21. 4.1 Scipione Del Ferro (1465 - 1526) (Dejiny Algebry) 4.1 scipione del ferro (1465 1526) 4.2 MikulᚠKopernik (1473 - 1543) 4.3Niccolo Fontana - Tartaglia (1500 - 1557) 4.4 Girolamo Cardano (1501 - 1576) http://www.matika.sk/zdroje/texty/recenz/Dejalg/Cast4/Part4-1.htm

4. Cardanove formule pre riešenie rovnice tretieho stupòa Obsah Úvod 4.1 Scipione del Ferro (1465 - 1526) MikulᚠKopernik (1473 - 1543) Niccolo Fontana - Tartaglia (1500 - 1557) Girolamo Cardano (1501 - 1576) Ludovico Ferrari (1522 - 1565) ... Literatúra 4.1 Scipione del Ferro (1465 - 1526) Bolonský matematik, uèite¾ Mikuláša Kopernika. Pôsobil najprv na Bolonskej a potom na Benátskej univerzite ako uèite¾ algebry a perspektívy. Objavil postup na riešenie rovnice x + bx = c r (b 0, c ale svoj objav držal v tajnosti. Svoje tajomstvo prezradil iba svojej manželke, svojmu nástupcovi na bolonskej univerzite Annibale della Navé a svojmu benátskemu kolegovi Antonio Maria Fioré Po smrti Scipione del Ferra vyzval Antonio Fioré roku 1530 na verejnú súaž poètára de Coita. Súaž sa týkala predovšetkým rovníc tretieho stupòa. De Coita sa obrátil o pomoc k svojmu kolegovi Niccolovi Fontanovi . Ten mu síce odmietol pomôc, ale vyhlásil, že rovnice typu cubus plus vec sa rovná èíslo vie rieši. O tom sa dopoèul Fioré a preto roku 1535 vyzval Fontanu na súaž. Fontana túto súaž vyhral, lebo nezávisle od Scipiona del Ferro aj on objavil postup na riešenie rovníc tretieho stupòa. Avšak rovnako ako všetci èo tento postup poznali, aj Fontana ho držal v tajnosti. Až keï sa roku 1542 pozostalos Scipione del Ferra dostala do rúk

22. 4.4 Girolamo Cardano (1501 - 1576) (Dejiny Algebry) Vtedy sa dopocul, že scipione del ferro, profesor matematiky na univerzite vBologni, a Niccolo Fontana, poctár z Brescie, objavili postup na riešenie http://www.matika.sk/zdroje/texty/recenz/Dejalg/Cast4/Part4-4.htm

4. Cardanove formule pre riešenie rovnice tretieho stupòa Obsah Úvod Scipione del Ferro (1465 - 1526) MikulᚠKopernik (1473 - 1543) ... Niccolo Fontana - Tartaglia (1500 - 1557) 4.4 Girolamo Cardano (1501 - 1576) Ludovico Ferrari (1522 - 1565) Literatúra 4.4 Girolamo Cardano (1501 - 1576) Poèiatky jeho kariéry neboli ¾ahké. Roku 1534 dosiahol, že ho v Miláne zamestnali ako lekára mestského chudobinca. Jeden jeho priate¾ ho doporuèil aj do školy pre chudobných, kde vyuèoval matematiku, astronómiu a zemepis. V tomto roku napísal pojednanie o Euklidových Základoch, Ptolemaiovej Geografii a o jednej geometrickej práci anglického scholastika Sacrobosca (1200 - 1256). Roku 1536 prijal do svojho domu za pomocníka štrnásroèného Ludovica Ferrariho , ktorý sa postupne stal jeho žiakom a spolupracovníkom, a neskôr to dotiahol až na profesora matematiky Milánskej univerzity. Roku Cardano dokonèil svoju prácu Praktická aritmetika a jednoduché merania . Vtedy sa dopoèul, že Scipione del Ferro, profesor matematiky na univerzite v Bologni, a Niccolo Fontana, poètár z Brescie, objavili postup na riešenie rovnice tretieho stupòa. Ve¾mi túžil uvies vo svojej knihe tento výsledok, lebo jeho Praktická aritmetika bola kritikou Summy Luca Pacoliho, ktorý tvrdil, že riešenie rovníc tretieho stupòa je nemožné. Avšak Cardano sám nájs riešenie nedokázal, a Fontana nebol ochotný svoje tajomstvo vyzradi. Cardanova kniha preto vyšla bez tohto výsledku v roku

23. Scipione Del Ferro Professor De Matemática Italiano Nascido Em Translate this page scipione del ferro Filho de Floriano, empregado de uma fábrica de papel, ede Filippa ferro. Pouco se sabe sobre a sua educação mas deve ter estudado na http://www.educ.fc.ul.pt/docentes/opombo/seminario/renascenca/scipionedelferro.h

[Home] [O Episódio] [Os personagens] [O problema] ... [Quem somos] Scipione del Ferro Professor de matemática italiano nascido em Bolonha, que descobriu a resolução das equações de terceiro grau (1520), as cúbicas mistas, porém não tornou pública a sua descoberta, divulgando-a apenas entre os seus alunos. Convém lembrar que a solução das quadráticas ax +bx+c=0 ) era conhecida pelos babilónios e que até meados do século XVI o ZERO não era usado na Europa. Também não se usava os números negativos e, portanto não se sabia que as quadráticas tinham duas soluções. Filho de Floriano, empregado de uma fábrica de papel, e de Filippa Ferro. Pouco se sabe sobre a sua educação mas deve ter estudado na Universidade de Bolonha, uma das mais antigas e tradicionais universidades medievais. Sabe-se que foi nomeado professor de aritmética e geometria dessa universidade (1496), ali permanecendo pelo resto da vida. Nos anos de 1501 e 1502 Ferro conheceu Pacioli pois eram os dois professores na universidade de Bolonha. Nessa altura, Pacioli afirmava ser impossível a solução da cúbica . Ferro iniciou então a sua pesquisa para obter a resolução da cúbica tendo obtido bons resultados. Os seus escritos não chegaram aos nossos dias, mas sabe-se que o seu caderno de anotações foi passado, após a sua morte em Bolonha, ao seu genro, Hannibal della Nave, que o teria mostrado a

24. Index.htm Translate this page Em 1515, scipione del ferro conseguiu determinar um método que lhe permitiuencontrar a scipione del ferro manteve em segredo o seu método de resolução, http://www.educ.fc.ul.pt/docentes/opombo/seminario/renascenca/

Um Episódio Célebre da Matemática Renacentista Italiana [O Episódio] [Os personagens] [O problema] [Exemplos] ... [Quem somos] Entre 1501 e 1502 Scipione del Ferro conheceu Pacioli que na altura dizia que as cúbicas não tinham solução. Ferro iniciou então uma pesquisa para encontrar a solução da cúbica obtendo bons resultados. Em 1515, Scipione del Ferro conseguiu determinar um método que lhe permitiu encontrar a solução x +px=q . No entanto, não o chegou a publicar. Apenas o revelou a dois discípulos seus: Della Nave e Antonio Fior, dando a demonstração apenas ao primeiro. Scipione del Ferro manteve em segredo o seu método de resolução, pois era costume, na época, os sábios desafiarem os seus rivais para a resolução de problemas, beneficiando o vencedor, alem da fama, de uma recompensa em dinheiro. Em 1530 Tonini da Coi propôs a Tartaglia um desafio que consistia na resolução das duas equações x +8x=1000 e x Tartaglia não respondeu pois não sabia solucionar tais problemas.

25. Algebra In The Renaissance scipione del ferro (c.1465 1526), one of the teachers at the University ofBologna, found an algorithm for the solution of the cubic equation sometime http://www.maths.wlv.ac.uk/mm2217/ar.htm

The Development of Algebra in the Renaissance Notation The existing knowledge of both arithmetic and algebra came to Western Europe through the study of Arab mathematics. But not until the fifteenth century were symbols used, as Diophantus had done, for the commonest arithmetical operations. About that time, the symbols and for plus and minus were usual in Italy and France. They had been introduced by Lucia Pacioli (1445-1514) as abreviations for the words piu (more) and meno ( less). The symbols + and - occurred in Germany in 1480. These symbols were first to be printed in 1489 in a book by the Rechenmeister Johan Widmann. The symbols and for multiplication and division do not appear until the 17th century. At this time, the sign for equality caught on, although it occurs earlier in an algebra textbook by the englishman Robert Recorde (1510-58), which appeared in 1557. Recorde introduced the sign with the justification that no two things can be more equal than a pair of parallel lines. Albert Girard (1595-1632) seems to have been the first to give negative solutions full recognition. Also, the interpretation of negative numbers as line segments in the opposite direction was taken up again. However a precise foundation for the arithmetic of negative numbers had to wait until the beginning of the nineteenth century. Complex numbers were used from the 16th century, initially to aid in the solution of cubic equations, but these were viewed with even more scepticism.

26. History Of Algebra scipione del ferro was a profeesor of mathematics at Bologna, Italy. del ferrohad rediscovered the trick for solving equations of the form http://www.ux1.eiu.edu/~cfprc/clsrm/alg4810/histalg.html

The History of Algebra Let me begin in the middle, for my story truly begins there. The rain poured from the sky in torrents. It was peculiar, since it was not the rainy season in Venice. The forces of nature had turned against the city at a most inopportune moment. Ah ... Venice. The streets were filled with that thick mud which clings to ones sandals like a dull slippery weight. Still, there was an enormous crowd gathered in St. Mark's Square ringing the Opera House. And though the auditorium was filled, the overflow crowd lingered outside in the rain waiting ... not for the beautiful sounds of arias, but for news of a contest of wits and wills. Inside the auditorium the noise was deafening. As the arch-deacon rose slowly from his chair in the middle of a bank of chairs to the left side of the stage and rang the bell, a hush fell over the audience. The arch-deacon, acting as master of ceremonies, introduced the competitors, Nicoli Tartaglia and Antonio Maria Fiore, who sat at tables covered with books and papers in the middle of the stage. Tartaglia said nothing, simply nodding his bushy head of unkempt hair to the introductory remarks. Fiore walked out to the apron of the stage and thanked the organizers and the arch-deacon for his generous words of introduction. Tartaglia, who looked more like a bear than a man, appeared to be upset, nervous and pale. Fiore seemed more self assured... Project 1 Due June 18th Complete the story above in narrative style. The project should be about 600 to 1000 words. Include at least two references at the end of the story and some explanation of the mathematics. The project can be written in HTML. I will post on www those written in HTML. Simply email the HTML document to

27. Disputas Matemáticas En El Siglo XVI Translate this page Sería scipione del ferro, hijo de un imprentero de Bolonia, el primero en scipione del ferro nació el 6 de Febrero de 1465 en Bolonia ciudad en la que http://www.portalplanetasedna.com.ar/disputas_matematicas.htm

DISPUTAS MATEMATICAS Fuente: Matemáticos Que Hicieron La Historia de Alejandro García Venturini Introducción: Erase el siglo XVI, en la Italia renacentista, tres notable matemáticos conocidos como Del Ferro, Tartaglia y Cardano, que trabajaban arduamente en busca de encontrar un método práctico para resolver una ecuación matemática, conocida como de tercer grado. Desde la época de los babilonios, 2500 a.d.C.,cuando estos ya conocían la solución de las ecuaciones de segundo grado, (para aplicarlo a sus construcciones) y hasta esa fecha no hubo avances significativos con respecto a este tema. Unos cuántos años antes los famosos matemáticos medievales Fibonacci y Luca Pacioli, habían tratado someramente estos problemas, pero sólo resolviendo algunos casos particulares, e inclusive sin llegar a una demostración racional de tales soluciones. Sería Scipione del Ferro, hijo de un imprentero de Bolonia, el primero en estudiar con un método ortodoxo, la obtención de las raíces (soluciones) de estas funciones matemáticas. Más tarde otras grandes figuras continuarian con estos trabajos, pero sin antes, atravesar un dificil camino de encuentros violentos, dramáticos y deshonestos, por el afán de lograr la primacía en la concrención de sus búsqueda. A través de sus biografía se reflejará esta historia de tristes disputas, y que muestra también la pasión que dominaba a estos genios de los números, que muchas veces viviendo en un ámbito de miserias humanas y materiales , no se dejaban vencer por la adversidad, y siempre se esforzaban para llegar a conocer la verdad de estos dificultosos problemas.

28. Tartaglia Et Cardan Translate this page Remarque scipione del ferro (1465-1 526) fut un précurseur de Tartaglia dansce domaine mais les papiers de celui-ci sont perdus. http://www.math93.com/Tartaglia-Cardan.htm

skip to: page content links on this page site navigation footer (site information) ... Kelkoo visiteurs ] Alexandrie Les Symboles Les nombres Etymologie ... Equations Liens sur la page Tartaglia Cardan Le conflit Evariste galois Tartaglia (Brescia, 1500?-Venise, 1557) Nicolo Fontana était surnommé Tartaglia (le bègue) parce que, gravement blessé par l'épée d'un cavalier français, entré dans la grande église de Brescia le 19 février 1512 dans laquelle il se réfugiait avec sa mère, il lui en restait des difficultés d'élocution. (Les troupes françaises étaient menées par le terrible Gaston de Foix, surnommé "foudre d'Italie".) On raconte que le père de Niccolo (Fontana) avait engagé un professeur pour instruire son fils de 6 ans et que celui-ci arrêta les cours (-après la mort de Monsieur Fontana-) alors qu'il ne lui avait enseigné qu'un tiers de l'alphabet (de A à I). Il poursuivit seul son apprentissage. "Tout ce que je sais, je l'ai appris en travaillant sur les œuvres d'hommes défunts", disait-il. Cependant il est surtout célèbre par la découverte d'une méthode de résolution des équations du 3° degré ; cette découverte, faite en 1537, fut dévoilée à Cardan en 1539 et c'est celui-ci qui la diffusa (on lui donne le nom de "méthode de Cardan" encore aujourd'hui dans les livres de premier cycle universitaire).

29. Historia Matematica Mailing List Archive: Re: [HM] The Tartaglia/Cardano Controv Anonio Maria Fiore got the information on the cubic from scipione del ferro. He was in the possession of del ferro s papers Cardano and Ferrari saw http://sunsite.utk.edu/math_archives/.http/hypermail/historia/may99/0184.html

Re: [HM] The Tartaglia/Cardano controversy Prof. Lueneburg luene@mathematik.uni-kl.de Fri, 21 May 1999 09:35:15 +0200 (MESZ) Messages sorted by: [ date ] [ thread ] [ subject ] [ author ] Next message: Milo Gardner: "Re: [HM] Roman Numerals" Previous message: Prof. Lueneburg: "Re: [HM] Earliest priority dispute?" In reply to: Prof. Lueneburg: "Re: [HM] The Tartaglia/Cardano controversy" On Thur, May 20, Dr. John W. Dawson, Jr. wrote among other things: The plural "students" here is actually a dual. Annibale dalla Nave and Anonio Maria Fiore got the information on the cubic from Scipione del Ferro. Annibale dalla Nave was the son-in-law of del Ferro and his successor as a professor of mathematics at the University of Bologna. He was in the possession of del Ferro's papers Cardano and Ferrari saw visiting Bologna. Antonio Maria Fiore was the one who challenged Tartaglia. The thirty problems he posed to Tartaglia were published by Tartaglia in Quesito XXXI. They all lead to equations of the form x^3 + px = q except the 16th one which leads to the equation 14 + x = x^5 + 2x^3. One of the

30. Historia Matematica Mailing List Archive: Re: [HM] Earliest Priority Dispute? very similar formula in the handwriting of scipione del ferro, the man who hadfirst made the breakthrough. And so, in this infamous http://sunsite.utk.edu/math_archives/.http/hypermail/historia/may99/0206.html

Re: [HM] Earliest priority dispute? llusk@ccmail.gc.cc.fl.us Tue, 25 May 99 11:31:18 -0600 Messages sorted by: [ date ] [ thread ] [ subject ] [ author ] Next message: Dirk Schlimm: "Re: [HM] well-known saying" Previous message: Prof. Lueneburg: "Re: [HM] Earliest priority dispute?" Maybe in reply to: Phill Schultz: "[HM] Earliest priority dispute?" Next in thread: Michael Fried: "Re: [HM] Earliest priority dispute?" First Prof. Lueneburg wrote: Then Arturo Mena replied: Prof. Lueneburg, I assume, is referring to Ferrari's second letter which was sent to Tartaglia on 1 April, 1547, which is known in the US as "April Fool's Day." (Little pun intended.) He (Ferrari) claims to have been present in Cardano's house when Tartaglia gave Cardano his 'inventiunculam', and as Prof. Lueneburg states, that no promises were made, and, in effect or by implication, the gift was in return for Cardano's hospitality. (Must have been a wonderful evening.) As Arturo Mena points out, in assessing the value of this statement one must not forget of Ferrari's strong partisanship towards Cardano.

31. CATHOLIC ENCYCLOPEDIA: Nicolo Tartaglia he had shown the superiority of his methods to the method previously obtainedby scipione del ferro (d. 1526) and known at that time to del Fiore alone. http://www.newadvent.org/cathen/14461c.htm

Home Encyclopedia Summa Fathers ... Z (T ARTALEA TARTAGLIA'S Quesiti (Venice, 1554); BITTANTI, (Brescia, 1871); BUONCOMPAGNI, ed. CREMONA AND BELTRAMI, in Collectanea math., Mem. Dom. Chelini (Milan, 1881), 363-410; GIORDANI, I sei cartelli di mat. disfida primamente intorno alla generale risoluzione delle equazioni cubiche con sei Contro-Cartelli in risposta di N. T. (Milan, 1876); ROSSI, Elogi di Bresciani illustri (Brescia, 1620), 386; TONNI-BAZZA, in R. Accad. dei Lincei, Rendiconti, Classe d. sci. fis. , ser. 5, X, pt. II (Rome, 1901), 39-42; TONNI-BAZZA, , loc. cit., ser. 5, XIII, pt. I (Rome, 1904), 27-30. PAUL H. LINEHAN Transcribed by Thomas J. Bress The Catholic Encyclopedia, Volume XIV Nihil Obstat, July 1, 1912. Remy Lafort, S.T.D., Censor Imprimatur. +John Cardinal Farley, Archbishop of New York If an ad appears here that contradicts Catholic teachings, please click here to notify the webmaster. Praise Jesus Christ in His Angels and in His Saints New Advent is dedicated to the Immaculate Heart of Mary

32. HistoryMole: Mathematics (0190-) 1520, scipione ferro develops a method for solving cubic equations. 1520,scipione del ferro, Italian mathematician, solved cubic equations for the http://www.historymole.com/cgi-bin/main/results.pl?type=theme&theme=Mathematics

33. Wikipedia:Encarta Encyclopedia Topics/7 - Wikipedia, The Free Encyclopedia Ferreting Kathleen Mary Ferrier or Ferrier, Kathleen Mary scipione delferro or ferro, scipione del Fescennine verses Festivals and feasts http://en.wikipedia.org/wiki/Wikipedia:Encarta_Encyclopedia_topics/7

Wikimedia needs your help in its 21-day fund drive. See our fundraising page Over US$155,000 has been donated since the drive began on 19 August. Thank you for your generosity! Wikipedia:Encarta Encyclopedia topics/7 From Wikipedia, the free encyclopedia. Wikipedia:Encarta Encyclopedia topics View 79 deleted edits Wikipedia does not have an article with this exact name. Start the Encarta Encyclopedia topics/7 article Search for Encarta Encyclopedia topics/7 in other articles. Look for Encarta Encyclopedia topics/7 in Wiktionary, our sister dictionary project. Look for Encarta Encyclopedia topics/7 in the Commons, our repository for free images, music, sound, and video. Look for pages linking to this page If you have created this page in the past few minutes and it has not yet appeared, it may not be visible due to a delay in updating the database. Try purge , otherwise please wait and check again later before attempting to recreate the page. If you created an article under this title previously, it may have been deleted. See candidates for speedy deletion for possible reasons.

34. Cardano, Geronimo: Information From Answers.com But scipione del ferro partially solved the cubic early in the 16th century,keeping his solution to himself. Before his death, however, del ferro passed http://www.answers.com/topic/cardano-geronimo

showHide_TellMeAbout2('false'); Business Entertainment Games Health ... More... On this page: Encyclopedia Essay Or search: - The Web - Images - News - Blogs - Shopping Cardano, Geronimo Encyclopedia Cardano, Geronimo jār´ nēmō k¤rd¤ nō ) , 1501–76, Italian physician and mathematician. His works on arithmetic and algebra established his reputation. Barred from official status as a physician because of his illegitimate birth, he practiced as a medical astrologer. His major work, De subtilitate rerum (1550), on natural history, is perceptive and implies a grasp of evolutionary principles. His book on games of chance represents the first organized theory of probability. Cardano described a tactile system similar to Braille for teaching the blind and thought it possible to teach the deaf by signs. Bibliography See his The Book of my Life (1643, tr. 1930); studies by O. Ore (with a tr. of Cardano's Book of Games of Chance, 1965) and A. Wykes (1969). Essay A great scoundrel In the Italian Renaissance, the professions of scientist and mathematician were just beginning to be defined. One such scholar was Girolamo Cardano, known in English as Jerome Cardan. Cardan's basic source of income was his work as a physician, but he was also at various times a professor of mathematics at the universities of Milan, Pavia, and Bologna. Other sources of income included gambling and astrology; however, he was imprisoned for heresy after he cast Christ's horoscope. Cardan's reputation as a mathematician is deservedly great, but marred by scandal. His 1545 work

35. Cubic Formula -- From MathWorld at the University of Bologna by the name of scipione del ferro (ca. 14651526).While del ferro did not publish his solution, he disclosed it to his http://mathworld.wolfram.com/CubicFormula.html

INDEX Algebra Applied Mathematics Calculus and Analysis Discrete Mathematics ... Alphabetical Index DESTINATIONS About MathWorld About the Author Headline News ... Random Entry CONTACT Contribute an Entry Send a Message to the Team MATHWORLD - IN PRINT Order book from Amazon Algebra Algebraic Equations Algebra ... Polynomials Cubic Formula The cubic formula is the closed-form solution for a cubic equation , i.e., the roots of a cubic polynomial . A general cubic equation is of the form (the coefficient of may be taken as 1 without loss of generality by dividing the entire equation through by Mathematica can solve cubic equations exactly using the built-in command Solve a3 x^3 + a2 x^2 + a1 x + a0 == x ]. The solution can also be expressed in terms of Mathematica algebraic root objects by first issuing SetOptions Roots The solution to the cubic (as well as the quartic ) was published by Gerolamo Cardano (1501-1576) in his treatise Ars Magna . However, Cardano was not the original discoverer of either of these results. The hint for the cubic had been provided by , while the quartic had been solved by Ludovico Ferrari. However

36. Recupero Edificio Via Scipione Dal Ferro/Bando Translate this page DI VIA scipione DAL ferro N. 12, DA ADIBIRE AD UFFICI del QUARTIERE SAN VITALE (CIP Fac-simile dichiarazione scipione dal ferro dichiarazione.doc http://urp.comune.bologna.it/WebCity/WebCity.nsf/0/5304d5cc880764a2c125700400233

37. Recupero Edificio Via Scipione Dal Ferro/Esito scipione DALFERRO N. 12, DA ADIBIRE AD UFFICI del QUARTIERE SAN VITALE (CIP C1756) http://urp.comune.bologna.it/WebCity/WebCity.nsf/0/83c276b2d359bc12c125700400233

38. \documentclass{article} \usepackage{amstex} \usepackage{amssymb in modern notation the case $y^3+cy=d$ where $c$ and $d$ are positive, wassolved by scipione del ferro (14651626) early in the sixteenth century. http://www.york.ac.uk/depts/maths/histstat/cubic.htm

LaTeX source for solution of cubic and quartic

39. Giuseppa Carr Ferro - ResearchIndex Document Query for polynomials of degrees 3 and 4 (scipione del ferro, Nicolo Tartaglia, LudovicoFerrari, Geronimo epubs.siam.org/sambin/getfile/SIREV/articles/28855.ps. http://citeseer.ist.psu.edu/cis?q=Giuseppa Carrà Ferro

40. Biographie Cardan Translate this page Il faut leur adjoindre en ce domaine scipione del ferro, 1465-1526, Il semblebien que ce soit scipione del ferro qui ait le premier résolu les http://mathematiques.ac-bordeaux.fr/viemaths/hist/mthacc/cardan.htm

e Al Khwarizmi Ars Magna C'est dans l' Ars Magna nombres complexes (-15) et 5 - (-15), et constate que leur produit et leur somme sont tous deux des nombres positifs ordinaires : 40 et 10. Il qualifie lui-même ces considérations de "subtiles et inutiles". Toujours dans le contexte des équations du troisième degré, c'est Rafaele Bombelli qui systématisera l'emploi des nombres complexes dans le cas où les trois racines sont réelles. , dans son

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