Greek mathematician Euclid: i Kawaihae o ke nä känaka 'epekema, hamama a me ka hana hoihoi kūʻiʻo

Mākou e kaumaha aku oe i ka e ike i ka mathematician nui me Euclid. Kawaihae, he hōʻuluʻulu manaʻo i kona papa kuhikuhi hana a me kekahi mau hana hoihoi kūʻiʻo e pili ana i keia nä känaka 'epekema no ka mea, ua hōʻike mai iā ia i loko o kēia' atikala. Euclid (makahiki o ke ola ana - 365-300 BC ..) - mathematician, Ua haawiia i ka Hellenic'āina. He hana ia ma Alexandria ma lalo o Ptolemy I Soter. Aia i mau papa kuhikuhiE wale nō o kahi āna i hānauʻia ai. E like me ka mea mua - ma Atenai, e like me ka lua - i loko o Turo (Suria).

Kawaihae no Euclid: Mea kūʻiʻo hoihoi

About ke ola ana o keia nä känaka 'epekema ua ike ole ai nui. Aia He He memo mea a pau Pappa Alexandria. Kēia kanaka i ka mathematician e noho ana i loko o ka 2nd hapalua o ka 3rd kenekulia AD. He kaulana ia mākou e hoihoi i loko o ke nä känaka 'epekema i ano a me ka akahai a me ka poe a pau, ka poe i somehow hiki ke haawi i ke kūpono' ana o ka poʻe 'ole' ē aʻe makemakika sciences.

Aia mea no hoi he moolelo i olelo mai Archimedes. Kona papa kuhikuhiE ano - Euclid. Pōkole Kawaihae o nā keiki nō kāu komo ai i ka moolelo, e like me ka mea i loa 'ike, a hiki paha ke kuleana i loko o ka makemakika ma opiopio heluhelu. Ua hākālia nō i King Ptolemy i makemake e noiʻi i anahonua. Naʻe, ka mea huli mai ia ia mea i oluolu i ka hana. A laila, i ke aliʻi i kapaʻia ka poʻe puni hoʻonaʻauao Euclid, a noi aku la ia ia, ina paha he mea maʻalahi ala, e hoomaopopo i ka 'epekema. Akā, Euclid Olelo aku i ka mea, aohe alii alanui e anahonua. Pela ia mea he 'aoʻao o ia i lilo eheu, hele mai ia iā mākou i loko o ka palapala o ke kaao.

I ka hoʻomaka o ka 3rd kenekulia BC. e ka. He hoʻokumu i ka Alexandria Museum a me ka Waihona Puke o Alexandria Euclid. Pōkole Kawaihae a me kona mau discoveries i pili i kēia mau hui, i mea i ke aʻo-oaio? A.

Euclid - He haumāna o Plato

Kēia nä känaka 'epekema ua hala ma ka Academy ma muli Plato (kona kiʻi Ua hōʻike mai iā ia ma lalo nei). He aʻo i nā kiʻi i ka manaʻo o kēia philosophical thinker, a ua i ka mea i loaʻa o ka honua kaawale o ka manaʻo. He pakele i ka olelo i Euclid, nona Kawaihae mea pī me nā lāliʻi, ua he Platonist kālaiʻike. Kēia AUOO hoʻoikaika nä känaka 'epekema e maopopo i na mea a pau i ka hana a me ka hōʻikeʻia e ia i loko o kona "He," i kū i mau loa.

He mea hoihoi i loko o ka thinker ka mea i hanau 205 makahiki ma hope o Pythagoras, ma ka 63 makahiki - Plato 33 - Eudoxus, 19 - Aristotle. He hālāwai me lākou philosophical a me ka makemakika hana kekahi kū kaʻawale 'ole ma intermediaries.

Palapala "oihana mua" o Euclid me na hana o nā haumana

Proclus, i ka poe akeakamai-Platonist (makahiki o ke ola ana - 412-485), ka mea kākau manaʻo ma luna o ka "hoʻomaka",'ōlelo i loko o kēia hana Hōʻike 'ka cosmology o Plato, a "Pythagorean ao ...". I kona like no Euclid oia ua hōʻolokeʻaʻia i ka pähola 'ana o ka pauku gula (puke 2nd, 6th a me ka 13th) a me ka pololei, polyhedra (Book 13th). E like me ka poʻe kākoʻo iā ia o Platonism, ke nä känaka 'epekema ike i kona "mua" he hoʻonui i ka cosmology o Plato a me ka manaʻo hoʻomohalaʻia kona mau mua, no ka laulā lokahi e characterizes ka ke ao holoʻokoʻa.

'Aʻole kekahi Proclus i hoʻomaopopo ai Platonic puaʻa hiwa a me ka pauku gula. Iogann Kepler (makahiki o ke ola - 1571-1630) mea i pili i loko o ia mau mea. Kēia German astronomer kaulana i ka anahonua, he mau waiwai - o ke gula lākiō (mahele o ka apana ma ka waena, a me ka loihi pili) a me ka Pythagorean theorem. Ke kumukuai o ka hope o ka mea ana i hoʻohālike au i ke gula, a me ka mea mua - me ka pohaku makamae. Iogann Kepler hoʻohana i ka Platonic puaʻa hiwa ma ka hanaiia'na mai o kona cosmological kuhiakau.

Ka waiwai o "ka hoʻomaka '"

Ka puke "Ka hoʻomaka '" - o ka papa hana, a ua hana e Euclid. Ke Kawaihae o keia nä känaka 'epekema, o ka papa, i alohaia, a me ka hana, a ke wehewehe mai i hope ma ka pauku. It E e hoʻomaopopo i ka hana i kapaia "Start", a kau mai i nā kūʻiʻo nui o kaʻimi naʻauao makemakika a me ka anahonua, a ua ohi ia e kona mua. Kekahi o ia mau mea - Hippocrates o Kio, he mathematician e noho ana i loko o ka 5th kenekulia BC. e ka. O Teuda (2nd hapalua o ka 4th kenekulia BC. E.) A Leontes (4th kenekulia BC. E.) no hoi i kākau i ka puke me ia inoa. Naʻe, a me ka Hekikai o Euclidean "I ka hoʻomaka '" a pau o kēia mau hana i pahu mai mai o hoʻohana. Euclid ka puke i ke kumu o puke haʻawina ma ka anahonua no ma 2 tausani makahiki. Nä känaka 'epekema e pili ana i kana hana, hoʻohana nui o ka piʻi like o kona mau mua. Euclid Ua hoʻokō 'ia ai ka loaʻa' ike, a me ka mea i lawe mai i.

I kona puke, no ka mea kākau summed i ka hooulu ana o ka makemakika ma ka wa kahiko Greece, a ua hana i ka paa kahua no ka hou discoveries. Kēia mea i ka manaʻo nui o ka Euclid ka papa hana no ke ao nei o ke akeakamai, makemakika, a me nā mea a pau 'epekema like me ka a pau. He mea e hewa ke manaoio ia ia mea, e hoʻoikaika i ka mysticism o Plato, a Pythagoras i loko o kā lākou psevdomirozdanii.

Ua nuiʻepekema Ua oaeuiinoe ka "hoʻomaka" o Euclid, a me Albert Einstein. Heʻike i ia mea he huahana mea kupaianaha i haawi i ke kanaka manao i ka pakiko-manao maopopo pono no hou haʻawina. Einstein mai la oia i kekahi kanaka i mea ole mahalo ma o kona wa opiopio ua i hanau keia mea i hanaia no kaʻimi naʻauao noiʻi.

axiomatic hana

Ma ka hookaawale leo i ka waiwai o ka hana ana o ke nä känaka 'epekema mākou e hoihoi i loko o ka maikaʻi loa h ÷ ike ike ana o ka axiomatic hana i loko o kona "He". Kēia hana i ke kālā no makemakika o ka loa nui o ka poe mea i hoʻohana e hoapono ia ia theories. Ma mechanics, ka mea, ua hoi hoʻomano i hoʻohana. Ua nui nä känaka 'epekema Newton kūkulu i ka "nā loina o Natural kālaiʻike" hana ÷ a hana Euclid.

Kawaihae o ka hoihoi ia mai i ka mea kākau e hele ma e wehewehe i nā mea i ho'ākāka 'ka papa kuhikuhiE kana papa hana o ka.

Ke kumu nui i hoakaka ia ana o ka "hoʻomaka"

Ma ka puke "kumu" kau mai systematically Euclidean anahonua. Kona i kahi kūlike o'ōnaehana ua nānā 'ana ma luna o manaÿo e like me ka pelane, pololei, wahi, ana. Aina i e lawelawe i loko o laila, na kēia: "He wahi aia ma pololei o ka laina e moe ana i loko o ka pelane," a me "wahi ua aia ma waena o ka mau wahi'ē aʻe."

System na olelo o Euclidean anahonua, a hooku iho la ia ma ka ke kālā no ka hōʻike, IeAUPIIe, IAa IO Wāwahi i loko o 5 pūʻulu o axioms: noi, mea, ka hoʻomauʻana, a me ka hui pu ana, o ka laua o Euclid.

Ka heʻumikumamākolu nā puke o ka "hoʻomaka"ʻepekema, hooku iho la ia a me ka makemakika, stereometry, planimetry, i ka pilina o Eudoxus. It E e hoʻomaopopo i ka mea a pau e wehewehe ana i keia hana pololei deductively. I ka ho'ākāka 'ana kaʻina kānāwai nā puke o Euclid, a me ka mea mua o lākou ma muli o nā axioms a me postulates. Eia ka mea, ua hāpai 'ana ma luna o ka mahele ana i hana (kahi kupono i kekahi hana) a me Theorem (kahi au i ke hooiaio i kekahi mea).

Ka nele o ka makemakika a Euclid

I ka papa kuhikuhiE drawback mea i keia axiomatic nä känaka 'epekema nele i completeness. No axiom o ka noi, ka hoʻomauʻana a me ka pono. Nolaila,ʻepekema pinepine i e hilinai aku ma luna o ka maka, pono o ke kilo. Books 14th a 15th - he nui nā lewa i ka hana, i ke kumu o ka a - Euclid. Kona Kawaihae i wale i ka loa pōkole, no laila, e hiki ole ke olelo no kaʻoiaʻiʻo paha ka mea mua 13 puke i ka kekahi kanaka i hana ai i ka hopena o ka like hana o ke kula, i alakaiia e kekahi nä känaka 'epekema.

E möakäka hou ulu o ka 'epekema

Ka muli o Euclidean anahonua ua pili i ka hanana o ka pilikia makapō e hoohalike ai ia o ko ke ao nei a puni mākou (i nā kukuna o ka malamalama, aole i lalau mai filament me he ki i ka pololei laina, a no laila, ma luna o. N.). Lakou hoi Mamua, no laila, ua loaʻa i ka oi Hōʻuluʻulu naʻauao o kēia 'epekema, e like me ka anahonua. N. I. Lobachevsky (makahiki o ke ola - 1792-1856) - Russian mathematician nana i i nui i loaʻa. He kaulana i loaʻa mea he anahonua e oko a mai ka Euclidean. Ua Ua loli ka noiʻi 'manaʻo e pili ana i ka lewa. Ua huli mai i ka mea, i ole he priori. Ma nā hua'ōlelo, ka anahonua hookuu aku la i loko o ka "hehee wale" o Euclid, hiki ole ke noʻonoʻo i ka wale wehewehe i ka waiwai o ka makahiki i hoopuni iho la iā mākou. 'ana i ka' epekema maoli (oi kilohōkū a me ke kālaikūlohea) hoike i ka mea wehewehe i ka 'ole me ka kekahi pololei wale. Eia hou, ka mea hiki ole ke pili i ka mea a pau a puni e like me ka a pau. Euclidean anahonua - keia mea i ka mua hoʻokokoke i ka naʻauao, a me ka ho'ākāka 'ana o kona' ole.

Ma ke ala, Lobachevsky hopena ua lono kaumaha. He ia i maliuʻia i loko o ka 'epekema ao no kā lākou mau kāʻeʻaʻeʻa manaʻo. Naʻe,ʻaʻole i ka paio ana o ke nä känaka 'epekema ua ma ka makehewa. I ka lanakila o ka manaʻo hoakaka Lobachevsky, Gauss, nona ka palapala, ua paʻi ma ka makahiki 1860. Mawaena o na palapala, he rave hōʻike manaʻo e pili ana i ke nä känaka 'epekema Lobachevsky anahonua.

Other hana Euclid

Great hoihoi i loko o mākou manawa o ke Kawaihae o Euclid me he nä känaka 'epekema. I ka makemakika,ʻo ia i nui discoveries. Keia ua hookupaa iho la ia ma ka mea i mai 1482 "o ka hoʻomaka" puke i oi aku mamua o elima haneri paʻi puke i loko o kekahi 'ōlelo. Naʻe, ke Kawaihae o mathematician Euclid ua hoailono aku la i wale i ka hana ana o keia puke. He nona i ka helu ana o na hana ma optics, kilohōkū, ke kūpili, mele. Kekahi o ia mau mea - ka puke "Ikepili", e hōʻike ana i nā kūlana i e ka mea e hiki ai i ka noonoo "i" keia ai i ka makemakika maximal kiʻi. Other hana Euclid - puke ma luna o optics, a he 'ike e pili ana i ka wā e hiki mai. Mākou e hoihoi i loko o ka noiʻi ka palapala iho la i ka (essay) a me catoptrics (oia waiho ia ma keia hana o ka pähola 'ana o ei i kupu mai ana ma ke aniani). Ike a me ka puke Euclid i kapaia "mahele o nā huahelu." E hana ma ka makemakika "Ka hopena a wahahee", Eia naʻe, i ole e holo.

No laila, i oe hālāwaiʻepekema nui e like me Euclid. Pōkole Kawaihae no ia, hopefully, e pono ia oe.