Parallel kab rau lub dav hlau thiab nyob rau hauv qhov chaw

Nyob rau lub dav hlau kab no hu ua thaum uas tig mus yog hais tias lawv tsis muaj cov ntsiab lus nyob rau hauv ntau, uas yog, lawv tsis sib tshuam. Rau thaum uas tig mus designations siv ib tug tshwj xeeb icon || (Thaum uas tig mus kab ib || b).

Rau cov kab dag nyob rau hauv lub qhov chaw uas yuav tsum tau ntawm cov tsis muaj ntau cov ntsiab lus yog tsis txaus - hais tias lawv yog thaum uas tig mus nyob rau hauv qhov chaw, lawv yuav tsum yuav mus rau tib lub dav hlau (txwv tsis pub lawv yuav Skew).

Rau cov piv txwv ntawm thaum uas tig mus kab tsis tas yuav mus deb, lawv nrog peb qhov txhia chaw, nyob rau hauv lub chav tsev - ib tug kab ntawm kev sib tshuam ntawm cov phab ntsa rau saum qab nthab thiab hauv pem teb, nyob rau hauv phau ntawv sau daim ntawv - cov lus rov sawv, thiab lwm yam

Nws yog pom tseeb tias, nrog rau cov parallelism ntawm ob kab thiab ib tug thib peb kab thaum uas tig mus rau ib qho ntawm thawj ob, nws yuav tsum tig mus rau lub thib ob.

Parallel kab rau ib tug dav hlau khi daim ntawv yog tsis muaj pov thawj siv axioms ntawm lub dav hlau geometry. Nws yog muab raws li ib tug qhov tseeb, raws li ib tug axiom: rau tej taw tes rau lub dav hlau tsis dag rau ib tug ncaj kab, muaj ib tug tshwj xeeb txoj kab uas kis tau los ntawm nws thaum uas tig mus no. Qhov no axiom yog lub npe hu mus rau txhua txhua rau voom.

Nws spatial generalization, uas yog lub ntsiab lus hais tias rau tej taw tes nyob rau hauv qhov chaw, tsis yog nyob rau txoj kab, muaj ib tug tshwj xeeb txoj kab uas kis tau los ntawm nws thaum uas tig mus li no, yog yooj yim muaj pov thawj nrog rau cov kev pab los ntawm lub twb paub axiom ntawm parallelism rau lub dav hlau.

Cov khoom ntawm thaum uas tig mus kab

• Yog hais tias ib yam ntawm cov ob thaum uas tig mus kab thaum uas tig mus rau ib tug thib peb, ces lawv yog cov mus tib seem.

Qhov no tej khoom vaj tse yog muaj los ntawm thaum uas tig mus kab rau lub dav hlau thiab nyob rau hauv qhov chaw.
Raws li ib qho piv txwv, xav txog nws ua neeg ncajncees nyob rau hauv cov khoom geometry.

Piv txwv thaum uas tig mus kab b thiab c ncaj a.

Cov ntaub ntawv nyob qhov twg tag nrho cov kab pw nyob rau hauv tib lub dav hlau tawm hauv lub dav hlau geometry.

Xav hais tias, ib tug thiab b mus rau lub dav hlau beta thiab gamma - dav hlau, uas tuav ib tug thiab c (rau kev txiav txim ntawm thaum uas tig mus kab nyob rau hauv qhov chaw yuav tsum yuav mus rau tib lub dav hlau).

Piv txwv tias yog hais tias ib tug dav hlau txawv beta thiab gamma thiab kos rau ntawm lub kab b los ntawm lub dav hlau beta taw tes B, lub dav hlau dua los ntawm tus taw tes B thiab txoj kab yuav tsum tshuam nrog cov dav hlau nyob hauv ib tug ncaj beta (denoted B1).

Yog hais tias lub resulting direct B1 hla lub dav hlau ntawm gamma, ces, nyob rau hauv ib tes, cov hla taw tes yuav tsum dag rau ib tug, vim hais tias B1 belongs rau lub beta dav hlau, thiab nyob rau lwm yam, nws yuav tsum yuav mus rau thiab, txij li thaum B1 belongs rau lub thib peb lub dav hlau.
Tab sis thaum uas tig mus kab ib tug thiab c tsis sib tshooj.

Yog li, ncaj B1 yuav tsum yuav mus rau lub dav hlau beta thiab tsis muaj ntau cov ntsiab lus nrog ib tug, yog li ntawd, raws li axiom ntawm parallelism, nws coincides nrog b.
Peb tau txais coincides nrog lub txoj kab ncaj nraim b B1, uas belongs rau tib lub dav hlau nrog rau cov kab ncaj nraim nrog thiab nyob rau tib lub sij hawm nws tsis tshuam, uas yog, b thiab c - thaum uas tig mus

• Los ntawm ib tug taw tes uas tsis dag rau ib tug muab txoj kab ncaj nraim, thaum uas tig mus qhov no yuav muab qhov chaw tsuas yog ib cim kab.

• Dag nyob rau hauv ib tug dav hlau perpendicular mus rau lub thib peb ob kab yog mus tib seem.

• Muab dav hlau hla ib tug ntawm cov uas tig mus ob kab ncaj nraim tshuam cov tib dav hlau thiab lub thib ob txoj kab ncaj nraim.

• Tsim Nyog thiab crosswise pw sab hauv ces kaum tsim los ntawm cov kev tshuam ntawm ob kab ncaj nraim thaum uas tig mus rau ib tug thib peb, sib npaug zos nyob rau hauv tus nqi tsim nrog internal unilateral sib npaug zos rau 180 °.

Lub converse yog muaj tseeb, uas yuav tsum tau yuam kev rau tej yam tshwm sim ntawm parallelism ntawm ob kab.

Tus mob ntawm thaum uas tig mus kab

zog thiab nta tau muab teev tseg saum toj no tej yam kev mob sawv cev rau thaum uas tig mus kab, thiab lawv txoj kev muaj peev xwm ua pov thawj heev geometry. Nyob rau hauv lwm yam lus, los ua pov thawj rau hauv lub parallelism ntawm ob uas twb muaj lawm kab yog txaus los ua pov thawj lawv cov thib peb ncaj thaum uas tig mus los yog koob pheej ntawm lawv ntawm cov ces kaum, seb nws yog tsim nyog los yog paub qab hau dag, thiab lwm yam

Ua pov thawj rau feem ntau siv txoj kev "los ntawm contradiction" uas yog, nrog lub assumption tias cov kab tsis thaum uas tig. Raws li cov ntawm no lub assumption, ib tug yuav tau yooj yim qhia tau tias nyob rau hauv cov ntaub ntawv no tau ua txhaum lub predetermined tej yam kev mob, piv txwv li, dag crosswise sab hauv ces kaum yog zoo tib, uas proves tsis yog kev xav tau.