɬɪɨɦ
ɢɨɬɫɟɤɚɟɦɨɣɢɦ ɱɚɫɬɶɸ!ɨɤɪɭɠɧɨɫɬɢɐɟɧɬɪɠɟɩɨɥɭɤɪɭɝɚ ± ɬɨɠɟɫɚɦɨɟɱɬɨɢɭɤɪɭɝɚ
1.
2.
22
ȻɈȽɋɈɁȾȺɅɐȿɅɕȿɑɂɋɅȺ
19. ɉɪɹɦɨɥɢɧɟɣɧɵɟɮɢɝɭɪɵɫɭɬɶɬɟɤɨɬɨɪɵɟɫɨɞɟɪɠɚɬɫɹɦɟɠɞɭ ɩɪɹɦɵɦɢ ɬɪɟɯɫɬɨɪɨɧɧɢɟ ± ɦɟɠɞɭ ɬɪɟɦɹ ɱɟɬɵɪɟɯɫɬɨɪɨɧɧɢɟɠɟ ± ɱɟɬɵɪɶɦɹɦɧɨɝɨɫɬɨɪɨɧɧɢɟɠɟ ± ɤɨɬɨɪɵɟɫɨɞɟɪɠɚɬɫɹɦɟɠɞɭɛɨɥɟɟɱɟɦɱɟɬɵɪɶɦɹɩɪɹɦɵɦɢ
ɂɡ ɬɪɟɯɫɬɨɪɨɧɧɢɯ ɮɢɝɭɪ ɪɚɜɧɨɫɬɨɪɨɧɧɢɣ ɬɪɟɭɝɨɥɶɧɢɤ
ɟɫɬɶ ɮɢɝɭɪɚ ɢɦɟɸɳɚɹ ɬɪɢ ɪɚɜɧɵɟ ɫɬɨɪɨɧɵ ɪɚɜɧɨɛɟɞɪɟɧɧɵɣɠɟ ± ɢɦɟɸɳɚɹɬɨɥɶɤɨɞɜɟɪɚɜɧɵɟɫɬɨɪɨɧɵɪɚɡɧɨɫɬɨɪɨɧɧɢɣɠɟ ± ɢɦɟɸɳɚɹɬɪɢɧɟɪɚɜɧɵɟɫɬɨɪɨɧɵ
Ʉɪɨɦɟ ɬɨɝɨ ɢɡ ɬɪɟɯɫɬɨɪɨɧɧɢɯ ɮɢɝɭɪ ɩɪɹɦɨɭɝɨɥɶɧɵɣ ɬɪɟɭɝɨɥɶɧɢɤ ɟɫɬɶ ɢɦɟɸɳɢɣ ɩɪɹɦɨɣ ɭɝɨɥ ɬɭɩɨɭɝɨɥɶɧɵɣ
ɠɟ ± ɢɦɟɸɳɢɣɬɭɩɨɣɭɝɨɥɚɨɫɬɪɨɭɝɨɥɶɧɵɣ ± ɢɦɟɸɳɢɣɬɪɢ
ɨɫɬɪɵɯɭɝɥɚ
ɂɡɱɟɬɵɪɟɯɫɬɨɪɨɧɧɢɯɮɢɝɭɪɤɜɚɞɪɚɬɟɫɬɶɬɚɤɨɬɨɪɚɹɢɪɚɜɧɨɫɬɨɪɨɧɧɹɹ ɢ ɩɪɹɦɨɭɝɨɥɶɧɚɹ ɪɚɡɧɨɫɬɨɪɨɧɧɢɤ ɠɟ ± ɩɪɹɦɨɭɝɨɥɶɧɚɹ ɧɨ ɧɟ ɪɚɜɧɨɫɬɨɪɨɧɧɹɹ ɪɨɦɛ ± ɪɚɜɧɨɫɬɨɪɨɧɧɹɹ
ɧɨɧɟɩɪɹɦɨɭɝɨɥɶɧɚɹɪɨɦɛɨɢɞ ɩɚɪɚɥɥɟɥɨɝɪɚɦɦ ± ɢɦɟɸɳɚɹ
ɩɪɨɬɢɜɨɩɨɥɨɠɧɵɟ ɫɬɨɪɨɧɵ ɢ ɭɝɥɵ ɪɚɜɧɵɟ ɦɟɠɞɭ ɫɨɛɨɣ
ɧɨ ɧɟ ɹɜɥɹɸɳɚɹɫɹ ɧɢ ɪɚɜɧɨɫɬɨɪɨɧɧɟɣ ɧɢ ɩɪɹɦɨɭɝɨɥɶɧɨɣ
Ɉɫɬɚɥɶɧɵɟ ɠɟ ɱɟɬɵɪɟɯɫɬɨɪɨɧɧɢɤɢ ɛɭɞɟɦ ɧɚɡɵɜɚɬɶ ɬɪɚɩɟ
ɰɢɹɦɢ.
ɉɚɪɚɥɥɟɥɶɧɵɟ ɫɭɬɶ ɩɪɹɦɵɟ ɤɨɬɨɪɵɟ ɧɚɯɨɞɹɫɶ ɜ ɨɞɧɨɣ
ɩɥɨɫɤɨɫɬɢɢɛɭɞɭɱɢɩɪɨɞɨɥɠɟɧɵɜɨɛɟɫɬɨɪɨɧɵɧɟɨɝɪɚɧɢɱɟɧɧɨɧɢɫɬɨɣɧɢɫɞɪɭɝɨɣ©ɫɬɨɪɨɧɵªɦɟɠɞɭɫɨɛɨɣɧɟɜɫɬɪɟɱɚɸɬɫɹ
ɉɈɋɌɍɅȺɌɕ
Ⱦɨɩɭɫɬɢɦ
ɑɬɨɨɬɜɫɹɤɨɣɬɨɱɤɢɞɨɜɫɹɤɨɣɬɨɱɤɢ ɦɨɠɧɨ!ɩɪɨɜɟɫɬɢɩɪɹɦɭɸɥɢɧɢɸ
ɂɱɬɨɨɝɪɚɧɢɱɟɧɧɭɸɩɪɹɦɭɸ ɦɨɠɧɨ!ɧɟɩɪɟɪɵɜɧɨɩɪɨɞɨɥɠɚɬɶɩɨɩɪɹɦɨɣ
ɂɱɬɨɢɡɜɫɹɤɨɝɨɰɟɧɬɪɚɢɜɫɹɤɢɦɪɚɫɬɜɨɪɨɦ ɦɨɠɟɬɛɵɬɶ!
ɨɩɢɫɚɧɤɪɭɝ
Ⱥɤɫ ɂɱɬɨɜɫɟɩɪɹɦɵɟɭɝɥɵɪɚɜɧɵɦɟɠɞɭɫɨɛɨɣ
Ⱥɤɫ ɂɟɫɥɢɩɪɹɦɚɹɩɚɞɚɸɳɚɹɧɚɞɜɟɩɪɹɦɵɟɨɛɪɚɡɭɟɬ
ɜɧɭɬɪɟɧɧɢɟɢɩɨɨɞɧɭɫɬɨɪɨɧɭɭɝɥɵɦɟɧɶɲɢɟɞɜɭɯɩɪɹɦɵɯ
ɬɨɩɪɨɞɨɥɠɟɧɧɵɟɷɬɢɞɜɟɩɪɹɦɵɟɧɟɨɝɪɚɧɢɱɟɧɧɨɜɫɬɪɟɬɹɬɫɹ
ɫɬɨɣɫɬɨɪɨɧɵɝɞɟɭɝɥɵɦɟɧɶɲɢɟɞɜɭɯɩɪɹɦɵɯ
ȿȼɄɅɂȾ
ɈȻɓɂȿɉɈɇəɌɂə
Ⱥɤɫɢɨɦɵ
Ɋɚɜɧɵɟɨɞɧɨɦɭɢɬɨɦɭɠɟɪɚɜɧɵɢɦɟɠɞɭɫɨɛɨɣ
ɂɟɫɥɢɤɪɚɜɧɵɦɩɪɢɛɚɜɥɹɸɬɫɹɪɚɜɧɵɟɬɨɢɰɟɥɵɟɛɭɞɭɬɪɚɜɧɵ
ɂɟɫɥɢɨɬɪɚɜɧɵɯɨɬɧɢɦɚɸɬɫɹɪɚɜɧɵɟɬɨɨɫɬɚɬɤɢɛɭɞɭɬɪɚɜɧɵ
>ɂɟɫɥɢɤɧɟɪɚɜɧɵɦɩɪɢɛɚɜɥɹɸɬɫɹɪɚɜɧɵɟɬɨɰɟɥɵɟɛɭɞɭɬɧɟ
ɪɚɜɧɵ
ɂɭɞɜɨɟɧɧɵɟɨɞɧɨɝɨɢɬɨɝɨɠɟɪɚɜɧɵɦɟɠɞɭɫɨɛɨɣ
ɂɩɨɥɨɜɢɧɵɨɞɧɨɝɨɢɬɨɝɨɠɟɪɚɜɧɵɦɟɠɞɭɫɨɛɨɣ@
ɂɫɨɜɦɟɳɚɸɳɢɟɫɹɞɪɭɝɫɞɪɭɝɨɦɪɚɜɧɵɦɟɠɞɭɫɨɛɨɣ
ɂɰɟɥɨɟɛɨɥɶɲɟɱɚɫɬɢ
> ɂɞɜɟɩɪɹɦɵɟɧɟɫɨɞɟɪɠɚɬɩɪɨɫɬɪɚɧɫɬɜɚ@
ɉɪɟɞɥɨɠɟɧɢɟ
ȼɩɪɹɦɨɭɝɨɥɶɧɵɯɬɪɟɭɝɨɥɶɧɢɤɚɯɤɜɚɞɪɚɬɧɚɫɬɨɪɨɧɟɫɬɹɝɢɜɚɸ
ɳɟɣɩɪɹɦɨɣɭɝɨɥɪɚɜɟɧ ɜɦɟɫɬɟɜɡɹɬɵɦ!ɤɜɚɞɪɚɬɚɦɧɚɫɬɨɪɨɧɚɯ
ɡɚɤɥɸɱɚɸɳɢɯɩɪɹɦɨɣɭɝɨɥ
ɉɭɫɬɶABC ± ɩɪɹɦɨɭɝɨɥɶɧɵɣɬɪɟɭɝɨɥɶɧɢɤɢɦɟɸɳɢɣɩɪɹɦɨɣɭɝɨɥ
BAC ɹɭɬɜɟɪɠɞɚɸɱɬɨɤɜɚɞɪɚɬɧɚBCɪɚɜɟɧ ɜɦɟɫɬɟɜɡɹɬɵɦ!ɤɜɚɞɪɚɬɚɦɧɚBAɢAC ɱɟɪɬɟɠ
G
H
K
A
F
C
B
D
L
ɑɟɪɬɟɠ
E
ȻɈȽɋɈɁȾȺɅɐȿɅɕȿɑɂɋɅȺ
Ⱦɟɣɫɬɜɢɬɟɥɶɧɨ ɧɚɞɫɬɪɨɢɦ ɧɚ BC ɤɜɚɞɪɚɬ BDEC ɚ ɧɚ BA AC
ɧɚɞɫɬɪɨɢɦ ɤɜɚɞɪɚɬɵ!HBGC ɩɪɟɞɥɨɠɟɧɢɟ ɢɱɟɪɟɡAɩɪɨɜɟɞɟɦALɩɚɪɚɥɥɟɥɶɧɭɸɤɚɤBDɬɚɤɢCE ɩɪɟɞɥɨɠɟɧɢɟ ɫɨɟɞɢɧɢɦ
AD FC ɂ ɩɨɫɤɨɥɶɤɭ ɤɚɠɞɵɣ ɢɡ ɭɝɥɨɜ BAC BAH ɩɪɹɦɨɣ ɨɩɪɟɞɟɥɟɧɢɟ ɬɨɜɨɬɧɚɧɟɤɨɬɨɪɨɣɩɪɹɦɨɣBAɩɪɢɟɟɬɨɱɤɟAɞɜɟɩɪɹɦɵɟACAHɪɚɫɩɨɥɨɠɟɧɧɵɟɧɟɩɨɨɞɧɭɫɬɨɪɨɧɭɨɛɪɚɡɭɸɬɫɦɟɠɧɵɟ
ɭɝɥɵ ɜɦɟɫɬɟ!ɪɚɜɧɵɟɞɜɭɦɩɪɹɦɵɦ ɡɧɚɱɢɬCAɛɭɞɟɬɩɨ ɨɞɧɨɣ!
ɩɪɹɦɨɣɫAH ɩɪɟɞɥɨɠɟɧɢɟ ȼɫɥɟɞɫɬɜɢɟɬɨɝɨɠɟɜɨɬɢBAɛɭɞɟɬ
ɩɨɨɞɧɨɣɩɪɹɦɨɣɫAGɂɩɨɫɤɨɥɶɤɭɭɝɨɥDBCɪɚɜɟɧɭɝɥɭFBA ɚɤɫɢɨɦɚ ɢɛɨɤɚɠɞɵɣɢɡɧɢɯɩɪɹɦɨɣɬɨɩɪɢɛɚɜɢɦɨɛɳɢɣɭɝɨɥABC
ɡɧɚɱɢɬɜɟɫɶɭɝɨɥDBAɪɚɜɟɧɜɫɟɦɭFBC ɚɤɫɢɨɦɚ ɂɩɨɫɤɨɥɶɤɭDB
ɪɚɜɧɚBCɚFBɪɚɜɧɚBA ɨɩɪɟɞɟɥɟɧɢɟ ɬɨɜɨɬɞɜɟɫɬɨɪɨɧɵDB
BAɪɚɜɧɵɞɜɭɦɫɬɨɪɨɧɚɦBCFBɤɚɠɞɚɹɤɚɠɞɨɣ ɢɭɝɨɥDBAɪɚɜɟɧ
ɭɝɥɭFBC ɡɧɚɱɢɬɢɨɫɧɨɜɚɧɢɟ ɩɪɟɞɥɨɠɟɧɢɟ ADɪɚɜɧɨɨɫɧɨɜɚɧɢɸ
FC ɢ ɬɪɟɭɝɨɥɶɧɢɤ ABD ɪɚɜɟɧ ɬɪɟɭɝɨɥɶɧɢɤɭ FBC ɩɪɟɞɥɨɠɟɧɢɟ
ɂɭɞɜɨɟɧɧɵɣɬɪɟɭɝɨɥɶɧɢɤABDɟɫɬɶɩɚɪɚɥɥɟɥɨɝɪɚɦɦBL ɩɪɟɞɥɨɠɟɧɢɟ ɢɛɨɨɧɢɢɦɟɸɬɬɨɠɟɨɫɧɨɜɚɧɢɟBDɢɪɚɫɩɨɥɨɠɟɧɵɦɟɠɞɭ
ɬɟɦɢ ɠɟ ɩɚɪɚɥɥɟɥɶɧɵɦɢ BD AL ɩɪɟɞɥɨɠɟɧɢɟ ɍɞɜɨɟɧɧɵɣ ɠɟ
ɬɪɟɭɝɨɥɶɧɢɤFBC ɩɪɟɞɥɨɠɟɧɢɟ ɟɫɬɶɤɜɚɞɪɚɬHB ɢɛɨɨɧɢɢɦɟɸɬ
ɬɨɠɟɨɫɧɨɜɚɧɢɟFBɢɪɚɫɩɨɥɨɠɟɧɵɦɟɠɞɭɬɟɦɢɠɟɩɚɪɚɥɥɟɥɶɧɵɦɢ
FBɢHC >ɧɨɭɞɜɨɟɧɧɵɟɪɚɜɧɵɯɜɟɥɢɱɢɧɪɚɜɧɵɦɟɠɞɭɫɨɛɨɣ ɚɤɫɢɨ
ɦɚ
ЦЕЛЫЕ ЧИСЛА
МАТЕМАТИЧЕСКИЕ ОТКРЫТИЯ,
ИЗМЕНИВШИЕ ИСТОРИЮ
ИЗДАТЕЛЬСТВО АСТ
МОСКВА
ɍȾɄ
ȻȻɄ
51(091)
ɝ
ɏ
ɉɟɪɟɜɨɞɨɪɢɝɢɧɚɥɶɧɨɝɨɢɡɞɚɧɢɹ
Stephen Hawking
GOD CREATED THE INTEGERS
The Mathematical Breakthroughs that Changed History
ɉɟɱɚɬɚɟɬɫɹɫɪɚɡɪɟɲɟɧɢɹɢɡɞɚɬɟɥɶɫɬɜɚ5XQQLQJ3UHVV$GXOW
DQLPSULQWRI3HUVHXV%RRNV//&DVXEVLGLDU\RI+DFKHWWH%RRNV1HZɤɨɬɨɪɚɹ ɧɚɡɵɜɚɟɬɫɹ ɨɤɪɭɠɧɨɫɬɶɸ@ ɧɚ ɤɨɬɨɪɭɸ ɜɫɟ
ɢɡ ɨɞɧɨɣ ɬɨɱɤɢ ɜɧɭɬɪɢ ɮɢɝɭɪɵ ɩɚɞɚɸɳɢɟ >ɧɚ ɨɤɪɭɠɧɨɫɬɶ
ɤɪɭɝɚ@ɩɪɹɦɵɟɪɚɜɧɵɦɟɠɞɭɫɨɛɨɣ
ɐɟɧɬɪɨɦɠɟɤɪɭɝɚɧɚɡɵɜɚɟɬɫɹɷɬɚɬɨɱɤɚ
Ⱦɢɚɦɟɬɪ ɠɟ ɤɪɭɝɚ ɟɫɬɶ ɤɚɤɚɹ ɭɝɨɞɧɨ ɩɪɹɦɚɹ ɩɪɨɜɟɞɟɧɧɚɹ
ɱɟɪɟɡɰɟɧɬɪɢɨɝɪɚɧɢɱɢɜɚɟɦɚɹɫɨɛɟɢɯɫɬɨɪɨɧɨɤɪɭɠɧɨɫɬɶɸ
ɤɪɭɝɚɨɧɚɠɟɢɪɚɫɫɟɤɚɟɬɤɪɭɝɩɨɩɨɥɚɦ
ɉɨɥɭɤɪɭɝɠɟɟɫɬɶɮɢɝɭɪɚɫɨɞɟɪɠɚɳɚɹɫɹɦɟɠɞɭɞɢɚɦɟɬɪɨɦ
ɢɨɬɫɟɤɚɟɦɨɣɢɦ ɱɚɫɬɶɸ!ɨɤɪɭɠɧɨɫɬɢɐɟɧɬɪɠɟɩɨɥɭɤɪɭɝɚ ± ɬɨɠɟɫɚɦɨɟɱɬɨɢɭɤɪɭɝɚ
1.
2.
22
ȻɈȽɋɈɁȾȺɅɐȿɅɕȿɑɂɋɅȺ
19. ɉɪɹɦɨɥɢɧɟɣɧɵɟɮɢɝɭɪɵɫɭɬɶɬɟɤɨɬɨɪɵɟɫɨɞɟɪɠɚɬɫɹɦɟɠɞɭ ɩɪɹɦɵɦɢ ɬɪɟɯɫɬɨɪɨɧɧɢɟ ± ɦɟɠɞɭ ɬɪɟɦɹ ɱɟɬɵɪɟɯɫɬɨɪɨɧɧɢɟɠɟ ± ɱɟɬɵɪɶɦɹɦɧɨɝɨɫɬɨɪɨɧɧɢɟɠɟ ± ɤɨɬɨɪɵɟɫɨɞɟɪɠɚɬɫɹɦɟɠɞɭɛɨɥɟɟɱɟɦɱɟɬɵɪɶɦɹɩɪɹɦɵɦɢ
ɂɡ ɬɪɟɯɫɬɨɪɨɧɧɢɯ ɮɢɝɭɪ ɪɚɜɧɨɫɬɨɪɨɧɧɢɣ ɬɪɟɭɝɨɥɶɧɢɤ
ɟɫɬɶ ɮɢɝɭɪɚ ɢɦɟɸɳɚɹ ɬɪɢ ɪɚɜɧɵɟ ɫɬɨɪɨɧɵ ɪɚɜɧɨɛɟɞɪɟɧɧɵɣɠɟ ± ɢɦɟɸɳɚɹɬɨɥɶɤɨɞɜɟɪɚɜɧɵɟɫɬɨɪɨɧɵɪɚɡɧɨɫɬɨɪɨɧɧɢɣɠɟ ± ɢɦɟɸɳɚɹɬɪɢɧɟɪɚɜɧɵɟɫɬɨɪɨɧɵ
Ʉɪɨɦɟ ɬɨɝɨ ɢɡ ɬɪɟɯɫɬɨɪɨɧɧɢɯ ɮɢɝɭɪ ɩɪɹɦɨɭɝɨɥɶɧɵɣ ɬɪɟɭɝɨɥɶɧɢɤ ɟɫɬɶ ɢɦɟɸɳɢɣ ɩɪɹɦɨɣ ɭɝɨɥ ɬɭɩɨɭɝɨɥɶɧɵɣ
ɠɟ ± ɢɦɟɸɳɢɣɬɭɩɨɣɭɝɨɥɚɨɫɬɪɨɭɝɨɥɶɧɵɣ ± ɢɦɟɸɳɢɣɬɪɢ
ɨɫɬɪɵɯɭɝɥɚ
ɂɡɱɟɬɵɪɟɯɫɬɨɪɨɧɧɢɯɮɢɝɭɪɤɜɚɞɪɚɬɟɫɬɶɬɚɤɨɬɨɪɚɹɢɪɚɜɧɨɫɬɨɪɨɧɧɹɹ ɢ ɩɪɹɦɨɭɝɨɥɶɧɚɹ ɪɚɡɧɨɫɬɨɪɨɧɧɢɤ ɠɟ ± ɩɪɹɦɨɭɝɨɥɶɧɚɹ ɧɨ ɧɟ ɪɚɜɧɨɫɬɨɪɨɧɧɹɹ ɪɨɦɛ ± ɪɚɜɧɨɫɬɨɪɨɧɧɹɹ
ɧɨɧɟɩɪɹɦɨɭɝɨɥɶɧɚɹɪɨɦɛɨɢɞ ɩɚɪɚɥɥɟɥɨɝɪɚɦɦ ± ɢɦɟɸɳɚɹ
ɩɪɨɬɢɜɨɩɨɥɨɠɧɵɟ ɫɬɨɪɨɧɵ ɢ ɭɝɥɵ ɪɚɜɧɵɟ ɦɟɠɞɭ ɫɨɛɨɣ
ɧɨ ɧɟ ɹɜɥɹɸɳɚɹɫɹ ɧɢ ɪɚɜɧɨɫɬɨɪɨɧɧɟɣ ɧɢ ɩɪɹɦɨɭɝɨɥɶɧɨɣ
Ɉɫɬɚɥɶɧɵɟ ɠɟ ɱɟɬɵɪɟɯɫɬɨɪɨɧɧɢɤɢ ɛɭɞɟɦ ɧɚɡɵɜɚɬɶ ɬɪɚɩɟ
ɰɢɹɦɢ.
ɉɚɪɚɥɥɟɥɶɧɵɟ ɫɭɬɶ ɩɪɹɦɵɟ ɤɨɬɨɪɵɟ ɧɚɯɨɞɹɫɶ ɜ ɨɞɧɨɣ
ɩɥɨɫɤɨɫɬɢɢɛɭɞɭɱɢɩɪɨɞɨɥɠɟɧɵɜɨɛɟɫɬɨɪɨɧɵɧɟɨɝɪɚɧɢɱɟɧɧɨɧɢɫɬɨɣɧɢɫɞɪɭɝɨɣ©ɫɬɨɪɨɧɵªɦɟɠɞɭɫɨɛɨɣɧɟɜɫɬɪɟɱɚɸɬɫɹ
ɉɈɋɌɍɅȺɌɕ
Ⱦɨɩɭɫɬɢɦ
ɑɬɨɨɬɜɫɹɤɨɣɬɨɱɤɢɞɨɜɫɹɤɨɣɬɨɱɤɢ ɦɨɠɧɨ!ɩɪɨɜɟɫɬɢɩɪɹɦɭɸɥɢɧɢɸ
ɂɱɬɨɨɝɪɚɧɢɱɟɧɧɭɸɩɪɹɦɭɸ ɦɨɠɧɨ!ɧɟɩɪɟɪɵɜɧɨɩɪɨɞɨɥɠɚɬɶɩɨɩɪɹɦɨɣ
ɂɱɬɨɢɡɜɫɹɤɨɝɨɰɟɧɬɪɚɢɜɫɹɤɢɦɪɚɫɬɜɨɪɨɦ ɦɨɠɟɬɛɵɬɶ!
ɨɩɢɫɚɧɤɪɭɝ
Ⱥɤɫ ɂɱɬɨɜɫɟɩɪɹɦɵɟɭɝɥɵɪɚɜɧɵɦɟɠɞɭɫɨɛɨɣ
Ⱥɤɫ ɂɟɫɥɢɩɪɹɦɚɹɩɚɞɚɸɳɚɹɧɚɞɜɟɩɪɹɦɵɟɨɛɪɚɡɭɟɬ
ɜɧɭɬɪɟɧɧɢɟɢɩɨɨɞɧɭɫɬɨɪɨɧɭɭɝɥɵɦɟɧɶɲɢɟɞɜɭɯɩɪɹɦɵɯ
ɬɨɩɪɨɞɨɥɠɟɧɧɵɟɷɬɢɞɜɟɩɪɹɦɵɟɧɟɨɝɪɚɧɢɱɟɧɧɨɜɫɬɪɟɬɹɬɫɹ
ɫɬɨɣɫɬɨɪɨɧɵɝɞɟɭɝɥɵɦɟɧɶɲɢɟɞɜɭɯɩɪɹɦɵɯ
ȿȼɄɅɂȾ
ɈȻɓɂȿɉɈɇəɌɂə
Ⱥɤɫɢɨɦɵ
Ɋɚɜɧɵɟɨɞɧɨɦɭɢɬɨɦɭɠɟɪɚɜɧɵɢɦɟɠɞɭɫɨɛɨɣ
ɂɟɫɥɢɤɪɚɜɧɵɦɩɪɢɛɚɜɥɹɸɬɫɹɪɚɜɧɵɟɬɨɢɰɟɥɵɟɛɭɞɭɬɪɚɜɧɵ
ɂɟɫɥɢɨɬɪɚɜɧɵɯɨɬɧɢɦɚɸɬɫɹɪɚɜɧɵɟɬɨɨɫɬɚɬɤɢɛɭɞɭɬɪɚɜɧɵ
>ɂɟɫɥɢɤɧɟɪɚɜɧɵɦɩɪɢɛɚɜɥɹɸɬɫɹɪɚɜɧɵɟɬɨɰɟɥɵɟɛɭɞɭɬɧɟ
ɪɚɜɧɵ
ɂɭɞɜɨɟɧɧɵɟɨɞɧɨɝɨɢɬɨɝɨɠɟɪɚɜɧɵɦɟɠɞɭɫɨɛɨɣ
ɂɩɨɥɨɜɢɧɵɨɞɧɨɝɨɢɬɨɝɨɠɟɪɚɜɧɵɦɟɠɞɭɫɨɛɨɣ@
ɂɫɨɜɦɟɳɚɸɳɢɟɫɹɞɪɭɝɫɞɪɭɝɨɦɪɚɜɧɵɦɟɠɞɭɫɨɛɨɣ
ɂɰɟɥɨɟɛɨɥɶɲɟɱɚɫɬɢ
> ɂɞɜɟɩɪɹɦɵɟɧɟɫɨɞɟɪɠɚɬɩɪɨɫɬɪɚɧɫɬɜɚ@
ɉɪɟɞɥɨɠɟɧɢɟ
ȼɩɪɹɦɨɭɝɨɥɶɧɵɯɬɪɟɭɝɨɥɶɧɢɤɚɯɤɜɚɞɪɚɬɧɚɫɬɨɪɨɧɟɫɬɹɝɢɜɚɸ
ɳɟɣɩɪɹɦɨɣɭɝɨɥɪɚɜɟɧ ɜɦɟɫɬɟɜɡɹɬɵɦ!ɤɜɚɞɪɚɬɚɦɧɚɫɬɨɪɨɧɚɯ
ɡɚɤɥɸɱɚɸɳɢɯɩɪɹɦɨɣɭɝɨɥ
ɉɭɫɬɶABC ± ɩɪɹɦɨɭɝɨɥɶɧɵɣɬɪɟɭɝɨɥɶɧɢɤɢɦɟɸɳɢɣɩɪɹɦɨɣɭɝɨɥ
BAC ɹɭɬɜɟɪɠɞɚɸɱɬɨɤɜɚɞɪɚɬɧɚBCɪɚɜɟɧ ɜɦɟɫɬɟɜɡɹɬɵɦ!ɤɜɚɞɪɚɬɚɦɧɚBAɢAC ɱɟɪɬɟɠ
G
H
K
A
F
C
B
D
L
ɑɟɪɬɟɠ
E
ȻɈȽɋɈɁȾȺɅɐȿɅɕȿɑɂɋɅȺ
Ⱦɟɣɫɬɜɢɬɟɥɶɧɨ ɧɚɞɫɬɪɨɢɦ ɧɚ BC ɤɜɚɞɪɚɬ BDEC ɚ ɧɚ BA AC
ɧɚɞɫɬɪɨɢɦ ɤɜɚɞɪɚɬɵ!HBGC ɩɪɟɞɥɨɠɟɧɢɟ ɢɱɟɪɟɡAɩɪɨɜɟɞɟɦALɩɚɪɚɥɥɟɥɶɧɭɸɤɚɤBDɬɚɤɢCE ɩɪɟɞɥɨɠɟɧɢɟ ɫɨɟɞɢɧɢɦ
AD FC ɂ ɩɨɫɤɨɥɶɤɭ ɤɚɠɞɵɣ ɢɡ ɭɝɥɨɜ BAC BAH ɩɪɹɦɨɣ ɨɩɪɟɞɟɥɟɧɢɟ ɬɨɜɨɬɧɚɧɟɤɨɬɨɪɨɣɩɪɹɦɨɣBAɩɪɢɟɟɬɨɱɤɟAɞɜɟɩɪɹɦɵɟACAHɪɚɫɩɨɥɨɠɟɧɧɵɟɧɟɩɨɨɞɧɭɫɬɨɪɨɧɭɨɛɪɚɡɭɸɬɫɦɟɠɧɵɟ
ɭɝɥɵ ɜɦɟɫɬɟ!ɪɚɜɧɵɟɞɜɭɦɩɪɹɦɵɦ ɡɧɚɱɢɬCAɛɭɞɟɬɩɨ ɨɞɧɨɣ!
ɩɪɹɦɨɣɫAH ɩɪɟɞɥɨɠɟɧɢɟ ȼɫɥɟɞɫɬɜɢɟɬɨɝɨɠɟɜɨɬɢBAɛɭɞɟɬ
ɩɨɨɞɧɨɣɩɪɹɦɨɣɫAGɂɩɨɫɤɨɥɶɤɭɭɝɨɥDBCɪɚɜɟɧɭɝɥɭFBA ɚɤɫɢɨɦɚ ɢɛɨɤɚɠɞɵɣɢɡɧɢɯɩɪɹɦɨɣɬɨɩɪɢɛɚɜɢɦɨɛɳɢɣɭɝɨɥABC
ɡɧɚɱɢɬɜɟɫɶɭɝɨɥDBAɪɚɜɟɧɜɫɟɦɭFBC ɚɤɫɢɨɦɚ ɂɩɨɫɤɨɥɶɤɭDB
ɪɚɜɧɚBCɚFBɪɚɜɧɚBA ɨɩɪɟɞɟɥɟɧɢɟ ɬɨɜɨɬɞɜɟɫɬɨɪɨɧɵDB
BAɪɚɜɧɵɞɜɭɦɫɬɨɪɨɧɚɦBCFBɤɚɠɞɚɹɤɚɠɞɨɣ ɢɭɝɨɥDBAɪɚɜɟɧ
ɭɝɥɭFBC ɡɧɚɱɢɬɢɨɫɧɨɜɚɧɢɟ ɩɪɟɞɥɨɠɟɧɢɟ ADɪɚɜɧɨɨɫɧɨɜɚɧɢɸ
FC ɢ ɬɪɟɭɝɨɥɶɧɢɤ ABD ɪɚɜɟɧ ɬɪɟɭɝɨɥɶɧɢɤɭ FBC ɩɪɟɞɥɨɠɟɧɢɟ
ɂɭɞɜɨɟɧɧɵɣɬɪɟɭɝɨɥɶɧɢɤABDɟɫɬɶɩɚɪɚɥɥɟɥɨɝɪɚɦɦBL ɩɪɟɞɥɨɠɟɧɢɟ ɢɛɨɨɧɢɢɦɟɸɬɬɨɠɟɨɫɧɨɜɚɧɢɟBDɢɪɚɫɩɨɥɨɠɟɧɵɦɟɠɞɭ
ɬɟɦɢ ɠɟ ɩɚɪɚɥɥɟɥɶɧɵɦɢ BD AL ɩɪɟɞɥɨɠɟɧɢɟ ɍɞɜɨɟɧɧɵɣ ɠɟ
ɬɪɟɭɝɨɥɶɧɢɤFBC ɩɪɟɞɥɨɠɟɧɢɟ ɟɫɬɶɤɜɚɞɪɚɬHB ɢɛɨɨɧɢɢɦɟɸɬ
ɬɨɠɟɨɫɧɨɜɚɧɢɟFBɢɪɚɫɩɨɥɨɠɟɧɵɦɟɠɞɭɬɟɦɢɠɟɩɚɪɚɥɥɟɥɶɧɵɦɢ
FBɢHC >ɧɨɭɞɜɨɟɧɧɵɟɪɚɜɧɵɯɜɟɥɢɱɢɧɪɚɜɧɵɦɟɠɞɭɫɨɛɨɣ ɚɤɫɢɨ
ɦɚ
- 123 . . . последняя (13) »