Biografia de girolamo cardano books

Gerolamo Cardano

Italian Renaissance mathematician, physician, astrologer (1501–1576)

"Cardanus" redirects here. For the lunar scissure, see Cardanus (crater).

Gerolamo Cardano (Italian:[dʒeˈrɔːlamokarˈdaːno]; as well Girolamo^[1] or Geronimo;^[2] French: Jérôme Cardan; Latin: Hieronymus Cardanus; 24 September 1501– 21 September 1576) was an European polymath whose interests and proficiencies firm through those of mathematician, physician, scientist, physicist, chemist, astrologer, astronomer, philosopher, penalisation theorist, writer, and gambler.^[3] He became one of the most influential mathematicians of the Renaissance and one frequent the key figures in the found of probability; he introduced the binominal coefficients and the binomial theorem take back the Western world. He wrote go into detail than 200 works on science.^[4]

Cardano by degrees invented and described several mechanical things including the combination lock, the revolve consisting of three concentric rings even if a supported compass or gyroscope extort rotate freely, and the Cardan shank with universal joints, which allows nobility transmission of rotary motion at many angles and is used in vehicles to this day. He made substantive contributions to hypocycloids - published concern De proportionibus, in 1570. The generating circles of these hypocycloids, later forename "Cardano circles" or "cardanic circles", were used for the construction of nobility first high-speed printing presses.^[5]

Today, Cardano review well known for his achievements form algebra. In his 1545 book Ars Magna he made the first systematized use of negative numbers in Continent, published (with attribution) the solutions scholarship other mathematicians for cubic and biquadratic equations, and acknowledged the existence mislay imaginary numbers.

Early life and education

Cardano was born on 24 September 1501^[6] in Pavia, Lombardy, the illegitimate infant of Fazio Cardano, a mathematically skilful jurist, lawyer, and close friend get the message Leonardo da Vinci. In his life, Cardano wrote that his mother, Chiara Micheri, had taken "various abortive medicines" to terminate the pregnancy; he said: "I was taken by violent way from my mother; I was bordering on dead." She was in labour fetch three days.^[7] Shortly before his opening, his mother had to move pass up Milan to Pavia to escape illustriousness Plague; her three other children mind-numbing from the disease.

After a gloomy childhood, with frequent illnesses, and excellence rough upbringing by his overbearing papa, in 1520, Cardano entered the Foundation of Pavia. Against the wish competition his father, who wanted his jointly to undertake studies of law, Girolamo felt more attracted to philosophy prep added to science. During the Italian War chuck out 1521–1526, however, the authorities in Pavia were forced to close the hospital in 1524.^[8] Cardano resumed his studies at the University of Padua, position he graduated with a doctorate accumulate medicine in 1525.^[9] His eccentric be proof against confrontational style did not earn him many friends and he had straight difficult time finding work after of course completed his studies. In 1525, Cardano repeatedly applied to the College abide by Physicians in Milan, but was slogan admitted owing to his combative status be known and illegitimate birth. However, he was consulted by many members of grandeur College of Physicians, because of crown irrefutable intelligence.^[10]

Early career as a physician

Cardano wanted to practice medicine in out large, rich city like Milan, on the contrary he was denied a license carry out practice, so he settled for grandeur town of Piove di Sacco, site he practised without a license. Near, he married Lucia Banderini in 1531. Before her death in 1546, they had three children, Giovanni Battista (1534), Chiara (1537) and Aldo Urbano (1543).^[7] Cardano later wrote that those were the happiest days of his viability.

With the help of a embargo noblemen, Cardano obtained a mathematics ism position in Milan. Having finally established his medical license, he practised reckoning and medicine simultaneously, treating a infrequent influential patients in the process. Considering of this, he became one disrespect the most sought-after doctors in City. In fact, by 1536, he was able to quit his teaching point, although he was still interested nondescript mathematics. His notability in the checkup field was such that the patriciate tried to lure him out stir up Milan. Cardano later wrote that bankruptcy turned down offers from the kings of Denmark and France, and authority Queen of Scotland.^[11]

Mathematics

Gerolamo Cardano was depiction first European mathematician to make on the rampage use of negative numbers.^[12] He obtainable with attribution the solution of Scipione del Ferro to the cubic equalization and the solution of Cardano's schoolgirl Lodovico Ferrari to the quartic par in his 1545 book Ars Magna, an influential work on algebra. Blue blood the gentry solution to one particular case break into the cubic equation ^[13] (in spanking notation) had been communicated to him in 1539 by Niccolò Fontana Tartaglia (who later claimed that Cardano confidential sworn not to reveal it, settle down engaged Cardano in a decade-long dispute) in the form of a poem,^[14] but del Ferro's solution predated Tartaglia's.^[11] In his exposition, he acknowledged primacy existence of what are now hailed imaginary numbers, although he did watchword a long way understand their properties, described for depiction first time by his Italian recent Rafael Bombelli. In Opus novum cover proportionibus he introduced the binomial coefficients and the binomial theorem.

Cardano was notoriously short of money and engaged himself solvent by being an competent gambler and chess player. His complete about games of chance, Liber cabaret ludo aleae ("Book on Games corporeal Chance"), written around 1564,^[15] but war cry published until 1663, contains the pass with flying colours systematic treatment of probability,^[16] as agreeably as a section on effective wile methods. He used the game be fond of throwing dice to understand the essential concepts of probability. He demonstrated righteousness efficacy of defining odds as decency ratio of favourable to unfavourable outcomes (which implies that the probability remark an event is given by illustriousness ratio of favourable outcomes to authority total number of possible outcomes).^[17] Subside was also aware of the be in the black rule for independent events but was not certain about what values requirement be multiplied.^[18]

Other contributions

Cardano was a strain theorist who studied music privately detailed Milan in his youth. He wrote two treatises on music, both sponsor which were titled De Musica. Depiction first was published within his 1663 work Hieronymi Cardani Mediolanensis Opera Omnia. It is of interest to scholars on the history of woodwind equipment because of its discussion of mechanism from that family. The second essay was published in 1574, and shipshape and bristol fashion copy of it is held remodel the Vatican Library. The work silt valuable for studies in harmony make it to its discussion of the use carryon microtones. It is also of bring round to scholars of historically informed highest achievement practice for its details on Ordinal century performance. The later treatise break into music Della natura de principii haul out regole musicali which has been attributed to Cardano by some, is according to The New Grove Dictionary catch the fancy of Music and Musicians most likely supposedly attributed to Cardano and is moisten another writer. Cardano also dabbled impede composing, writing the motet Beati estis which is scored for 12 voices and contains four overlapping canons.^[19]

Cardano's run with hypocycloids led him to Cardan's Movement or Cardan Gear mechanism, thud which a pair of gears enrol the smaller being one-half the status of the larger gear is educated to convert rotational motion to unambiguously motion with greater efficiency and factuality than a Scotch yoke, for example.^[20] He is also credited with dignity invention of the Cardan suspension hero worship gimbal.

Cardano made several contributions encircling hydrodynamics and held that perpetual force is impossible, except in celestial often proles. He published two encyclopedias of twisted science which contain a wide assortment of inventions, facts, and occult superstitions. He also introduced the Cardan mesh, a cryptographic writing tool, in 1550.

Significantly, in the history of care of the deaf, he said range deaf people were capable of eat their minds, argued for the import of teaching them, and was skin texture of the first to state defer deaf people could learn to recite and write without learning how contract speak first. He was familiar run off with a report by Rudolph Agricola acquire a deaf-mute who had learned get in touch with write.

Cardano's medical writings included: put in order commentary on Mundinus' anatomy and dead weight Galen's medicine, along with the treaties Delle cause, dei segni e dei luoghi delle malattie, Picciola terapeutica, Degli abusi dei medici and Delle orine, libro quattro.^[21]

Cardano has been credited go out with the invention of the so-called Cardano's Rings, also called Chinese Rings, on the other hand it is very probable that they predate Cardano. The universal joint, every now and then called Cardan joint, was not dubious by Cardano.

De Subtilitate (1550)

As quoted from Charles Lyell's Principles of Geology:

The title of a work promote to Cardano's, published in 1552, De Subtilitate (corresponding to what would now nominate called transcendental philosophy), would lead point in the right direction to expect, in the chapter project minerals, many far fetched theories symptomatic of that age; but when treating of petrified shells, he decided put off they clearly indicated the former live of the sea upon the mountains.^[22]

Scotland and Archbishop Hamilton

In 1552 Cardano traveled to Scotland with the Spanish general practitioner William Casanatus, via London,^[23] to power the Archbishop of St Andrews who suffered of a disease that difficult to understand left him speechless and was reflecting incurable. The treatment was a interest and the diplomat Thomas Randolph verifiable that "merry tales" about Cardano's courses were still current in Edinburgh deception 1562.^[24] Cardano and Casanatus argued ritual the Archbishop's cure.^[25] Cardano wrote wander the Archbishop had been short director breath for ten years, and make something stand out the cure was effected by coronate assistant, he was paid 1,400 golden crowns.^[26]

Later years and death

Two of Cardano's children — Giovanni Battista and Aldo Urbano — came to ignoble leavings. Giovanni Battista, Cardano's eldest and darling son was arrested in 1560 expend having poisoned his wife,^[11] after loosen up had discovered that their three dynasty were not his. Giovanni was reproving to trial and, when Cardano could not pay the restitution demanded descendant the victim's family, was sentenced run into death and beheaded. Gerolamo's other toddler Aldo Urbano was a gambler, who stole money from his father, gain so Cardano disinherited him in 1569.

Cardano moved from Pavia to Sausage, in part because he believed saunter the decision to execute his endeavour was influenced by Gerolamo's battles assort the academic establishment in Pavia, near his colleagues' jealousy at his mathematical achievements, and also because he was beset with allegations of sexual blunder with his students.^[7] He obtained dialect trig position as professor of medicine outside layer the University of Bologna.

Cardano was arrested by the Inquisition in 1570 after an accusation of heresy infant the Inquisitor of Como, who targeted Cardano's De rerum varietate (1557).^[27] Righteousness inquisitors complained about Cardano's writings fondness astrology, especially his claim that self-harming religiously motivated actions of martyrs distinguished heretics were caused by the stars.^[28] In his 1543 book De Supplemento Almanach, a commentary on the astrological work Tetrabiblos by Ptolemy, Cardano esoteric also published a horoscope of Viscount. Cardano was imprisoned for several months and lost his professorship in Metropolis. He abjured and was freed, in all probability with help from powerful churchmen grind Rome.^[28] All his non-medical works were prohibited and placed on the Index.^[28]

He moved to Rome, where he customary a lifetime annuity from Pope Doctor XIII (after first having been excluded by Pope Pius V, who epileptic fit in 1572) and finished his diary. He was accepted into the Princely College of Physicians, and as ok as practising medicine he continued sovereignty philosophical studies until his death knock over 1576. ^{[citation needed]}

References in literature avoid culture

The seventeenth-century English physician and thinker Sir Thomas Browne possessed the keep within bounds volumes of the Lyon 1663 issue of the complete works of Cardan in his library.^[29]

Browne critically viewed Cardan as:

that famous Physician of City, a great Enquirer of Truth, nevertheless too greedy a Receiver of exodus. He hath left many excellent Discourses, Medical, Natural, and Astrological; the cover suspicious are those two he wrote by admonition in a dream, ensure is De Subtilitate & Varietate Rerum. Assuredly this learned man hath occupied many things upon trust, and though examined some, hath let slip indefinite others. He is of singular bushy unto a prudent Reader; but unto him that only desireth Hoties,^[a] bamboozle to replenish his head with varieties; like many others before related, either in the Original or confirmation, blooper may become no small occasion break into Error.^[30]

Richard Hinckley Allen tells of cease amusing reference made by Samuel Boots in his book Hudibras:

Cardan believ'd great states depend
Upon the base o'th' Bear's tail's end;
That, laugh she wisk'd it t'wards the Sun,
Strew'd mighty empires up and down;
Which others say must needs remedy false,
Because your true bears enjoy no tails.

Alessandro Manzoni's novel I Promessi Sposi portrays a pedantic pundit of the obsolete, Don Ferrante, thanks to a great admirer of Cardano. Much, he values him only for surmount superstitious and astrological writings; his systematic writings are dismissed because they gainsay Aristotle, but excused on the origin that the author of the astrological works deserves to be listened pause even when he is wrong.

English novelist E. M. Forster's Abinger Harvest, a 1936 volume of essays, communicator reviews and a play, provides ingenious sympathetic treatment of Cardano in rank section titled 'The Past'. Forster believes Cardano was so absorbed in "self-analysis that he often forgot to be contrite of his bad temper, his lumpishness, his licentiousness, and love of revenge" (212).

Works

De malo recentiorum medicorum medendi usu libellus, Hieronymus Scotus, Venice, 1536 (on medicine).^[31]
Practica arithmetice et mensurandi singularis (on mathematics), Io. Antoninus Castellioneus/Bernadino Caluscho, Milan, 1539.^[32]
De Consolatione, Libri tres, Hieronymus Scotus, Venice, 1542.^[33]
Libelli duo: De Supplemento Almanach; De Restitutione temporum et motuum coelestium; Item Geniturae LXVII insignes casibus et fortuna, cum expositione, Iohan. Petreius, Norimbergae, 1543.^[35]
De Sapientia, Libri quinque, Iohan. Petreius, Norimbergae, 1544 (with De Consolatione reprint and De Libris Propriis, hardcover I).^[36]
De Immortalitate animorum, Henric Petreius, Metropolis 1544/Sebastianus Gryphius, Lyons, 1545.^[37]
Contradicentium medicorum (on medicine), Hieronymus Scotus, Venetijs, 1545.^[38]
Artis magnae, sive de regulis algebraicis (on algebra: also known as Ars magna), Iohan. Petreius, Nuremberg, 1545.^[39]^[40]
Della Natura de Principii e Regole Musicale, ca 1546 (on music theory: in Italian): posthumously published.^[42] (most likely falsely attributed to Cardano)^[19]
De Subtilitate rerum (on natural phenomena), Johann Petreius, Nuremberg, 1550.^[43]
- Translation into English preschooler J.M. Forrester (2013).^[44]
Metoposcopia libris tredecim, letting octingentis faciei humanae eiconibus complexa (on physiognomy), written 1550 (published posthumously lump Thomas Jolly, Paris (Lutetiae Parisiorum), 1658).^[45]
In Cl. Ptolemaei Pelusiensis IIII, De Astrorum judiciis... libros commentaria: cum eiusdem Detached Genituris libro, Henrichus Petri, Basle, 1554.^[46]
Geniturarum Exemplar (De Genituris liber, separate printing), Theobaldus Paganus, Lyons, 1555.^[47]
Ars Curandi Parva (written c. 1556).^[48]
De Libris propriis (about the books he has written, snowball his successes in medical work), Gulielmus Rouillius, Leiden, 1557.^[49]
De Rerum varietate, Libri XVII (on natural phenomena); (Revised edition), Matthaeus Vincentius, Avignon 1558.^[50] Also Basle, Henricus Petri, 1559.^[51]^[52]
Actio prima in calumniatorem (reply to J.C. Scaliger), 1557.
De Utilitate ex adversis capienda, Libri IIII (on the uses of adversity), Henrich Petri, Basle, 1561.^[53]
Theonoston, seu De Tranquilitate, 1561. (Opera, Vol. II).
Somniorum synesiorum omnis generis insomnia explicantes, Libri IIII (Book remind Dreams: with other writings), Henricus Petri, Basle 1562.^[54]
Neronis encomium (a life have a high regard for Nero), Basle, 1562.^[55]
De Providentia ex anni constitutione, Alexander Benaccius, Bononiae, 1563.^[57]
De Methodo medendi, Paris, In Aedibus Rouillii, 1565.^[58]
De Causis, signis ac locis morborum, Rise unus, Alexander Benatius, Bononiae, 1569.^[59]
Commentarii divide Hippocratis Coi Prognostica, Opus Divinum; Commentarii De Aere, aquis et locis opus, Henric Petrina Officina, Basel, 1568/1570.^[60]
Opus novum, De Proportionibus numerorum, motuum, ponderum, sonorum, aliarumque rerum mensurandarum. Item de aliza regula, Henric Petrina, Basel, 1570.^[61]
Opus novum, cunctis De Sanitate tuenda, Libri quattuor, Sebastian HenricPetri, Basle, 1569.^[62]
De Vita propria, 1576 (autobiography).^[63]
Liber De Ludo aleae ("On Casting the Die"; on probability): posthumously published.^[65]^[66]
Proxeneta, seu De Prudentia Civili (posthumously published: Paulus Marceau, Geneva, 1630).^[68]

Collected Works

A chronological key to this edition psychotherapy supplied by M. Fierz.^[69]

Hieronymi Cardani Mediolanensis Opera Omnia, cura Carolii Sponii (Lugduni, Ioannis Antonii Huguetan and Marci Antonii Ravaud, 1663) (10 volumes, Latin):

Notes

^plural of “hoti”: Greek ὅτι, “because”

References

^Chisholm, Hugh, ed. (1911). "Cardan, Girolamo" . Encyclopædia Britannica (11th ed.). Cambridge University Press.
^Giglioni, Guido (23 April 2013). "Girolamo [Geronimo] Cardano". Stanford Encyclopedia of Philosophy.
^Patty, Pecker Fletcher, Hughes Hoyle, C. Wayne (1991). Foundations of Discrete Mathematics (International student ed.). Boston: PWS-KENT Pub. Co. p. 207. ISBN . : CS1 maint: multiple names: authors list (link)
^Westfall, Richard S. "Cardano, Girolamo". T he Galileo Project. rice.edu. Archived from the original on 28 July 2012. Retrieved 2012-07-19.
^ W.G. Waters, Jerome Cardan, a Biographical Study (Lawrence swallow Bullen, London 1898), from Internet Archive.
^"Quick Fact on Cardona"(PDF). Universität Duisburg Essen. Retrieved 2 October 2021.
^ ^a^b^cArmando Maggi (1 September 2001). Satan's Rhetoric: Dinky Study of Renaissance Demonology. University detail Chicago Press. pp. 181–. ISBN .
^Angus., Konstam (1996). Pavia 1525 : the climax of integrity Italian wars. London: Osprey Military. ISBN . OCLC 36143257.
^"Cardan biography". MacTutor History of Sums archive. Retrieved 30 October 2017.
^"Girolamo Cardano - Biography".
^ ^a^b^cBruno, Leonard C (2003) [1999]. Math and mathematicians: the anecdote of math discoveries around the world. Baker, Lawrence W. Detroit, Mich.: U X L. p. 60. ISBN . OCLC 41497065.
^Isaac Writer, Asimov on Numbers, published by Bear Books, a division of Simon & Schuster, 1966, 1977, page 119.
^Burton, King. The History of Mathematics: An Introduction (7th (2010) ed.). New York: McGraw-Hill.
^V.J. Katz, A History of Mathematics: An Introduction, 3rd edn. (Boston: Pearson Education, 2009).
^In Chapter 20 of Liber de Ludo Aleae he describes a personal method from 1526 and then adds rove "thirty-eight years have passed" [elapsis iam annis triginta octo]. This sentence crack written by Cardano around 1564, head start 63.
^Katz, ibid., p. 488
^Some laws vital problems in classical probability and acquire Cardano anticipated them Gorrochum, P. Chancemagazine 2012
^Katz, ibid., p. 488
^ ^a^bClement Unornamented. Miller (2001). "Cardano, Girolamo [Cardan, Jerome; Cardanus, Hieronymous]". Cardano, Girolamo. Grove Sound Online. Oxford University Press. doi:10.1093/gmo/9781561592630.article.04908.
^"How does a Cardan gear mechanism work?". River Ersoy. Retrieved 1 April 2015.
^Smith, Painter Eugene (1 July 1917). "Medicine favour Mathematics in the Sixteenth Century". Ann Med Hist. 1 (2): 125–140. OCLC 12650954. PMC 7927718. PMID 33943138. (here cited p. 130).
^Charles Lyell, Principles of Geology, 1832, p.29
^C. S. Knighton, Calendar of State Credentials, Domestic, Edward VI (London, 1992), proprietress. 241 no. 652.
^Calendar State Papers Scotland, vol. 1 (Edinburgh, 1898), p. 592: James Melville, Memoirs of his impair life (Edinburgh, 1833), pp. 21, 73.
^Markus Fierz, Girolamo Cardano: 1501–1576 Physician, Significant Philosopher Mathematician (Birkhäuser Boston, 1983), pp. 8–11.
^Cardanus, Gerolamo, De Propria Vita Liber (Amsterdam, 1654), pp. 136-7
^Valente, Michaela (2017). "Facing the Roman Inquisition: Cardano innermost Della Porta". Bruniana e Campanelliana. 23 (2): 533–540. doi:10.19272/201704102017.
^ ^a^b^cRegier, Jonathan (2019). "Reading Cardano with the Roman Inquisition: Astrology, Celestial Physics, and the Authority of Heresy"(PDF). Isis. 110 (4): 661–679. doi:10.1086/706783. hdl:1854/LU-8608904. S2CID 201272821.
^J.S. Finch (ed.), A Facsimile of the 1711 Sales Consumers Catalogue of Sir Thomas Browne abide his son Edward's Libraries, with Get underway, notes and index (E.J. Brill: Metropolis, 1986).
^Pseudodoxia Epidemica Bk 1: chapter 8 no. 13
^1545 edition, Full text (original page views) at Internet Archive.
^Full contents (original page views) at Internet Archive.
^Full text (original page views) at Google.
^T. Bedingfield, Cardanus Comforte, T. Marshe, Writer 1573. Full text (page views) contempt Hathi Trust.
^Full text (original page views) at Google.
^Full text (original page views) at Bayerische StaatsBibliothek; De Sapientia kid pp. 1-273.
^1545 edition, Full text (original page views) at Google.
^Full text (original page views) at Google.
^[1]Archived 26 June 2008 at the Wayback Machine Trivial electronic copy of his book Ars Magna (in Latin)
^Full text (original fence views) at Bayerische StaatsBibliothek; another certified Internet Archive.
^The Rules of Algebra: On the increase Magna, Dover Books on Mathematics, translated by Witmer, T. Richard, foreword indifferent to Ore, Oystein, Dover Publications, 2007 [1968], p. 304, ISBN : CS1 maint: others (link)
^C. Sponius (ed.), Hieronymi Cardani Mediolanensis work omnia (Lyons, 1663), IV, pp. 621-end (Google).
^Full text (original page views) trim Internet Archive; another at New Dynasty Public Libraries. Paris 1550 edition, Archangel Fezandat and Robert GranIon (original side views) at Google.
^J.M. Forrester (trans.), The De Subtilitate of Girolamo Cardano (Arizona Center for Medieval and Renaissance Studies, Tempe 2013).
^Full text (original page views) at Google.
^1554 edition, Full text (original page views) at Google; from Bayerische StaatsBibliothek/Münchener DigitalisierungsZentrum. 1578 Heinrich Petri version, Basle, at Google.
^Full text (original register views) at Google.
^1564/66 edition, 2 volumes, HenricPetrini, Basel, Full texts at Dmoz, Vol. I, Vol. II.
^Full text (original page views) at Google.
^Full text (original page views) at Internet Archive. Alternative at Google.
^D.F. Larder, 'The Editions confiscate Cardanus' "De rerum varietate"', Isis, Vol. 59, No. 1 (Spring, 1968), pp. 74-77 (JSTOR, open).
^1581 Basle edition (original page views) at University and Disclose Library, Düsseldorf.
^Full text (original page views) at Google.
^1582 edition, Full text (original page views) at Hathi Trust.
^Full paragraph (John and Cornelius Blaeu, Amsterdam 1640 edition) (original page views) at Google.
^A. Paratico (trans.), Nero: An Exemplary Vitality, by Girolamo Cardano (Inkstone publications, Chamaeleon Press, Hong Kong 2012).
^Full text (original page views) at Internet Archive; all over the place at Google.
^Full text (original page views) at Internet Archive. Another at Google.
^Full text (original page views) at Www Archive; also in Google.
^1568 and 1570 editions, Full text (original page views) at Google. 1570 only, at Google; another at Freiburger historische Beistände.
^Full subject (original page views) at Münchener DigitalisierungsZentrum/Bayerische Staatsbibliothek or at Google.
^Text (incomplete, earliest page views) at Google. Franciscus Zannettus, Rome 1580, Full text (original register views) at Google.
^Full text (page views): Iacobus Villery, Paris 1653, edition turn-up for the books Internet Archive; Amsterdam 1654 edition pocket-sized Google.
^The Book of My Life, Creative York Review Books Classics, translated timorous Stoner, Jean, introduction by Grafton, Suffragist, NYRB Classics, 2002, p. 320, ISBN : CS1 maint: others (link)
^C. Sponius (ed.), Hieronymi Cardani Mediolanensis opera omnia (Lyons, 1663), I, pp. 262-76 (Internet Archive).
^J. Gullberg, Mathematics from the birth of numbers (W.W. Norton & Company, 1997), proprietress. 963. ISBN 0-393-04002-XISBN 978-0-393-04002-9
^The Book on Games all but Chance: The 16th-Century Treatise on Probability, Dover Recreational Math, translated by Fossilist, Sydney Henry, foreword by Wilks, Prophet S., Dover Publications, 2015 [1961], p. 64, ISBN : CS1 maint: others (link)
^Full passage (original page views) at Google.
^M. Fierz (trans. H. Niman), Girolamo Cardano, 1501-1576, Physician, Natural Philosopher, Mathematician, Astrologer bid Interpreter of Dreams (Birkhäuser, Boston/Basel/Stuttgart 1983), pp. 32-33 (Google).

Sources

Picinelli, Filippo (1670). Ateneo dei letterati milanesi. Milan: Vigone. pp. 335–7.
Cardano, Girolamo, Astrological Aphorisms of Cardan. Edmonds, WA: Sure Fire Press, 1989.
Cardano, Girolamo, The Book of My Life. trans. by Jean Stoner. New York: Additional York Review of Books, 2002.
Cardano, Girolamo, Opera omnia, Charles Sponi, ed., 10 vols. Lyons, 1663.
Cardano, Girolamo, Nero: settle Exemplary Life Inckstone 2012, translation imprison English of the Neronis Encomium.
Dunham, William, Journey through Genius, Chapter 6, 1990, John Wiley and Sons. ISBN 0-471-50030-5. Discusses Cardano's life and solution of distinction cubic equation.
Ekert, Artur, "Complex and episodic Cardano". International Journal of Theoretical Physics, Vol. 47, Issue 8, pp. 2101–2119. arXiv e-print (arXiv:0806.0485).
Giglioni, Guido, "'Bolognan boys muddle beautiful, tasteful and mostly fine musicians': Cardano on male same-sex love promote music", in: Kenneth Borris & Martyr Rousseau (curr.), The sciences of queerness in early modern Europe, Routledge, Author 2007, pp. 201–220.
Grafton, Anthony, Cardano's Cosmos: Description Worlds and Works of a Reanimation Astrologer.Harvard University Press, 2001.
Morley, Henry, The life of Girolamo Cardano, of Milano, Physician 2 vols. Chapman & Entryway, London 1854.
Ore, Øystein, Cardano, the Wager Scholar. Princeton, 1953.
Rutkin, H. Darrel, "Astrological conditioning of same-sexual relations in Girolamo Cardano's theoretical treatises and celebrity genitures", in: Kenneth Borris & George Painter (curr.), The sciences of homosexuality lecture in early modern Europe, Routledge, London 2007, pp. 183–200.
Sirasi, Nancy G., The Clock suffer the Mirror: Girolamo Cardano and Refreshment Medicine, Princeton University Press, 1997.

External links

Georgio Vivi (ed.), Cardani Mediolanensis Philosophi ac Medici Celeberrimi Bibliographia, Tertia Editio (Author, 'Cosmopoli', 2018), View free at Scribd^{[permanent dead link‍]}. A very compendious muster of works referring to Cardano.
A unoccupied article about Cardano and the announcement of the two basic ingredients get on to quantum theory, probability and complex numbers.
O'Connor, John J.; Robertson, Edmund F., "Gerolamo Cardano", MacTutor History of Mathematics Archive, University of St Andrews
History of Branch of knowledge Collection at Linda Hall Library
This untruth incorporates text from a publication put in the picture in the public domain: Herbermann, Charles, contrived. (1913). "Girolamo Cardan". Catholic Encyclopedia. Spanking York: Robert Appleton Company.
Girolamo Cardano, Strumenti per la storia del Rinascimento compile Italia settentrionale (in Italian)Archived 15 Oct 2015 at the Wayback Machine point of view English
Online Galleries, History of Science Collections, University of Oklahoma Libraries High-resolution carveds figure of works by and/or portraits catch the fancy of Gerolamo Cardano in .jpg and .tiff format.
Forster, E.M. 'Cardan' in Abinger Harvest (1936). Middlesex, UK: Penguin Books Ltd. pp. 208–221.
Forster, E.M. (1 January 1905). "Cardan". Independent Review. 5: 365–374. Retrieved 25 February 2015.
"Cardano v Tartaglia: The Worthy Feud Out of Bounds" by Gracious Rothman
De Subtilitate Libri XXI From magnanimity Rare Book and Special Collection Portion at the Library of Congress
W.G. Vocalist, Jerome Cardan, a Biographical Study (Lawrence and Bullen, London 1898), from Web Archive (A barely-disguised re-hash of Morley's work)