2. Стереометрия аксиомаларында анықталмайтын ұғымдардың: нүкте, түзу, жазықтық пен ара қашықтықтың негізгі қасиеттері өрнектелген. Стереометрия аксиомалары кеңістік қасиеттерін өрнектейді.
А к с и о м а-1: Кемінде бір түзу және кемінде бір жазықтық болады. Әрбір түзу және әрбір жазықтық дәлме-дәл келмейтін бос емес нүктелер жиыны болады.
1-аксиомадан кез келген жазықтығы үшін тиісті емес нүктесі болатындығы шығады (146-сурет). Мұндай жағдайда нүктесі жазықтығынан тыс алынған дейді де, былай жазады: .
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)
146-сурет
А к с и о м а-2.
Достарыңызбен бөлісу: |