. . "Bretschneiders formel \u00E4r inom geometrin en formel f\u00F6r ber\u00E4kning av arean av en godtycklig konvex fyrh\u00F6rning: d\u00E4r a, b, c och d \u00E4r sidl\u00E4ngderna, s \u00E4r semiperimetern och , \u00E4r tv\u00E5 godtyckligt valda, motst\u00E5ende vinklar. Formeln g\u00E4ller f\u00F6r alla konvexa fyrh\u00F6rningar (oberoende av om dessa \u00E4r cykliska eller inte) inklusive godtyckliga kvadrater, romber och rektanglar. Formeln tillskrivs fr\u00E5n \u00E5r 1842."@sv . "5615284"^^ . "En geometr\u00EDa, la f\u00F3rmula de Bretschneider es una expresi\u00F3n que permite calcular el \u00E1rea de un cuadril\u00E1tero general: Aqu\u00ED, a, b, c, d son los lados del cuadrilatero, s es el semiper\u00EDmetro, y \u03B1 y \u03B3 son dos \u00E1ngulos opuestos. Se cumple en cualquier cuadril\u00E1tero, ya sea c\u00EDclico o no. El matem\u00E1tico alem\u00E1n Carl Anton Bretschneider descubri\u00F3 la f\u00F3rmula en 1842. Tambi\u00E9n fue deducida ese mismo a\u00F1o por el matem\u00E1tico alem\u00E1n Karl Georg Christian von Staudt."@es . . "V geometrii je Bretschneider\u016Fv vzorec n\u00E1sleduj\u00EDc\u00ED v\u00FDraz pro obsah obecn\u00E9ho \u010Dty\u0159\u00FAheln\u00EDku: Zde, a, b, c, d jsou strany \u010Dty\u0159\u00FAheln\u00EDka, s je polovi\u010Dn\u00ED obvod, a \u03B1 a \u03B3 jsou dva protilehl\u00E9 \u00FAhly. Bretschneider\u016Fv vzorec lze pou\u017E\u00EDt na jak\u00E9mkoli \u010Dty\u0159\u00FAheln\u00EDku, a\u0165 u\u017E je pravideln\u00FD, nebo ne. N\u011Bmeck\u00FD matematik Carl Anton Bretschneider objevil vzorec v roce 1842. Vzorec byl tak\u00E9 odvozen ve stejn\u00E9m roce n\u011Bmeck\u00FDm matematikem Karlem Georgem Christianem Staudtem."@cs . "5774"^^ . . "Twierdzenie Bretschneidera \u2013 twierdzenie geometryczne pozwalaj\u0105ce obliczy\u0107 pole powierzchni dowolnego czworok\u0105ta znaj\u0105c jedynie d\u0142ugo\u015Bci jego bok\u00F3w oraz miary jego k\u0105t\u00F3w. Zosta\u0142o ono udowodnione niezale\u017Cnie w 1842 roku przez Carla Bretschneidera oraz przez F. Strehlkego."@pl . . . . . "Formule de Bretschneider"@fr . "\u0645\u0628\u0631\u0647\u0646\u0629 \u0628\u0631\u064A\u062A\u0634\u0646\u0627\u064A\u062F\u0631"@ar . . . "Die Formel von Bretschneider, benannt nach Carl Anton Bretschneider, berechnet die Fl\u00E4che eines Vierecks basierend auf seinen Seiten und Diagonalen. Sie ist damit eine Verallgemeinerung der Formel von Brahmagupta, die nur f\u00FCr Sehnenvierecke gilt und selbst eine Verallgemeinerung der Formel von Heron f\u00FCr die Fl\u00E4che eines Dreiecks darstellt. Die Fl\u00E4che eines Vierecks ABCD mit Seiten und Diagonalen berechnet sich wie folgt: Hierbei ist der halbe Umfang des Vierecks mit und der Korrekturterm ist nach dem Satz von Ptolem\u00E4us genau dann 0, wenn es sich um ein Sehnenviereck handelt."@de . "BretschneidersFormula"@en . "\uBE0C\uB808\uCE58\uB098\uC774\uB354 \uACF5\uC2DD"@ko . . . . . "\uBE0C\uB808\uCE58\uB098\uC774\uB354 \uACF5\uC2DD(Bretschneider's formula)\uC740 \uC784\uC758\uC758 \uC0AC\uAC01\uD615\uC758 \uB124 \uBCC0\uC758 \uAE38\uC774\uB97C \uC54C\uACE0 \uC788\uC744 \uB54C \uADF8 \uC0AC\uAC01\uD615\uC758 \uBA74\uC801\uC744 \uAD6C\uD558\uB294 \uACF5\uC2DD\uC774\uB2E4. \uCE74\uB97C \uC548\uD1A4 \uBE0C\uB808\uCE58\uB098\uC774\uB354\uAC00 \uBC1C\uACAC\uD55C \uC774 \uACF5\uC2DD\uC740 \uBE0C\uB77C\uB9C8\uAD7D\uD0C0 \uACF5\uC2DD\uC774 \uC77C\uBC18\uD654\uB41C \uACF5\uC2DD\uC73C\uB85C\uC11C \uBE0C\uB808\uCE58\uB098\uC774\uB354 \uACF5\uC2DD\uC744 \uC5BB\uC744 \uC218 \uC788\uB2E4. \uD5E4\uB860\uC758 \uACF5\uC2DD\uACFC \uBE0C\uB77C\uB9C8\uAD7D\uD0C0 \uACF5\uC2DD\uC740 \uBE0C\uB808\uCE58\uB098\uC774\uB354 \uACF5\uC2DD\uC758 \uC0AC\uBCC0\uD615\uC5D0 \uB300\uD55C \uD2B9\uBCC4\uD55C \uACBD\uC6B0\uC774\uB2E4."@ko . . . . "\u5728\u5E7E\u4F55\u5B78\u7576\u4E2D\uFF0C\u5E03\u96F7\u7279\u65BD\u5948\u5FB7\u516C\u5F0F\u662F\u4E00\u689D\u4EFB\u610F\u56DB\u908A\u5F62\u7684\u9762\u7A4D\u516C\u5F0F\uFF0C\u7531\u5FB7\u570B\u7684\u6578\u5B78\u5BB6\u6240\u767C\u73FE\uFF1A \u5176\u4E2D\uFF0C\u70BA\u56DB\u908A\u5F62\u7684\u908A\u9577\uFF0C\u70BA\u534A\u5468\u9577\uFF0C\u5373\uFF0C\u800C\u70BA\u5176\u4E2D\u4E8C\u500B\u5C0D\u89D2\u3002 \u6B64\u516C\u5F0F\u53EF\u7528\u65BC\u4EFB\u4F55\u56DB\u908A\u5F62\uFF0C\u4E0D\u8AD6\u662F\u5426\u70BA\u5706\u5185\u63A5\u56DB\u8FB9\u5F62\uFF0C\u53EF\u8996\u70BA\u5A46\u7F85\u6469\u7B08\u591A\u516C\u5F0F\u4E4B\u63A8\u5EE3\u3002"@zh . . . . . . "\u0421\u043E\u043E\u0442\u043D\u043E\u0448\u0435\u043D\u0438\u0435 \u0411\u0440\u0435\u0442\u0448\u043D\u0430\u0439\u0434\u0435\u0440\u0430"@ru . . "\u5728\u5E7E\u4F55\u5B78\u7576\u4E2D\uFF0C\u5E03\u96F7\u7279\u65BD\u5948\u5FB7\u516C\u5F0F\u662F\u4E00\u689D\u4EFB\u610F\u56DB\u908A\u5F62\u7684\u9762\u7A4D\u516C\u5F0F\uFF0C\u7531\u5FB7\u570B\u7684\u6578\u5B78\u5BB6\u6240\u767C\u73FE\uFF1A \u5176\u4E2D\uFF0C\u70BA\u56DB\u908A\u5F62\u7684\u908A\u9577\uFF0C\u70BA\u534A\u5468\u9577\uFF0C\u5373\uFF0C\u800C\u70BA\u5176\u4E2D\u4E8C\u500B\u5C0D\u89D2\u3002 \u6B64\u516C\u5F0F\u53EF\u7528\u65BC\u4EFB\u4F55\u56DB\u908A\u5F62\uFF0C\u4E0D\u8AD6\u662F\u5426\u70BA\u5706\u5185\u63A5\u56DB\u8FB9\u5F62\uFF0C\u53EF\u8996\u70BA\u5A46\u7F85\u6469\u7B08\u591A\u516C\u5F0F\u4E4B\u63A8\u5EE3\u3002"@zh . . "\u0423 \u0433\u0435\u043E\u043C\u0435\u0442\u0440\u0456\u0457 \u0444\u043E\u0440\u043C\u0443\u043B\u043E\u044E \u0411\u0440\u0435\u0442\u0448\u043D\u0430\u0439\u0434\u0435\u0440\u0430 \u0454 \u043D\u0430\u0441\u0442\u0443\u043F\u043D\u0438\u0439 \u0432\u0438\u0440\u0430\u0437 \u0434\u043B\u044F \u043E\u0431\u0447\u0438\u0441\u043B\u0435\u043D\u043D\u044F \u043F\u043B\u043E\u0449\u0456 \u0437\u0430\u0433\u0430\u043B\u044C\u043D\u043E\u0433\u043E \u0447\u043E\u0442\u0438\u0440\u0438\u043A\u0443\u0442\u043D\u0438\u043A\u0430 : \u0422\u0443\u0442 a , b , c , d - \u0441\u0442\u043E\u0440\u043E\u043D\u0438 \u0447\u043E\u0442\u0438\u0440\u0438\u043A\u0443\u0442\u043D\u0438\u043A\u0430, p - \u043F\u0456\u0432\u043F\u0435\u0440\u0438\u043C\u0435\u0442\u0440 , \u0430 \u03B1 \u0456 \u03B3 - \u0434\u0432\u0430 \u043F\u0440\u043E\u0442\u0438\u043B\u0435\u0436\u043D\u0456 \u043A\u0443\u0442\u0438. \u0424\u043E\u0440\u043C\u0443\u043B\u0443 \u0411\u0440\u0435\u0442\u0448\u043D\u0430\u0439\u0434\u0435\u0440\u0430 \u043C\u043E\u0436\u043D\u0430 \u0437\u0430\u0441\u0442\u043E\u0441\u043E\u0432\u0443\u0432\u0430\u0442\u0438 \u0434\u043B\u044F \u043E\u0431\u0447\u0438\u0441\u043B\u0435\u043D\u043D\u044F \u043F\u043B\u043E\u0449\u0456 \u0431\u0443\u0434\u044C-\u044F\u043A\u043E\u0433\u043E \u0447\u043E\u0442\u0438\u0440\u0438\u043A\u0443\u0442\u043D\u0438\u043A\u0430. \u041D\u0456\u043C\u0435\u0446\u044C\u043A\u0438\u0439 \u043C\u0430\u0442\u0435\u043C\u0430\u0442\u0438\u043A \u041A\u0430\u0440\u043B \u0410\u043D\u0442\u043E\u043D \u0411\u0440\u0435\u0442\u0448\u043D\u0430\u0439\u0434\u0435\u0440 \u0432\u0456\u0434\u043A\u0440\u0438\u0432 \u0444\u043E\u0440\u043C\u0443\u043B\u0443 \u0432 1842 \u0440\u043E\u0446\u0456. \u0423 \u0442\u043E\u043C\u0443 \u0436 \u0440\u043E\u0446\u0456 \u0444\u043E\u0440\u043C\u0443\u043B\u0443 \u043E\u0442\u0440\u0438\u043C\u0430\u0432 \u0456 \u043D\u0456\u043C\u0435\u0446\u044C\u043A\u0438\u0439 \u043C\u0430\u0442\u0435\u043C\u0430\u0442\u0438\u043A \u041A\u0430\u0440\u043B \u0413\u0435\u043E\u0440\u0433 \u041A\u0440\u0456\u0441\u0442\u0456\u0430\u043D \u0444\u043E\u043D \u0428\u0442\u0430\u0443\u0434\u0442."@uk . "F\u00F3rmula de Bretschneider"@es . "In geometria, la formula di Bretschneider per il calcolo dell'area di un quadrilatero corrisponde alla seguente espressione: Dove a, b, c, d sono i lati del quadrilatero, p \u00E8 il semiperimetro, e sono i due angoli opposti. La scoperta di tale formula si deve al matematico tedesco nel 1842. La formula di Bretschneider funziona per ogni quadrilatero, a prescindere dal fatto che esso sia ciclico o meno."@it . "Bretschneider's formula"@en . . "\u5E03\u96F7\u7279\u65BD\u5948\u5FB7\u516C\u5F0F"@zh . . . "Die Formel von Bretschneider, benannt nach Carl Anton Bretschneider, berechnet die Fl\u00E4che eines Vierecks basierend auf seinen Seiten und Diagonalen. Sie ist damit eine Verallgemeinerung der Formel von Brahmagupta, die nur f\u00FCr Sehnenvierecke gilt und selbst eine Verallgemeinerung der Formel von Heron f\u00FCr die Fl\u00E4che eines Dreiecks darstellt. Die Fl\u00E4che eines Vierecks ABCD mit Seiten und Diagonalen berechnet sich wie folgt: Hierbei ist der halbe Umfang des Vierecks mit und der Korrekturterm ist nach dem Satz von Ptolem\u00E4us genau dann 0, wenn es sich um ein Sehnenviereck handelt. Die Formel besitzt auch trigonometrische Varianten, bei denen statt der Diagonalen zwei gegen\u00FCberliegende Innenwinkel des Vierecks verwendet werden: Auch hier f\u00E4llt der Korrekturterm im Spezialfall des Sehnenvierecks weg, da sich in diesem gegen\u00FCberliegende Winkel zu erg\u00E4nzen und beziehungsweise gilt. Sowohl F. Strehlke als auch C. A. Bretschneider ver\u00F6ffentlichten trigonometrische Varianten der Formel erstmals 1842 in zwei separaten Artikeln, die erste Darstellung mit Hilfe der Diagonalen erschien in einer Publikation von G. Dostor (1868), w\u00E4hrend zweite Darstellung mit den Diagonalen und dem Korrekturterm auf J. L. Coolidge (1939) zur\u00FCckgeht."@de . . . . . . . "En g\u00E9om\u00E9trie, la formule de Bretschneider permet de calculer l'aire d'un quadrilat\u00E8re non crois\u00E9 : o\u00F9, a, b, c, d, sont les longueurs des c\u00F4t\u00E9s du quadrilat\u00E8re, p le demi-p\u00E9rim\u00E8tre, et \u03B1 et \u03B3 deux angles oppos\u00E9s quelconques . Remarquons que puisque . Cette formule fonctionne pour un quadrilat\u00E8re convexe ou concave (mais non crois\u00E9), non forc\u00E9ment inscriptible. Elle contient la formule de Brahmagupta de l'aire d'un quadrilat\u00E8re inscriptible (cas ), ainsi que la formule de H\u00E9ron de l'aire d'un triangle (cas ). Elle montre qu'un quadrilat\u00E8re articul\u00E9 poss\u00E8de une aire maximale lorsqu'on inscrit ses sommets dans un cercle. Elle a \u00E9t\u00E9 d\u00E9couverte en 1842 par le math\u00E9maticien allemand Carl Anton Bretschneider ."@fr . "Bretschneider\u016Fv vzorec"@cs . "Formula di Bretschneider"@it . "Bretschneiders formel \u00E4r inom geometrin en formel f\u00F6r ber\u00E4kning av arean av en godtycklig konvex fyrh\u00F6rning: d\u00E4r a, b, c och d \u00E4r sidl\u00E4ngderna, s \u00E4r semiperimetern och , \u00E4r tv\u00E5 godtyckligt valda, motst\u00E5ende vinklar. Formeln g\u00E4ller f\u00F6r alla konvexa fyrh\u00F6rningar (oberoende av om dessa \u00E4r cykliska eller inte) inklusive godtyckliga kvadrater, romber och rektanglar. Formeln tillskrivs fr\u00E5n \u00E5r 1842."@sv . . . . . . . "\u0421\u043E\u043E\u0442\u043D\u043E\u0448\u0435\u043D\u0438\u0435 \u0411\u0440\u0435\u0442\u0448\u043D\u0430\u0439\u0434\u0435\u0440\u0430 \u2014 \u0441\u043E\u043E\u0442\u043D\u043E\u0448\u0435\u043D\u0438\u0435 \u0432 \u0447\u0435\u0442\u044B\u0440\u0451\u0445\u0443\u0433\u043E\u043B\u044C\u043D\u0438\u043A\u0435, \u0430\u043D\u0430\u043B\u043E\u0433 \u0442\u0435\u043E\u0440\u0435\u043C\u044B \u043A\u043E\u0441\u0438\u043D\u0443\u0441\u043E\u0432."@ru . . "Formel von Bretschneider"@de . "Bretschneiders formel"@sv . . "\u0421\u043E\u043E\u0442\u043D\u043E\u0448\u0435\u043D\u0438\u0435 \u0411\u0440\u0435\u0442\u0448\u043D\u0430\u0439\u0434\u0435\u0440\u0430 \u2014 \u0441\u043E\u043E\u0442\u043D\u043E\u0448\u0435\u043D\u0438\u0435 \u0432 \u0447\u0435\u0442\u044B\u0440\u0451\u0445\u0443\u0433\u043E\u043B\u044C\u043D\u0438\u043A\u0435, \u0430\u043D\u0430\u043B\u043E\u0433 \u0442\u0435\u043E\u0440\u0435\u043C\u044B \u043A\u043E\u0441\u0438\u043D\u0443\u0441\u043E\u0432."@ru . . "Twierdzenie Bretschneidera \u2013 twierdzenie geometryczne pozwalaj\u0105ce obliczy\u0107 pole powierzchni dowolnego czworok\u0105ta znaj\u0105c jedynie d\u0142ugo\u015Bci jego bok\u00F3w oraz miary jego k\u0105t\u00F3w. Zosta\u0142o ono udowodnione niezale\u017Cnie w 1842 roku przez Carla Bretschneidera oraz przez F. Strehlkego."@pl . . . . . . "In geometry, Bretschneider's formula is the following expression for the area of a general quadrilateral: Here, a, b, c, d are the sides of the quadrilateral, s is the semiperimeter, and \u03B1 and \u03B3 are any two opposite angles, since as long as Bretschneider's formula works on both convex and concave quadrilaterals (but not crossed ones), whether it is cyclic or not. The German mathematician Carl Anton Bretschneider discovered the formula in 1842. The formula was also derived in the same year by the German mathematician Karl Georg Christian von Staudt."@en . "\u30D6\u30EC\u30FC\u30C8\u30B7\u30E5\u30CA\u30A4\u30C0\u30FC\u306E\u516C\u5F0F\uFF08\u30D6\u30EC\u30FC\u30C8\u30B7\u30E5\u30CA\u30A4\u30C0\u30FC\u306E\u3053\u3046\u3057\u304D\u3001Bretschneider's formula\uFF09\u306F\u3001\u56DB\u89D2\u5F62\u306E\u9762\u7A4D\u3092\u4E0E\u3048\u308B\u516C\u5F0F\u3067\u3042\u308B\u3002\u56DB\u89D2\u5F62ABCD \u306B\u3064\u3044\u3066\u3001p, q, r, s \u3092\u305D\u308C\u305E\u308C\u306E\u8FBA\u306E\u9577\u3055\u3001T \u3092\u534A\u5468\u9577\u3001A \u3068 C \u3092\u4E92\u3044\u306B\u5BFE\u89D2\u3068\u3059\u308B\u3068\u3001\u56DB\u89D2\u5F62\u306E\u9762\u7A4D\u306F \u306B\u7B49\u3057\u3044\u3002\u5186\u306B\u5185\u63A5\u3059\u308B\u56DB\u89D2\u5F62\u306E\u9762\u7A4D\u3092\u8868\u3057\u305F\u30D6\u30E9\u30FC\u30DE\u30B0\u30D7\u30BF\u306E\u516C\u5F0F\u306E\u4E00\u822C\u5316\u3067\u3042\u308A\u3001\u4EFB\u610F\u306E\u56DB\u89D2\u5F62\u306B\u3064\u3044\u3066\u6210\u308A\u7ACB\u3064\u3002\u540D\u524D\u306E\u7531\u6765\u306F\u30C9\u30A4\u30C4\u306E\u6570\u5B66\u8005\uFF081808\u20131878\uFF09\u306B\u3061\u306A\u3080\u3002"@ja . "Bretschneider's formula"@en . "In geometry, Bretschneider's formula is the following expression for the area of a general quadrilateral: Here, a, b, c, d are the sides of the quadrilateral, s is the semiperimeter, and \u03B1 and \u03B3 are any two opposite angles, since as long as Bretschneider's formula works on both convex and concave quadrilaterals (but not crossed ones), whether it is cyclic or not. The German mathematician Carl Anton Bretschneider discovered the formula in 1842. The formula was also derived in the same year by the German mathematician Karl Georg Christian von Staudt."@en . . "Twierdzenie Bretschneidera"@pl . . "1115349393"^^ . . . "In geometria, la formula di Bretschneider per il calcolo dell'area di un quadrilatero corrisponde alla seguente espressione: Dove a, b, c, d sono i lati del quadrilatero, p \u00E8 il semiperimetro, e sono i due angoli opposti. La scoperta di tale formula si deve al matematico tedesco nel 1842. La formula di Bretschneider funziona per ogni quadrilatero, a prescindere dal fatto che esso sia ciclico o meno."@it . . . "En g\u00E9om\u00E9trie, la formule de Bretschneider permet de calculer l'aire d'un quadrilat\u00E8re non crois\u00E9 : o\u00F9, a, b, c, d, sont les longueurs des c\u00F4t\u00E9s du quadrilat\u00E8re, p le demi-p\u00E9rim\u00E8tre, et \u03B1 et \u03B3 deux angles oppos\u00E9s quelconques . Remarquons que puisque . Cette formule fonctionne pour un quadrilat\u00E8re convexe ou concave (mais non crois\u00E9), non forc\u00E9ment inscriptible. Elle contient la formule de Brahmagupta de l'aire d'un quadrilat\u00E8re inscriptible (cas ), ainsi que la formule de H\u00E9ron de l'aire d'un triangle (cas ). Elle a \u00E9t\u00E9 d\u00E9couverte en 1842 par le math\u00E9maticien allemand Carl Anton Bretschneider ."@fr . . "\u30D6\u30EC\u30FC\u30C8\u30B7\u30E5\u30CA\u30A4\u30C0\u30FC\u306E\u516C\u5F0F\uFF08\u30D6\u30EC\u30FC\u30C8\u30B7\u30E5\u30CA\u30A4\u30C0\u30FC\u306E\u3053\u3046\u3057\u304D\u3001Bretschneider's formula\uFF09\u306F\u3001\u56DB\u89D2\u5F62\u306E\u9762\u7A4D\u3092\u4E0E\u3048\u308B\u516C\u5F0F\u3067\u3042\u308B\u3002\u56DB\u89D2\u5F62ABCD \u306B\u3064\u3044\u3066\u3001p, q, r, s \u3092\u305D\u308C\u305E\u308C\u306E\u8FBA\u306E\u9577\u3055\u3001T \u3092\u534A\u5468\u9577\u3001A \u3068 C \u3092\u4E92\u3044\u306B\u5BFE\u89D2\u3068\u3059\u308B\u3068\u3001\u56DB\u89D2\u5F62\u306E\u9762\u7A4D\u306F \u306B\u7B49\u3057\u3044\u3002\u5186\u306B\u5185\u63A5\u3059\u308B\u56DB\u89D2\u5F62\u306E\u9762\u7A4D\u3092\u8868\u3057\u305F\u30D6\u30E9\u30FC\u30DE\u30B0\u30D7\u30BF\u306E\u516C\u5F0F\u306E\u4E00\u822C\u5316\u3067\u3042\u308A\u3001\u4EFB\u610F\u306E\u56DB\u89D2\u5F62\u306B\u3064\u3044\u3066\u6210\u308A\u7ACB\u3064\u3002\u540D\u524D\u306E\u7531\u6765\u306F\u30C9\u30A4\u30C4\u306E\u6570\u5B66\u8005\uFF081808\u20131878\uFF09\u306B\u3061\u306A\u3080\u3002"@ja . . . . . . "\u0423 \u0433\u0435\u043E\u043C\u0435\u0442\u0440\u0456\u0457 \u0444\u043E\u0440\u043C\u0443\u043B\u043E\u044E \u0411\u0440\u0435\u0442\u0448\u043D\u0430\u0439\u0434\u0435\u0440\u0430 \u0454 \u043D\u0430\u0441\u0442\u0443\u043F\u043D\u0438\u0439 \u0432\u0438\u0440\u0430\u0437 \u0434\u043B\u044F \u043E\u0431\u0447\u0438\u0441\u043B\u0435\u043D\u043D\u044F \u043F\u043B\u043E\u0449\u0456 \u0437\u0430\u0433\u0430\u043B\u044C\u043D\u043E\u0433\u043E \u0447\u043E\u0442\u0438\u0440\u0438\u043A\u0443\u0442\u043D\u0438\u043A\u0430 : \u0422\u0443\u0442 a , b , c , d - \u0441\u0442\u043E\u0440\u043E\u043D\u0438 \u0447\u043E\u0442\u0438\u0440\u0438\u043A\u0443\u0442\u043D\u0438\u043A\u0430, p - \u043F\u0456\u0432\u043F\u0435\u0440\u0438\u043C\u0435\u0442\u0440 , \u0430 \u03B1 \u0456 \u03B3 - \u0434\u0432\u0430 \u043F\u0440\u043E\u0442\u0438\u043B\u0435\u0436\u043D\u0456 \u043A\u0443\u0442\u0438. \u0424\u043E\u0440\u043C\u0443\u043B\u0443 \u0411\u0440\u0435\u0442\u0448\u043D\u0430\u0439\u0434\u0435\u0440\u0430 \u043C\u043E\u0436\u043D\u0430 \u0437\u0430\u0441\u0442\u043E\u0441\u043E\u0432\u0443\u0432\u0430\u0442\u0438 \u0434\u043B\u044F \u043E\u0431\u0447\u0438\u0441\u043B\u0435\u043D\u043D\u044F \u043F\u043B\u043E\u0449\u0456 \u0431\u0443\u0434\u044C-\u044F\u043A\u043E\u0433\u043E \u0447\u043E\u0442\u0438\u0440\u0438\u043A\u0443\u0442\u043D\u0438\u043A\u0430. \u041D\u0456\u043C\u0435\u0446\u044C\u043A\u0438\u0439 \u043C\u0430\u0442\u0435\u043C\u0430\u0442\u0438\u043A \u041A\u0430\u0440\u043B \u0410\u043D\u0442\u043E\u043D \u0411\u0440\u0435\u0442\u0448\u043D\u0430\u0439\u0434\u0435\u0440 \u0432\u0456\u0434\u043A\u0440\u0438\u0432 \u0444\u043E\u0440\u043C\u0443\u043B\u0443 \u0432 1842 \u0440\u043E\u0446\u0456. \u0423 \u0442\u043E\u043C\u0443 \u0436 \u0440\u043E\u0446\u0456 \u0444\u043E\u0440\u043C\u0443\u043B\u0443 \u043E\u0442\u0440\u0438\u043C\u0430\u0432 \u0456 \u043D\u0456\u043C\u0435\u0446\u044C\u043A\u0438\u0439 \u043C\u0430\u0442\u0435\u043C\u0430\u0442\u0438\u043A \u041A\u0430\u0440\u043B \u0413\u0435\u043E\u0440\u0433 \u041A\u0440\u0456\u0441\u0442\u0456\u0430\u043D \u0444\u043E\u043D \u0428\u0442\u0430\u0443\u0434\u0442."@uk . . "V geometrii je Bretschneider\u016Fv vzorec n\u00E1sleduj\u00EDc\u00ED v\u00FDraz pro obsah obecn\u00E9ho \u010Dty\u0159\u00FAheln\u00EDku: Zde, a, b, c, d jsou strany \u010Dty\u0159\u00FAheln\u00EDka, s je polovi\u010Dn\u00ED obvod, a \u03B1 a \u03B3 jsou dva protilehl\u00E9 \u00FAhly. Bretschneider\u016Fv vzorec lze pou\u017E\u00EDt na jak\u00E9mkoli \u010Dty\u0159\u00FAheln\u00EDku, a\u0165 u\u017E je pravideln\u00FD, nebo ne. N\u011Bmeck\u00FD matematik Carl Anton Bretschneider objevil vzorec v roce 1842. Vzorec byl tak\u00E9 odvozen ve stejn\u00E9m roce n\u011Bmeck\u00FDm matematikem Karlem Georgem Christianem Staudtem."@cs . . "En geometr\u00EDa, la f\u00F3rmula de Bretschneider es una expresi\u00F3n que permite calcular el \u00E1rea de un cuadril\u00E1tero general: Aqu\u00ED, a, b, c, d son los lados del cuadrilatero, s es el semiper\u00EDmetro, y \u03B1 y \u03B3 son dos \u00E1ngulos opuestos. Se cumple en cualquier cuadril\u00E1tero, ya sea c\u00EDclico o no. El matem\u00E1tico alem\u00E1n Carl Anton Bretschneider descubri\u00F3 la f\u00F3rmula en 1842. Tambi\u00E9n fue deducida ese mismo a\u00F1o por el matem\u00E1tico alem\u00E1n Karl Georg Christian von Staudt."@es . "\u0424\u043E\u0440\u043C\u0443\u043B\u0430 \u0411\u0440\u0435\u0442\u0448\u043D\u0430\u0439\u0434\u0435\u0440\u0430"@uk . . "\u0641\u064A \u0627\u0644\u0647\u0646\u062F\u0633\u0629 \u0627\u0644\u0631\u064A\u0627\u0636\u064A\u0629\u060C \u062A\u0646\u0635 \u0645\u0628\u0631\u0647\u0646\u0629 \u0628\u0631\u064A\u062A\u0634\u0646\u0627\u064A\u062F\u0631 \u0639\u0644\u0649 \u0627\u0644\u0639\u0644\u0627\u0642\u0629 \u0627\u0644\u062A\u0627\u0644\u064A\u0629 \u0641\u064A \u0645\u0633\u0627\u062D\u0629 \u0631\u0628\u0627\u0639\u064A \u0627\u0644\u0623\u0636\u0644\u0627\u0639\u060C \u062D\u064A\u062B p, q, r \u0648s \u0647\u064A \u0623\u0636\u0644\u0627\u0639 \u0631\u0628\u0627\u0639\u064A \u0627\u0644\u0623\u0636\u0644\u0627\u0639\u060C T \u0646\u0635\u0641 \u0627\u0644\u0645\u062D\u064A\u0637\u060C \u0648A \u0648C \u0647\u064A \u0632\u0627\u0648\u064A\u062A\u064A\u0646 \u0645\u062A\u0642\u0627\u0628\u0644\u062A\u064A\u0646. \u062A\u0635\u0644\u062D \u0647\u0630\u0647 \u0627\u0644\u0639\u0644\u0627\u0642\u0629 \u0644\u0623\u064A \u0631\u0628\u0627\u0639\u064A \u0623\u0636\u0644\u0627\u0639 \u0633\u0648\u0627\u0621 \u0643\u0627\u0646 \u0631\u0628\u0627\u0639\u064A \u062F\u0627\u0626\u0631\u064A \u0623\u0645 \u0644\u0627. \u0627\u0643\u062A\u0634\u0641 \u0639\u0627\u0644\u0645 \u0627\u0644\u0631\u064A\u0627\u0636\u064A\u0627\u062A \u0627\u0644\u0623\u0644\u0645\u0627\u0646\u064A \u0627\u0644\u0635\u064A\u063A\u0629 \u0641\u064A \u0639\u0627\u0645 1842. \u0648\u0642\u062F \u0627\u0634\u062A\u0642 \u0627\u0644\u0635\u064A\u063A\u0629 \u0623\u064A\u0636\u064B\u0627 \u0641\u064A \u0646\u0641\u0633 \u0627\u0644\u0639\u0627\u0645 \u0645\u0646 \u0642\u0628\u0644 \u0639\u0627\u0644\u0645 \u0627\u0644\u0631\u064A\u0627\u0636\u064A\u0627\u062A \u0627\u0644\u0623\u0644\u0645\u0627\u0646\u064A \u0643\u0627\u0631\u0644 \u062C\u0648\u0631\u062C \u0643\u0631\u064A\u0633\u062A\u064A\u0627\u0646 \u0641\u0648\u0646 \u0634\u062A\u0627\u0648\u062A."@ar . "\u30D6\u30EC\u30FC\u30C8\u30B7\u30E5\u30CA\u30A4\u30C0\u30FC\u306E\u516C\u5F0F"@ja . . "\u0641\u064A \u0627\u0644\u0647\u0646\u062F\u0633\u0629 \u0627\u0644\u0631\u064A\u0627\u0636\u064A\u0629\u060C \u062A\u0646\u0635 \u0645\u0628\u0631\u0647\u0646\u0629 \u0628\u0631\u064A\u062A\u0634\u0646\u0627\u064A\u062F\u0631 \u0639\u0644\u0649 \u0627\u0644\u0639\u0644\u0627\u0642\u0629 \u0627\u0644\u062A\u0627\u0644\u064A\u0629 \u0641\u064A \u0645\u0633\u0627\u062D\u0629 \u0631\u0628\u0627\u0639\u064A \u0627\u0644\u0623\u0636\u0644\u0627\u0639\u060C \u062D\u064A\u062B p, q, r \u0648s \u0647\u064A \u0623\u0636\u0644\u0627\u0639 \u0631\u0628\u0627\u0639\u064A \u0627\u0644\u0623\u0636\u0644\u0627\u0639\u060C T \u0646\u0635\u0641 \u0627\u0644\u0645\u062D\u064A\u0637\u060C \u0648A \u0648C \u0647\u064A \u0632\u0627\u0648\u064A\u062A\u064A\u0646 \u0645\u062A\u0642\u0627\u0628\u0644\u062A\u064A\u0646. \u062A\u0635\u0644\u062D \u0647\u0630\u0647 \u0627\u0644\u0639\u0644\u0627\u0642\u0629 \u0644\u0623\u064A \u0631\u0628\u0627\u0639\u064A \u0623\u0636\u0644\u0627\u0639 \u0633\u0648\u0627\u0621 \u0643\u0627\u0646 \u0631\u0628\u0627\u0639\u064A \u062F\u0627\u0626\u0631\u064A \u0623\u0645 \u0644\u0627. \u0627\u0643\u062A\u0634\u0641 \u0639\u0627\u0644\u0645 \u0627\u0644\u0631\u064A\u0627\u0636\u064A\u0627\u062A \u0627\u0644\u0623\u0644\u0645\u0627\u0646\u064A \u0627\u0644\u0635\u064A\u063A\u0629 \u0641\u064A \u0639\u0627\u0645 1842. \u0648\u0642\u062F \u0627\u0634\u062A\u0642 \u0627\u0644\u0635\u064A\u063A\u0629 \u0623\u064A\u0636\u064B\u0627 \u0641\u064A \u0646\u0641\u0633 \u0627\u0644\u0639\u0627\u0645 \u0645\u0646 \u0642\u0628\u0644 \u0639\u0627\u0644\u0645 \u0627\u0644\u0631\u064A\u0627\u0636\u064A\u0627\u062A \u0627\u0644\u0623\u0644\u0645\u0627\u0646\u064A \u0643\u0627\u0631\u0644 \u062C\u0648\u0631\u062C \u0643\u0631\u064A\u0633\u062A\u064A\u0627\u0646 \u0641\u0648\u0646 \u0634\u062A\u0627\u0648\u062A."@ar . . . "\uBE0C\uB808\uCE58\uB098\uC774\uB354 \uACF5\uC2DD(Bretschneider's formula)\uC740 \uC784\uC758\uC758 \uC0AC\uAC01\uD615\uC758 \uB124 \uBCC0\uC758 \uAE38\uC774\uB97C \uC54C\uACE0 \uC788\uC744 \uB54C \uADF8 \uC0AC\uAC01\uD615\uC758 \uBA74\uC801\uC744 \uAD6C\uD558\uB294 \uACF5\uC2DD\uC774\uB2E4. \uCE74\uB97C \uC548\uD1A4 \uBE0C\uB808\uCE58\uB098\uC774\uB354\uAC00 \uBC1C\uACAC\uD55C \uC774 \uACF5\uC2DD\uC740 \uBE0C\uB77C\uB9C8\uAD7D\uD0C0 \uACF5\uC2DD\uC774 \uC77C\uBC18\uD654\uB41C \uACF5\uC2DD\uC73C\uB85C\uC11C \uBE0C\uB808\uCE58\uB098\uC774\uB354 \uACF5\uC2DD\uC744 \uC5BB\uC744 \uC218 \uC788\uB2E4. \uD5E4\uB860\uC758 \uACF5\uC2DD\uACFC \uBE0C\uB77C\uB9C8\uAD7D\uD0C0 \uACF5\uC2DD\uC740 \uBE0C\uB808\uCE58\uB098\uC774\uB354 \uACF5\uC2DD\uC758 \uC0AC\uBCC0\uD615\uC5D0 \uB300\uD55C \uD2B9\uBCC4\uD55C \uACBD\uC6B0\uC774\uB2E4."@ko . . . . .