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href="/w/index.php?title=%D0%9F%D0%BE%D1%81%D0%B5%D0%B1%D0%BD%D0%BE:%D0%9A%D0%BE%D1%80%D0%B8%D1%81%D0%BD%D0%B8%D1%87%D0%BA%D0%B0_%D0%BF%D1%80%D0%B8%D1%98%D0%B0%D0%B2%D0%B0&returnto=%D0%95%D1%83%D0%BA%D0%BB%D0%B8%D0%B4%D0%BE%D0%B2%D0%B0+%D0%B3%D0%B5%D0%BE%D0%BC%D0%B5%D1%82%D1%80%D0%B8%D1%98%D0%B0&returntoquery=action%3Dedit%26section%3D3" title="Иако није обавезно, препоручујемо да се пријавите [o]" accesskey="o" class=""><span>Пријави ме</span></a> </li> </ul> </div> </div> </div> <div id="vector-user-links-dropdown" class="vector-dropdown vector-user-menu vector-button-flush-right vector-user-menu-logged-out user-links-collapsible-item" title="Више опција" > <input type="checkbox" id="vector-user-links-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-user-links-dropdown" class="vector-dropdown-checkbox " aria-label="Личне алатке" > <label id="vector-user-links-dropdown-label" for="vector-user-links-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-ellipsis mw-ui-icon-wikimedia-ellipsis"></span> <span class="vector-dropdown-label-text">Личне алатке</span> </label> <div class="vector-dropdown-content"> <div id="p-personal" class="vector-menu mw-portlet mw-portlet-personal user-links-collapsible-item" title="Кориснички мени" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-sitesupport" class="user-links-collapsible-item mw-list-item"><a href="https://donate.wikimedia.org/?utm_source=donate&utm_medium=sidebar&utm_campaign=spontaneous&uselang=sr"><span>Донације</span></a></li><li id="pt-createaccount" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=%D0%9F%D0%BE%D1%81%D0%B5%D0%B1%D0%BD%D0%BE:%D0%9E%D1%82%D0%B2%D0%BE%D1%80%D0%B8_%D0%BD%D0%B0%D0%BB%D0%BE%D0%B3&returnto=%D0%95%D1%83%D0%BA%D0%BB%D0%B8%D0%B4%D0%BE%D0%B2%D0%B0+%D0%B3%D0%B5%D0%BE%D0%BC%D0%B5%D1%82%D1%80%D0%B8%D1%98%D0%B0&returntoquery=action%3Dedit%26section%3D3" title="Иако није обавезно, препоручујемо да отворите налог и пријавите се"><span class="vector-icon mw-ui-icon-userAdd mw-ui-icon-wikimedia-userAdd"></span> <span>Отвори налог</span></a></li><li id="pt-login" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=%D0%9F%D0%BE%D1%81%D0%B5%D0%B1%D0%BD%D0%BE:%D0%9A%D0%BE%D1%80%D0%B8%D1%81%D0%BD%D0%B8%D1%87%D0%BA%D0%B0_%D0%BF%D1%80%D0%B8%D1%98%D0%B0%D0%B2%D0%B0&returnto=%D0%95%D1%83%D0%BA%D0%BB%D0%B8%D0%B4%D0%BE%D0%B2%D0%B0+%D0%B3%D0%B5%D0%BE%D0%BC%D0%B5%D1%82%D1%80%D0%B8%D1%98%D0%B0&returntoquery=action%3Dedit%26section%3D3" title="Иако није обавезно, препоручујемо да се пријавите [o]" accesskey="o"><span class="vector-icon mw-ui-icon-logIn mw-ui-icon-wikimedia-logIn"></span> <span>Пријави ме</span></a></li> </ul> </div> </div> </div> </div> </nav> </div> </header> </div> <div class="mw-page-container"> <div class="mw-page-container-inner"> <div class="vector-sitenotice-container"> <div id="siteNotice"><div id="mw-dismissablenotice-anonplace"></div><script>(function(){var node=document.getElementById("mw-dismissablenotice-anonplace");if(node){node.outerHTML="\u003Cdiv class=\"mw-dismissable-notice\"\u003E\u003Cdiv class=\"mw-dismissable-notice-close\"\u003E[\u003Ca tabindex=\"0\" role=\"button\"\u003Eодбаци\u003C/a\u003E]\u003C/div\u003E\u003Cdiv class=\"mw-dismissable-notice-body\"\u003E\u003C!-- CentralNotice --\u003E\u003Cdiv id=\"localNotice\" data-nosnippet=\"\"\u003E\u003Cdiv class=\"sitenotice\" lang=\"sr\" dir=\"ltr\"\u003E\u003Cdiv class=\"noticebanner\" style=\"display: none;\"\u003E\u003Cdiv class=\"plainlinks\" style=\"background-color: #f0f0f0; border-radius:5px; 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href=\"/wiki/%D0%92%D0%B8%D0%BA%D0%B8%D0%BF%D0%B5%D0%B4%D0%B8%D1%98%D0%B0:%D0%A2%D0%B0%D0%BA%D0%BC%D0%B8%D1%87%D0%B5%D1%9A%D0%B5_%D1%83_%D0%BF%D0%B8%D1%81%D0%B0%D1%9A%D1%83_%D1%87%D0%BB%D0%B0%D0%BD%D0%B0%D0%BA%D0%B0/%D0%A3_%D1%81%D0%B2%D0%B5%D1%82%D1%83_%D0%A4%D0%BB%D0%BE%D1%80%D0%B5_%D0%B8_%D0%A4%D0%B0%D1%83%D0%BD%D0%B5\" title=\"Википедија:Такмичење у писању чланака/У свету Флоре и Фауне\"\u003EФлоре и фауне\u003C/a\u003E\u003C/b\u003E.\u003C/div\u003E\u003C/div\u003E\u003C/div\u003E\u003C/div\u003E\u003C/div\u003E\n\u003Cdiv class=\"noticebanner\"\u003E\u003Cdiv class=\"plainlinks\" style=\"background-color: #FBEBEA; border-radius:5px; margin-top:10px; position:relative; border: 1px solid #aaa; font-family: \u0026#39;Helvetica\u0026#39;, \u0026#39;Arial\u0026#39;, sans-serif; line-height: 18px; box-shadow: 0 1px 1px rgba( 0, 0, 0, 0.15 ); overflow:hidden;\"\u003E\u003Cdiv style=\"display:block; top:4px; width:100%; text-align:center;;\"\u003E\u003Cdiv style=\"color:#000085; font-size:25px; line-height:25px\"\u003E\u003Cdiv style=\"padding-left:50px;\"\u003E\u003C/div\u003E\u003C/div\u003E\u003Cdiv style=\"padding-top:2px; color:#444; font-size:1.15em; line-height:1.5;\"\u003E\u003Cdiv style=\"padding-left:8px; padding-right:8px;\"\u003EПридружите се \u003Cb\u003E\u003Ca href=\"/wiki/%D0%92%D0%B8%D0%BA%D0%B8%D0%BF%D0%B5%D0%B4%D0%B8%D1%98%D0%B0:%D0%A3%D1%80%D0%B5%D1%92%D0%B8%D0%B2%D0%B0%D1%87%D0%BA%D0%B8_%D0%BC%D0%B0%D1%80%D0%B0%D1%82%D0%BE%D0%BD_%D0%92%D0%B8%D0%BA%D0%B8_%D0%B2%D0%BE%D0%BB%D0%B8_%D1%98%D0%B0%D0%B2%D0%BD%D1%83_%D1%83%D0%BC%D0%B5%D1%82%D0%BD%D0%BE%D1%81%D1%82_%D0%B8_%D0%B3%D1%80%D0%BE%D0%B1%D0%BD%D0%B0_%D0%BE%D0%B1%D0%B5%D0%BB%D0%B5%D0%B6%D1%98%D0%B0_2024.\" title=\"Википедија:Уређивачки маратон Вики воли јавну уметност и гробна обележја 2024.\"\u003EУређивачком маратону Вики воли јавну уметност и гробна обележја 2024\u003C/a\u003E\u003C/b\u003E.\u003C/div\u003E\u003C/div\u003E\u003C/div\u003E\u003C/div\u003E\u003C/div\u003E\n\u003Cdiv class=\"noticebanner\"\u003E\u003Cdiv class=\"plainlinks\" style=\"background-color: #FBEBEA; border-radius:5px; margin-top:10px; position:relative; border: 1px solid #aaa; font-family: \u0026#39;Helvetica\u0026#39;, \u0026#39;Arial\u0026#39;, sans-serif; line-height: 18px; box-shadow: 0 1px 1px rgba( 0, 0, 0, 0.15 ); overflow:hidden;\"\u003E\u003Cdiv style=\"display:block; top:4px; width:100%; text-align:center;;\"\u003E\u003Cdiv style=\"color:#000085; font-size:25px; line-height:25px\"\u003E\u003Cdiv style=\"padding-left:50px;\"\u003E\u003C/div\u003E\u003C/div\u003E\u003Cdiv style=\"padding-top:2px; color:#444; font-size:1.15em; line-height:1.5;\"\u003E\u003Cdiv style=\"padding-left:8px; padding-right:8px;\"\u003EУчествујте у \u003Cb\u003E\u003Ca href=\"https://sr.wikiquote.org/wiki/%D0%92%D0%B8%D0%BA%D0%B8%D1%86%D0%B8%D1%82%D0%B0%D1%82:%D0%9A%D0%B0%D0%BC%D0%BF%D0%B0%D1%9A%D0%B0_SheSaid_2024\" class=\"extiw\" title=\"q:Викицитат:Кампања SheSaid 2024\"\u003Eкампањи писања цитата значајних жена\u003C/a\u003E\u003C/b\u003E на Викицитату.\u003C/div\u003E\u003C/div\u003E\u003C/div\u003E\u003C/div\u003E\u003C/div\u003E\n\u003Cdiv class=\"noticebanner\"\u003E\u003Cdiv class=\"plainlinks\" style=\"background-color: #FBEBEA; border-radius:5px; margin-top:10px; position:relative; border: 1px solid #aaa; font-family: \u0026#39;Helvetica\u0026#39;, \u0026#39;Arial\u0026#39;, sans-serif; line-height: 18px; box-shadow: 0 1px 1px rgba( 0, 0, 0, 0.15 ); overflow:hidden;\"\u003E\u003Cdiv style=\"display:block; top:4px; width:100%; text-align:center;;\"\u003E\u003Cdiv style=\"color:#000085; font-size:25px; line-height:25px\"\u003E\u003Cdiv style=\"padding-left:50px;\"\u003E\u003C/div\u003E\u003C/div\u003E\u003Cdiv style=\"padding-top:2px; color:#444; font-size:1.15em; line-height:1.5;\"\u003E\u003Cdiv style=\"padding-left:8px; padding-right:8px;\"\u003EПридружите се \u003Cb\u003E\u003Ca href=\"/wiki/%D0%92%D0%B8%D0%BA%D0%B8%D0%BF%D0%B5%D0%B4%D0%B8%D1%98%D0%B0:%D0%90%D0%BA%D1%86%D0%B8%D1%98%D0%B0_%D0%BF%D1%80%D0%BE%D1%88%D0%B8%D1%80%D0%B8%D0%B2%D0%B0%D1%9A%D0%B0_%D0%BA%D0%BB%D0%B8%D1%86%D0%B0\" title=\"Википедија:Акција проширивања клица\"\u003Eакцији проширивања клица\u003C/a\u003E\u003C/b\u003E.\u003C/div\u003E\u003C/div\u003E\u003C/div\u003E\u003C/div\u003E\u003C/div\u003E\u003C/div\u003E\u003C/div\u003E\u003C/div\u003E\u003C/div\u003E";}}());</script></div> </div> <div class="vector-column-start"> <div class="vector-main-menu-container"> <div id="mw-navigation"> <nav id="mw-panel" class="vector-main-menu-landmark" aria-label="Сајт"> <div id="vector-main-menu-pinned-container" class="vector-pinned-container"> </div> </nav> </div> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <h1 id="firstHeading" class="firstHeading mw-first-heading">Извор странице Еуклидова геометрија</h1> 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Разлог <i><a href="https://meta.wikimedia.org/wiki/Special:MyLanguage/NOP" class="extiw" title="m:Special:MyLanguage/NOP">Open proxy/Webhost</a>: See the <a href="https://meta.wikimedia.org/wiki/WM:OP/H" class="extiw" title="m:WM:OP/H">help page</a> if you are affected </i>. </p> <ul><li>Почетак блокаде: 16:12, 27. август 2023.</li> <li>Крај блокаде: 16:12, 27. август 2028.</li></ul> <p>Ваша тренутна IP адреса је 8.222.208.146. Блокирани опсег је 8.222.128.0/17. </p><p>Наведите све горње податке при захтеву за деблокаду. Ако мислите да сте грешком блокирани додатне информације можете наћи на <a href="https://meta.wikimedia.org/wiki/Special:MyLanguage/No_open_proxies" class="extiw" title="m:Special:MyLanguage/No open proxies">без отворених проксија</a>. </p> За деблокаду поставите <a href="https://meta.wikimedia.org/wiki/Steward_requests/Global" class="extiw" title="m:Steward requests/Global">захтев на Метавикију</a>. Можете такође послати мејл <a href="https://meta.wikimedia.org/wiki/Special:MyLanguage/Stewards" class="extiw" title="m:Special:MyLanguage/Stewards">стјуардима</a> <a href="https://meta.wikimedia.org/wiki/Special:MyLanguage/VRT" class="extiw" title="m:Special:MyLanguage/VRT">VRT</a>-а на <kbd>stewards@wikimedia.org</kbd>; обавезно наведите све горње податке.</div></div><hr /> <p>Можете да видите и копирате извор ове странице. </p><textarea readonly="" accesskey="," id="wpTextbox1" cols="80" rows="25" style="" class="mw-editfont-monospace" lang="sr" dir="ltr" name="wpTextbox1">== Логичка основа == === Класична логика === Еуклид је често користио метод [[Свођење на контрадикцију|доказивања противречношћу]], те стога традиционално представљање Еуклидове геометрије претпоставља [[classical logic|класичну логику]], у којој је сваки исказ било тачан или нетачан, тј. за било који предлог П, предлог „П или не П” аутоматски је тачно. === Савремени стандарди ригорозности === Постављање еуклидске геометрије на чврсту аксиоматску основу била је преокупација математичара вековима.<ref name="Smith">A detailed discussion can be found in. {{cite book |title=Methods of geometry |author= James T. Smith |chapter-url=https://books.google.com/books?id=mWpWplOVQ6MC&pg=RA1-PA19 |chapter=Chapter 2: Foundations |pages=19 ''ff'' |isbn=0-471-25183-6 |publisher=Wiley |year=2000}}</ref> Улогу [[primitive notion|примитивних појмова]], или недефинисаних концепата, јасно је изнео [[Alessandro Padoa|Алесандро Падоа]] из [[Ђузепе Пеано|Пеанове]] делегације на конференцији у Паризу 1900. године:<ref name = Smith/><ref name="revue">{{cite book |title=Revue de métaphysique et de morale, Volume 8 |url=https://books.google.com/books?id=4aoLAAAAIAAJ&pg=PA592 |page=592 |author=Société française de philosophie |publisher=Hachette |year=1900}}</ref> {{blockquote|text=... кад почнемо да формулишемо теорију, можемо да замислимо да су недефинисани симболи потпуно лишени значења и да су недоказани предлози једноставно услови наметнути недефинисаним симболима. Тада је ''систем идеја'' који смо у почетку изабрали једноставно ''једно тумачење'' недефинисаних симбола; али..ово тумачење читатељ може занемарити и слободно га у свом уму заменити ''другим тумачењем'' .. које задовољава услове ... ''Логична'' питања тако постају потпуно независна од ''емпиријских'' или ''психолошких'' питања ... Тада се систем недефинисаних симбола може сматрати ''апстракцијом'' добијеном из ''специјализованих теорија'' које настају када ... систем недефинисаних симбола сукцесивно замењује свака од интерпретација ...|source=''Essai d'une théorie algébrique des nombre entiers, avec une Introduction logique à une théorie déductive quelconque'' |sign=Padoa}} Односно, математика је знање neзависно од контекста у хијерархијском оквиру. Као што је рекао [[Бертранд Расел]]:<ref name="Newman">{{cite book |title= The world of mathematics |volume=3 |editor=James Roy Newman |author=Bertrand Russell |chapter=Mathematics and the metaphysicians |isbn=0-486-41151-6 |year=2000|chapter-url=https://books.google.com/books?id=_b2ShqRj8YMC&pg=PA1577 |page=1577 |edition=Reprint of Simon and Schuster 1956 |publisher=Courier Dover Publications }}</ref> {{blockquote|text=Ако се наша хипотеза односи на ''било шта'', а не на неку једну или више одређених ствари, онда наша закључивања чине математику. Дакле, математика се може дефинисати као предмет у којем никада не знамо о чему говоримо, нити да ли је истина оно што говоримо.|source =''Mathematics and the metaphysicians'' |sign=Bertrand Russell}} Такви се темељни приступи крећу између [[foundationalism|фундаментализма]] и [[formalism (mathematics)|формализма]]. </textarea><div class="templatesUsed"></div><p id="mw-returnto">Назад на страницу <a href="/wiki/%D0%95%D1%83%D0%BA%D0%BB%D0%B8%D0%B4%D0%BE%D0%B2%D0%B0_%D0%B3%D0%B5%D0%BE%D0%BC%D0%B5%D1%82%D1%80%D0%B8%D1%98%D0%B0" title="Еуклидова геометрија">Еуклидова геометрија</a>.</p> <noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">Преузето из „<a dir="ltr" href="https://sr.wikipedia.org/wiki/Еуклидова_геометрија">https://sr.wikipedia.org/wiki/Еуклидова_геометрија</a>”</div></div> <div id="catlinks" class="catlinks catlinks-allhidden" data-mw="interface"></div> </div> </main> </div> <div class="mw-footer-container"> <footer id="footer" class="mw-footer" > <ul id="footer-info"> </ul> <ul id="footer-places"> <li id="footer-places-privacy"><a href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Privacy_policy">Политика приватности</a></li> <li id="footer-places-about"><a href="/wiki/%D0%92%D0%B8%D0%BA%D0%B8%D0%BF%D0%B5%D0%B4%D0%B8%D1%98%D0%B0:%D0%9E_%D0%BD%D0%B0%D0%BC%D0%B0">О Википедији</a></li> <li id="footer-places-disclaimers"><a href="/wiki/%D0%92%D0%B8%D0%BA%D0%B8%D0%BF%D0%B5%D0%B4%D0%B8%D1%98%D0%B0:%D0%9E%D0%B4%D1%80%D0%B8%D1%86%D0%B0%D1%9A%D0%B5_%D0%BE%D0%B4%D0%B3%D0%BE%D0%B2%D0%BE%D1%80%D0%BD%D0%BE%D1%81%D1%82%D0%B8">Одрицање одговорности</a></li> <li id="footer-places-wm-codeofconduct"><a href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Universal_Code_of_Conduct">Кодекс понашања</a></li> <li id="footer-places-developers"><a href="https://developer.wikimedia.org">За програмере</a></li> <li id="footer-places-statslink"><a href="https://stats.wikimedia.org/#/sr.wikipedia.org">Статистика</a></li> <li id="footer-places-cookiestatement"><a href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Cookie_statement">Изјава о колачићима</a></li> <li id="footer-places-mobileview"><a href="//sr.m.wikipedia.org/w/index.php?title=%D0%95%D1%83%D0%BA%D0%BB%D0%B8%D0%B4%D0%BE%D0%B2%D0%B0_%D0%B3%D0%B5%D0%BE%D0%BC%D0%B5%D1%82%D1%80%D0%B8%D1%98%D0%B0&action=edit&section=3&mobileaction=toggle_view_mobile" class="noprint stopMobileRedirectToggle">Мобилни приказ</a></li> </ul> <ul id="footer-icons" class="noprint"> <li id="footer-copyrightico"><a href="https://wikimediafoundation.org/" class="cdx-button cdx-button--fake-button cdx-button--size-large cdx-button--fake-button--enabled"><img src="/static/images/footer/wikimedia-button.svg" width="84" height="29" alt="Wikimedia Foundation" loading="lazy"></a></li> <li id="footer-poweredbyico"><a href="https://www.mediawiki.org/" class="cdx-button cdx-button--fake-button cdx-button--size-large cdx-button--fake-button--enabled"><img src="/w/resources/assets/poweredby_mediawiki.svg" alt="Powered by MediaWiki" width="88" height="31" loading="lazy"></a></li> </ul> </footer> </div> </div> </div> <div class="vector-settings" id="p-dock-bottom"> <ul></ul> </div><script>(RLQ=window.RLQ||[]).push(function(){mw.config.set({"wgHostname":"mw-web.codfw.main-697b7966c5-65vfh","wgBackendResponseTime":174,"wgPageParseReport":{"limitreport":{"cputime":"0.005","walltime":"0.007","ppvisitednodes":{"value":17,"limit":1000000},"postexpandincludesize":{"value":927,"limit":2097152},"templateargumentsize":{"value":0,"limit":2097152},"expansiondepth":{"value":2,"limit":100},"expensivefunctioncount":{"value":0,"limit":500},"unstrip-depth":{"value":0,"limit":20},"unstrip-size":{"value":0,"limit":5000000},"entityaccesscount":{"value":0,"limit":400},"timingprofile":["100.00% 0.000 1 -total"]},"cachereport":{"origin":"mw-web.codfw.main-697b7966c5-65vfh","timestamp":"20241126181916","ttl":2592000,"transientcontent":false}}});});</script> </body> </html>