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| {{Redirect|Cardanus|the lunar crater|Cardanus (crater)|the [[stag beetle]]|Cardanus (beetle)}}
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| {{Infobox scientist
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| |name = Gerolamo Cardano
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| |image = Jerôme Cardan.jpg
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| |image_size = 250px
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| |caption = Gerolamo Cardano
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| |birth_date = {{Birth date|1501|9|24|df=yes}}
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| |birth_place = [[Pavia]]
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| |death_date = {{Death date and age|1576|9|21|1501|9|24|df=yes}}
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| |death_place = [[Rome]]
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| |residence =
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| |citizenship =
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| |nationality = [[Italy|Italian]]
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| |ethnicity =
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| |field = [[Mathematics]]<br>[[Medicine]]
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| |work_institutions =
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| |alma_mater = [[University of Pavia]]
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| |doctoral_advisor =
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| |doctoral_students =
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| |known_for = [[Algebra]]
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| |author_abbrev_bot =
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| |author_abbrev_zoo =
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| |influences =
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| |influenced =
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| |prizes =
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| |religion =
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| |footnotes =
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| |signature =
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| }}
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| '''Gerolamo''' (or '''Girolamo''', or '''Geronimo''') '''Cardano''' ({{lang-fr|Jérôme Cardan}}; {{lang-la|Hieronymus Cardanus}}; 24 September 1501 – 21 September 1576) was an [[Italy|Italian]] [[Renaissance]] [[mathematician]], [[physician]], [[astrologer]] and [[gambler]].<ref>{{cite book|last=Patty|first=Peter Fletcher, Hughes Hoyle, C. Wayne|title=Foundations of Discrete Mathematics|year=1991|publisher=PWS-KENT Pub. Co.|location=Boston|isbn=0-53492-373-9|edition=International student ed.|page=207|quote=Cardano was a physician, astrologer, and mathematician.... [He] supported his wife and three children by gambling and casting horoscopes.}}</ref> He wrote more than 200 works on medicine, mathematics, physics, philosophy, religion, and music.<ref name=Westfall>{{cite web|last=Westfall|first=Richard S.|title=Cardano, Girolamo|url=http://galileo.rice.edu/Catalog/NewFiles/cardano.html|work=The Galileo Project |publisher=rice.edu |accessdate=2012-07-19 |archiveurl=http://www.webcitation.org/69HDd2llY |archivedate=2012-07-19}}</ref> His gambling led him to formulate elementary rules in [[Probability#History|probability]], making him one of the founders of the field.
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| ==Early life and education==
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| He was born in [[Pavia]], [[Lombardy]], the [[illegitimate]] child of [[Fazio Cardano]], a mathematically gifted [[lawyer]], who was a friend of [[Leonardo da Vinci]]. In his autobiography, Cardano claimed that his mother had attempted to [[abortion|abort]] him. Shortly before his birth, his mother had to move from [[Milan]] to [[Pavia]] to escape the [[Black Death|Plague]]; her three other children died from the disease.
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| In 1520, he entered the [[University of Pavia]] and later in [[Padua]] studied medicine. His eccentric and confrontational style did not earn him many friends and he had a difficult time finding work after his studies ended. In 1525, Cardano repeatedly applied to the College of Physicians in Milan, but was not admitted owing to his combative reputation and illegitimate birth.
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| Eventually, he managed to develop a considerable reputation as a physician and his services were highly valued at the courts. He was the first to describe [[typhoid fever]]. In 1553 he cured the Scottish [[John Hamilton (archbishop of St Andrews)|Archbishop of St Andrews]] of a disease that had left him speechless and was thought incurable. The diplomat [[Thomas Randolph (diplomat)|Thomas Randolph]] recorded the "merry tales" rumoured about his methods still current in Edinburgh nine years later.<ref>''Calendar State Papers Scotland'', vol.1 (1898), p.592: Melville, James, ''Memoirs of his own life'', Brookman, (1833), 21, 73</ref> Cardano himself wrote that the Archbishop had been short of breath for ten years, and after the cure was effected by his assistant, he was paid 1,400 gold crowns.<ref>Cardanus, Gerolamo, [http://books.google.co.uk/books?id=blA9AAAAcAAJ&source=gbs_navlinks_s ''De Propria Vita Liber: His Own Life'', Amsterdam, (1654)], pp.136-7, (Latin)</ref>
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| ==Mathematics==
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| Today, he is best known for his achievements in [[algebra]]. Cardano was the first mathematician to make systematic use of numbers less than zero.<ref>[[Isaac Asimov]], ''Asimov On Numbers'', published by [[Pocket Books]], a division of [[Simon & Schuster]], 1966, 1977, page 119.</ref> He published the solutions to the [[cubic equation|cubic]] and [[quartic equation]]s in his 1545 book ''[[Ars Magna (Gerolamo Cardano)|Ars Magna]]''. The solution to one particular case of the cubic equation <math>ax^3+bx+c=0</math><ref>{{cite book|last=Burton|first=David|title=The History of Mathematics: An Introduction|edition=7th (2010)|publisher= [[McGraw-Hill]]|location=New York}}</ref> (in modern notation), was communicated to him by [[Niccolò Fontana Tartaglia]] (who later claimed that Cardano had sworn not to reveal it, and engaged Cardano and in a decade-long fight) in the form of a poem <ref>Katz, Victor J. A History of Mathematics: An Introduction. 3rd ed. Boston: Pearson Education, 2009. Print.</ref> The quartic was solved by Cardano's student [[Lodovico Ferrari]]. Both were acknowledged in the foreword of the book, as well as in several places within its body. In his exposition, he acknowledged the existence of what are now called [[imaginary number]]s, although he did not understand their properties (described for the first time by his Italian contemporary [[Rafael Bombelli]], although the necessary mathematical theory of [[field (mathematics)|fields]] was not to be developed for hundreds of years). In ''Opus novum de proportionibus'' he introduced the [[binomial coefficient]]s and the [[binomial theorem]].
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| [[File:Gerolamo Cardano (colour).jpg|thumb|left|200px|Portrait of Cardano on display at the School of Mathematics and Statistics, [[University of St Andrews]].]]
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| Cardano was notoriously short of money and kept himself solvent by being an accomplished gambler and [[chess]] player. His book about games of chance, ''Liber de ludo aleae'' ("Book on Games of Chance"), written around 1564,<ref name="LudoYear">In Chapter 20 of ''Liber de Ludo Aleae'' he describes a personal experience from 1526 and then adds that "thirty-eight years have passed" [elapsis iam annis triginta octo]. This sentence is written by Cardano around 1564, age 63.</ref> but not published until 1663, contains the first systematic treatment of [[probability]],<ref>Katz, ibid., p. 488</ref> as well as a section on effective cheating methods. He used the game of throwing dice to understand the basic concepts of probability. He was aware of the multiplication rule for independent events but was not certain about what values should be multiplied. <ref>Katz, ibid., p. 488</ref> Cardano invented several mechanical devices including the [[combination lock]], the [[gimbal]] consisting of three concentric rings allowing a supported [[compass]] or [[gyroscope]] to rotate freely, and the [[driveshaft|Cardan shaft]] with [[universal joint]]s, which allows the transmission of rotary motion at various angles and is used in vehicles to this day. He studied [[hypocycloid]]s, published in ''de proportionibus'' 1570. The generating circles of these hypocycloids were later named Cardano circles or cardanic circles and were used for the construction of the first high-speed [[Printing press#The Industrial Revolution|printing presses]].<ref>{{cite book |url=http://books.google.co.uk/books/about/Jerome_Cardan.html?id=GNpEPgAACAAJ&redir_esc=y |title=Jerome Cardan: A Biographical Study |publisher= [[Dodo Press]] }}</ref>
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| He made several contributions to hydrodynamics and held that [[perpetual motion]] is impossible, except in celestial bodies. He published two [[encyclopedia]]s of natural science which contain a wide variety of inventions, facts, and occult superstitions. He also introduced the [[Cardan grille]], a cryptographic tool, in 1550.
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| Someone also assigned to Cardano the credit for the invention of the so-called ''[[Cardano's Rings]]'', also called [[Baguenaudier|Chinese Rings]], but it is very probable that they are more ancient than Cardano.
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| Significantly, in the history of [[education of the deaf]], he said that deaf people were capable of using their minds, argued for the importance of teaching them, and was one of the first to state that deaf people could learn to read and write without learning how to speak first. He was familiar with a report by [[Rudolph Agricola]] about a deaf mute who had learned to write.
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| ==''De Subtilitate'' 1552==
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| As quoted from [[Charles Lyell|Charles Lyell's]] ''[[Principles of Geology]]'':
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| <blockquote>
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| The title of a work of Cardano's, published in 1552, ''De Subtilitate'' (corresponding to what would now be called [[Friedrich_Wilhelm_Joseph_Schelling#Naturphilosophie|transcendental philosophy]]), would lead us to expect, in the chapter on minerals, many far fetched theories characteristic of that age; but when treating of petrified shells, he decided that they clearly indicated the former sojourn of the sea upon the mountains.<ref>[[wikiquote:Charles Lyell|Charles Lyell]], ''[http://books.google.com/books?id=mmIOAAAAQAAJ& Principles of Geology]'', 1832, p.29</ref>
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| </blockquote>
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| == Later years ==
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| Cardano's eldest and favorite son was executed in 1560 after he confessed to having [[poison]]ed his [[cuckold]]ing wife. His other son was a gambler, who stole money from him. He allegedly cropped the ears of one of his sons. Cardano himself was accused of [[Christian heresy|heresy]] in 1570 because he had computed and published the [[horoscope]] of [[Jesus]] in 1554. Despite numerous stories to the contrary, it is not true that his own son contributed to the prosecution after being bribed by [[Niccolò Fontana Tartaglia|Tartaglia]], as Tartagalia died 13 years previously. See http://arxiv.org/ftp/arxiv/papers/1308/1308.2181.pdf. He was arrested, had to spend several months in prison and was forced to abjure his [[professor]]ship. He moved to Rome, received a lifetime [[Annuity (financial contracts)|annuity]] from [[Pope Gregory XIII]] (after first having been rejected by [[Pope Pius V]]) and finished his [[autobiography]]. It appears that he was still practicing medicine up to his death in 1576.<ref name=Westfall />
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| The date of his death is disputed, but a death year is given as 1576. <ref>Katz, ibid., p. 401</ref>
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| ==References in literature==
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| [[Richard Hinckley Allen]] tells of an amusing reference made by [[Samuel Butler (poet)|Samuel Butler]] in his book ''[[Hudibras]]'':
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| <poem>
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| Cardan believ'd great states depend
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| Upon the tip o'th' Bear's tail's end;
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| That, as she wisk'd it t'wards the Sun,
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| Strew'd mighty empires up and down;
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| Which others say must needs be false,
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| Because your true bears have no tails.
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| </poem>
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| [[Alessandro Manzoni]]'s novel ''[[I Promessi Sposi]]'' portrays a pedantic scholar of the obsolete, Don Ferrante, as a great admirer of Cardano. Significantly, he values him only for his superstitious and astrological writings; his scientific writings are dismissed because they contradict [[Aristotle]], but excused on the ground that the author of the astrological works deserves to be listened to even when he is wrong.
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| English novelist E M Forster's ''[[Abinger Harvest]]'', a 1936 volume of essays, authorial reviews and a play, provides a sympathetic treatment of Cardano in the section titled 'The Past'. Forster believes Cardano was too absorbed in "self-analysis that he often forgot to repent of his bad temper, his stupidity, his licentiousness, and love of revenge" (212).<ref>Forster, E. M.</ref>
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| ==Works==
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| * ''De malo recentiorum medicorum usu libellus'', Venice, 1536 (on medicine).
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| * ''Practica arithmetice et mensurandi singularis'', Milan, 1577 (on mathematics).
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| * ''[[Ars Magna (Gerolamo Cardano)|Artis magnae, sive de regulis algebraicis]]'' (also known as ''Ars magna''), Nuremberg, 1545 (on algebra).<ref>http://www.filosofia.unimi.it/cardano/testi/operaomnia/vol_4_s_4.pdf An electronic copy of his book ''[[Ars Magna (Gerolamo Cardano)|Ars Magna]]'' (in Latin)</ref>
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| * ''De immortalitate'' (on alchemy).
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| * ''[http://archimedes.mpiwg-berlin.mpg.de/cgi-bin/toc/toc.cgi?dir=carda_propo_015_la_1570;step=thumb Opus novum de proportionibus]'' (on mechanics) (Archimedes Project).
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| * ''Contradicentium medicorum'' (on medicine).
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| * ''De subtilitate rerum'', Nuremberg, [[Johann Petreius]], 1550 (on natural phenomena).
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| * ''De libris propriis'', Leiden, 1557 (commentaries).
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| * ''De varietate rerum'', Basle, Heinrich Petri, 1559 (on natural phenomena).
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| * ''Neronis encomium'', Basle, 1562.
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| * ''De Methodo medendi,'' 1565
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| * ''Opus novum de proportionibus numerorum, motuum, ponderum, sonorum, aliarumque rerum mensurandarum. Item de aliza regula'', Basel, 1570.
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| * ''De vita propria'', 1576 ([[autobiography]]); a later edition, [http://books.google.co.uk/books?id=blA9AAAAcAAJ&source=gbs_navlinks_s ''De Propria Vita Liber'', Amsterdam, (1654)]
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| * ''Liber de ludo aleae'', ("On Casting the [[Dice|Die]]")<ref>p963, [[Jan Gullberg]], Mathematics from the birth of numbers, W. W. Norton & Company; ISBN 0-393-04002-X ISBN 978-0393040029</ref> posthumous (on probability).
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| * ''De Musica'', ca 1546 (on music theory), posthumously published in ''Hieronymi Cardani Mediolensis opera omnia, Sponius'', Lyons, 1663
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| * ''De Consolatione'', Venice, 1542
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| * ''HIERONY-||MI CARDANI ME=||DIOLANENSIS MEDICI,|| DE RERVM VARIETATE, LI-||BRI XVII. Iam denuò ab in numeris || mendis summa cura ac studio repur-||gati, & pristino nito-||ri restituti.|| ADIECTVS EST CAPITVM, RE-||rum & sententiarum ... || INDEX utilissimus.||'', Basel, 1581 [http://nbn-resolving.de/urn:nbn:de:hbz:061:2-30760 Digital edition] by the [[University and State Library Düsseldorf]]
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| ==Notes==
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| {{Reflist}}
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| ==References==
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| * Cardano, Girolamo, ''Astrological Aphorisms of Cardan''. Edmonds, WA: Sure Fire Press, 1989.
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| * Cardano, Girolamo, ''The Book of My Life.'' trans. by Jean Stoner. New York: [[New York Review of Books]], 2002.
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| * [[Øystein Ore|Ore, Øystein]]: ''Cardano, the Gambling Scholar''. Princeton, 1953.
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| * Cardano, Girolamo, ''Opera omnia'', Charles Sponi, ed., 10 vols. Lyons, 1663.
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| * [[William Dunham (mathematician)|Dunham, William]], ''Journey through Genius'', Chapter 6, 1990, [[John Wiley and Sons]]. ISBN 0-471-50030-5. Discusses Cardano's life and solution of the cubic equation.
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| * Sirasi, Nancy G. ''The Clock and the Mirror: Girolamo Cardano and Renaissance Medicine.'' [[Princeton University Press]],1997.
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| * [[Anthony Grafton|Grafton, Anthony]], ''[http://www.hup.harvard.edu/catalog.php?isbn=9780674006706 Cardano's Cosmos: The Worlds and Works of a Renaissance Astrologer.]'' [[Harvard University Press]], 2001.
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| * Morley, Henry ''The life of Girolamo Cardano, of Milan, Physician'' 2 vols. [[Chapman and Hall]], London 1854.
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| * [[Artur Ekert|Ekert, Artur]] "Complex and unpredictable Cardano". ''[[International Journal of Theoretical Physics]]'', Vol. 47, Issue 8, pp. 2101–2119. arXiv e-print (arXiv:0806.0485).
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| * Girolamo Cardano ''Nero: an Exemplary Life'' Inckstone 2012, translation in English of the ''Neronis Encomium''.
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| ==External links==
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| {{Wikiquote}}
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| * [http://www.arturekert.org/Site/Varia_files/NewCardano.pdf A recreational article about Cardano and the discovery of the two basic ingredients of quantum theory, probability and complex numbers.]
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| * {{MacTutor Biography|id=Cardan}}
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| * http://it.wikisource.org/wiki/Categoria:Testi_in_cui_%C3%A8_citato_Girolamo_Cardano
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| * [http://www.chlt.org/sandbox/lhl/dsb/page.64.php History of Science Collection] at [[Linda Hall Library]]
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| * ''[http://www.gutenberg.org/etext/19600 Jerome Cardan, a Biographical Study]'', 1898, by William George Waters, from [[Project Gutenberg]]
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| * {{cite web|url=http://www.newadvent.org/cathen/03332a.htm|title=Girolamo Cardan|work=[[Catholic Encyclopedia]]}}
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| * ''[http://www.filosofia.unimi.it/cardano/index.php Girolamo Cardano, Strumenti per la storia del Rinascimento in Italia settentrionale (in Italian)] and [http://translate.google.com/translate?hl=en&sl=it&u=http://www.filosofia.unimi.it/cardano/index.php%3Fpage%3Dbiblio&sa=X&oi=translate&resnum=2&ct=result&prev=/search%3Fq%3Dhttp://www.filosofia.unimi.it/cardano/index.php%26hl%3Den%26sa%3DG English]''
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| *[http://hos.ou.edu/galleries//16thCentury/Cardano/ Online Galleries], History of Science Collections, [[University of Oklahoma Libraries]] High resolution images of works by and/or portraits of Gerolamo Cardano in .jpg and .tiff format.
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| * [[E. M. Forster|Forster, E.M.]] 'Cardan' in ''Abinger Harvest'' (1936). Middlesex, UK: [[Penguin Books]] Ltd. pp. 208–221.
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| * [http://arxiv.org/ftp/arxiv/papers/1308/1308.2181.pdf "Cardano v Tartaglia: The Great Feud Out of Bounds"] by Tony Rothman
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| {{Authority control|VIAF=27062058}}
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| {{Persondata
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| |NAME = Cardano, Gerolamo
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| |ALTERNATIVE NAMES = Cardano, Girolamo; Cardan, Jerome; Cardanus, Hieronymus
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| |SHORT DESCRIPTION = [[Italy|Italian]] [[Renaissance]] [[mathematician]], [[physician]], [[astrologer]] and [[gambler]]
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| |DATE OF BIRTH = 24 September 1501
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| |PLACE OF BIRTH = [[Pavia]]
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| |DATE OF DEATH = 21 September 1576
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| |PLACE OF DEATH = [[Rome]]
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| }}
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| {{DEFAULTSORT:Cardano, Gerolamo}}
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| [[Category:1501 births]]
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| [[Category:1576 deaths]]
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| [[Category:16th-century Latin-language writers]]
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| [[Category:16th-century Italian mathematicians]]
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| [[Category:16th-century Italian physicians]]
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| [[Category:Italian astrologers]]
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| [[Category:Italian inventors]]
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| [[Category:People from Pavia]]
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