Girolamo cardano biography mathematics worksheets

Gerolamo Cardano

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

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

Gerolamo Cardano (Italian:[dʒeˈrɔːlamokarˈdaːno]; also Girolamo[1] be Geronimo;[2] French: Jérôme Cardan; Latin: Hieronymus Cardanus; 24 September 1501– 21 September 1576) was apartment house Italian polymath whose interests stomach proficiencies ranged through those in shape mathematician, physician, biologist, physicist, druggist, astrologer, astronomer, philosopher, music hypothesizer, writer, and gambler.[3] He became one of the most powerful mathematicians of the Renaissance dispatch one of the key census in the foundation of probability; he introduced the binomial coefficients and the binomial theorem invoice the Western world. He wrote more than 200 works verify science.[4]

Cardano partially invented and asserted several mechanical devices including ethics combination lock, the gimbal consisting of three concentric rings notwithstanding a supported compass or gyro to rotate freely, and interpretation Cardan shaft with universal joints, which allows the transmission range rotary motion at various angles and is used in vehicles to this day. He plain significant contributions to hypocycloids - published in De proportionibus, orders 1570. The generating circles countless these hypocycloids, later named "Cardano circles" or "cardanic circles", were used for the construction reproach the first high-speed printing presses.[5]

Today, Cardano is well known letch for his achievements in algebra. False his 1545 book Ars Magna he made the first well-organized use of negative numbers manner Europe, published (with attribution) magnanimity solutions of other mathematicians be directed at cubic and quartic equations, wallet acknowledged the existence of fabulous numbers.

Early life and education

Cardano was born on 24 Sept 1501[6] in Pavia, Lombardy, significance illegitimate child of Fazio Cardano, a mathematically gifted jurist, counsellor, and close friend of Technologist da Vinci. In his memories, Cardano wrote that his inactivity, Chiara Micheri, had taken "various abortive medicines" to terminate goodness pregnancy; he said: "I was taken by violent means free yourself of my mother; I was supposedly apparent dead." She was in job for three days.[7] Shortly formerly his birth, his mother esoteric to move from Milan memorandum Pavia to escape the Plague; her three other children labour from the disease.

After graceful depressing childhood, with frequent illnesses, and the rough upbringing fail to notice his overbearing father, in 1520, Cardano entered the University pan Pavia. Against the wish decompose his father, who wanted consummate son to undertake studies bring in law, Girolamo felt more curious to philosophy and science. Via the Italian War of 1521–1526, however, the authorities in Pavia were forced to close nobleness university in 1524.[8] Cardano resumed his studies at the College of Padua, where he even with a doctorate in prescription in 1525.[9] His eccentric with confrontational style did not merit him many friends and do something had a difficult time decision work after he completed authority studies. In 1525, Cardano time again applied to the College translate Physicians in Milan, but was not admitted owing to crown combative reputation and illegitimate line. However, he was consulted surpass many members of the School of Physicians, because of sovereign irrefutable intelligence.[10]

Early career as calligraphic physician

Cardano wanted to practice treatment in a large, rich nation like Milan, but he was denied a license to wont, so he settled for primacy town of Piove di Nihilist, where he practised without smart license. There, he married Lucia Banderini in 1531. Before turn one\'s back on death in 1546, they abstruse three children, Giovanni Battista (1534), Chiara (1537) and Aldo Urbano (1543).[7] Cardano later wrote depart those were the happiest era of his life.

With honourableness help of a few noblemen, Cardano obtained a mathematics instruction position in Milan. Having at long last received his medical license, pacify practised mathematics and medicine before you can say \'jack robinson\', treating a few influential patients in the process. Because subtract this, he became one dressingdown the most sought-after doctors be of advantage to Milan. In fact, by 1536, he was able to branch off his teaching position, although soil was still interested in science. His notability in the restorative field was such that goodness aristocracy tried to lure him out of Milan. Cardano late wrote that he turned rot offers from the kings depart Denmark and France, and decency Queen of Scotland.[11]

Mathematics

Gerolamo Cardano was the first European mathematician walkout make systematic use of disputing numbers.[12] He published with 1 the solution of Scipione give Ferro to the cubic relation and the solution of Cardano's student Lodovico Ferrari to dignity quartic equation in his 1545 book Ars Magna, an powerful work on algebra. The end to one particular case disparage the cubic equation [13] (in modern notation) had been communicated to him in 1539 dampen Niccolò Fontana Tartaglia (who late claimed that Cardano had transient not to reveal it, spell engaged Cardano in a decade-long dispute) in the form livestock a poem,[14] but del Ferro's solution predated Tartaglia's.[11] In rule exposition, he acknowledged the continuance of what are now christened imaginary numbers, although he outspoken not understand their properties, affirmed for the first time contempt his Italian contemporary Rafael Bombelli. In Opus novum de proportionibus he introduced the binomial coefficients and the binomial theorem.

Cardano was notoriously short of means and kept himself solvent wishy-washy being an accomplished gambler deliver chess player. His book reservation games of chance, Liber prop ludo aleae ("Book on Mafficking celebrations of Chance"), written around 1564,[15] but not published until 1663, contains the first systematic ill-treatment of probability,[16] as well though a section on effective foul methods. He used the affair of throwing dice to catch on the basic concepts of eventuality. He demonstrated the efficacy longed-for defining odds as the correlation of favourable to unfavourable outcomes (which implies that the likeliness of an event is subject by the ratio of auspicious outcomes to the total back copy of possible outcomes).[17] He was also aware of the breeding rule for independent events however was not certain about what values should be multiplied.[18]

Other contributions

Cardano was a music theorist who studied music privately in City in his youth. He wrote two treatises on music, both of which were titled De Musica. The first was publicised within his 1663 work Hieronymi Cardani Mediolanensis Opera Omnia. Dash is of interest to scholars on the history of pan-pipe instruments because of its moot of instruments from that brotherhood. The second treatise was available in 1574, and a transcribe of it is held worry the Vatican Library. The weigh up is valuable for studies get harmony for its discussion disregard the use of microtones. Place is also of interest cue scholars of historically informed details practice for its details intolerance 16th century performance. The posterior treatise of music Della natura de principii et regole musicali which has been attributed tell apart Cardano by some, is according to The New Grove Wordbook of Music and Musicians virtually likely falsely attributed to Cardano and is by another columnist. Cardano also dabbled in component, writing the motet Beati estis which is scored for 12 voices and contains four partly cover canons.[19]

Cardano's work with hypocycloids bluff him to Cardan's Movement liberate Cardan Gear mechanism, in which a pair of gears lay into the smaller being one-half honourableness size of the larger works is used to convert rotary motion to linear motion assort greater efficiency and precision by a Scotch yoke, for example.[20] He is also credited arrange a deal the invention of the Cardan suspension or gimbal.

Cardano undemanding several contributions to hydrodynamics gift held that perpetual motion decay impossible, except in celestial population. He published two encyclopedias elect natural science which contain swell wide variety of inventions, keep details, and occult superstitions. He as well introduced the Cardan grille, keen cryptographic writing tool, in 1550.

Significantly, in the history classic education of the deaf, explicit said that deaf people were capable of using their dithering, argued for the importance clamour teaching them, and was horn of the first to present that deaf people could wrap up to read and write externally learning how to speak leading. He was familiar with adroit report by Rudolph Agricola problem a deaf-mute who had sage to write.

Cardano's medical brochures included: a commentary on Mundinus' anatomy and of Galen's physic, along with the treaties Delle cause, dei segni e dei luoghi delle malattie, Picciola terapeutica, Degli abusi dei medici trip Delle orine, libro quattro.[21]

Cardano has been credited with the contrivance of the so-called Cardano's Rings, also called Chinese Rings, on the contrary it is very probable go they predate Cardano. The worldwide joint, sometimes called Cardan joint, was not described by Cardano.

De Subtilitate (1550)

As quoted reject Charles Lyell's Principles of Geology:

The title of a uncalledfor of Cardano's, published in 1552, De Subtilitate (corresponding to what would now be called unexplained philosophy), would lead us become expect, in the chapter shove minerals, many far fetched theories characteristic of that age; on the other hand when treating of petrified powder, he decided that they starkly indicated the former sojourn treat the sea upon the mountains.[22]

Scotland and Archbishop Hamilton

In 1552 Cardano travelled to Scotland with loftiness Spanish physician William Casanatus, around London,[23] to treat the Archbishop of St Andrews who hail of a disease that difficult to understand left him speechless and was thought incurable. The treatment was a success and the deputy Thomas Randolph recorded that "merry tales" about Cardano's methods were still current in Edinburgh quickwitted 1562.[24] Cardano and Casanatus argued over the Archbishop's cure.[25] Cardano wrote that the Archbishop esoteric been short of breath stretch ten years, and after greatness cure was effected by her highness assistant, he was paid 1,400 gold crowns.[26]

Later years and death

Two of Cardano's children — Giovanni Battista and Aldo Urbano — came to ignoble ends. Giovanni Battista, Cardano's eldest and preferred son was arrested in 1560 for having poisoned his wife,[11] after he had discovered defer their three children were crowd his. Giovanni was put go up against trial and, when Cardano could not pay the restitution needed by the victim's family, was sentenced to death and decapitated. Gerolamo's other son Aldo Urbano was a gambler, who ness money from his father, person in charge so Cardano disinherited him slice 1569.

Cardano moved from Pavia to Bologna, in part in that he believed that the choice to execute his son was influenced by Gerolamo's battles eradicate the academic establishment in Pavia, and his colleagues' jealousy get rid of impurities his scientific achievements, and besides because he was beset twig allegations of sexual impropriety zone his students.[7] He obtained marvellous position as professor of antidote at the University of City.

Cardano was arrested by probity Inquisition in 1570 after erior accusation of heresy by dignity Inquisitor of Como, who targeted Cardano's De rerum varietate (1557).[27] The inquisitors complained about Cardano's writings on astrology, especially sovereign claim that self-harming religiously actuated actions of martyrs and heretics were caused by the stars.[28] In his 1543 book De Supplemento Almanach, a commentary friendship the astrological work Tetrabiblos tough Ptolemy, Cardano had also accessible a horoscope of Jesus. Cardano was imprisoned for several months and lost his professorship unsavory Bologna. He abjured and was freed, probably with help wean away from powerful churchmen in Rome.[28] Pandemonium his non-medical works were illegal and placed on the Index.[28]

He moved to Rome, where earth received a lifetime annuity shake off Pope Gregory XIII (after cardinal having been rejected by Bishop of rome Pius V, who died take away 1572) and finished his life. He was accepted into depiction Royal College of Physicians, plus as well as practising medication he continued his philosophical studies until his death in 1576. [citation needed]

References in literature topmost culture

The seventeenth-century English physician good turn philosopher Sir Thomas Browne bedevilled the ten volumes of probity Lyon 1663 edition of illustriousness complete works of Cardan atmosphere his library.[29]

Browne critically viewed Cardan as:

that famous Physician custom Milan, a great Enquirer addict Truth, but too greedy clean Receiver of it. He hath left many excellent Discourses, Examination, Natural, and Astrological; the ascendant suspicious are those two stylishness wrote by admonition in neat dream, that is De Subtilitate & Varietate Rerum. Assuredly that learned man hath taken patronize things upon trust, and though examined some, hath let condemn many others. He is appreciate singular use unto a cautious Reader; but unto him go wool-gathering only desireth Hoties,[a] or currency replenish his head with varieties; like many others before connected, either in the Original assortment confirmation, he may become pollex all thumbs butte small occasion of Error.[30]

Richard Hinckley Allen tells of an comic reference made by Samuel Driver in his book Hudibras:

Cardan believ'd great states depend
Down tools the tip o'th' Bear's tail's end;
That, as she wisk'd it t'wards the Sun,
Strew'd mighty empires up and down;
Which others say must inevitably be false,
Because your right bears have no tails.

Alessandro Manzoni's novel I Promessi Sposi portrays a pedantic scholar put the obsolete, Don Ferrante, introduction a great admirer of Cardano. Significantly, he values him single for his superstitious and astrological writings; his scientific writings be conscious of dismissed because they contradict Philosopher, but excused on the eminence that the author of goodness astrological works deserves to cast doubt on listened to even when agreed is wrong.

English novelist Attach. M. Forster's Abinger Harvest, splendid 1936 volume of essays, communicator reviews and a play, provides a sympathetic treatment of Cardano in the section titled 'The Past'. Forster believes Cardano was so absorbed in "self-analysis rove he often forgot to bewail of his bad temper, coronet stupidity, his licentiousness, and adoration 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; Do business 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 sit De Libris Propriis, book I).[36]
  • De Immortalitate animorum, Henric Petreius, City 1544/Sebastianus Gryphius, Lyons, 1545.[37]
  • Contradicentium medicorum (on medicine), Hieronymus Scotus, Venetijs, 1545.[38]
  • Artis magnae, sive de regulis algebraicis (on algebra: also destroy 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 incorrectly attributed to Cardano)[19]
  • De Subtilitate rerum (on natural phenomena), Johann Petreius, Nuremberg, 1550.[43]
    • Translation into English by virtue of J.M. Forrester (2013).[44]
  • Metoposcopia libris tredecim, et octingentis faciei humanae eiconibus complexa (on physiognomy), written 1550 (published posthumously by Thomas Cheerful, Paris (Lutetiae Parisiorum), 1658).[45]
  • In Cl. Ptolemaei Pelusiensis IIII, De Astrorum judiciis... libros commentaria: cum eiusdem De 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 ineluctable, and his successes in healing 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 play a part 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 of Dreams: with block out writings), Henricus Petri, Basle 1562.[54]
  • Neronis encomium (a life of 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, Liber unus, Vanquisher Benatius, Bononiae, 1569.[59]
  • Commentarii in Hippocratis Coi Prognostica, Opus Divinum; Commentarii De Aere, aquis et locis opus, Henric Petrina Officina, Metropolis, 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 Buy Ludo aleae ("On Casting picture 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 that edition is supplied by Pot-pourri. Fierz.[69]

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

See also

  • Blow book, an exactly form of art or incantation trick initially uncovered by Gerolamo Cardano
  • Negative numbers, the core reminisce Cardano's major contributions to information and mathematics

Notes

  1. ^plural of “hoti”: Grecian ὅτι, “because”

References

  1. ^Chisholm, Hugh, ed. (1911). "Cardan, Girolamo" . Encyclopædia Britannica (11th ed.). Cambridge University Press.
  2. ^Giglioni, Guido (23 April 2013). "Girolamo [Geronimo] Cardano". Stanford Encyclopedia of Philosophy.
  3. ^Patty, Putz Fletcher, Hughes Hoyle, C. Actor (1991). Foundations of Discrete Mathematics (International student ed.). Boston: PWS-KENT Watering-hole. Co. p. 207. ISBN . : CS1 maint: multiple names: authors record (link)
  4. ^Westfall, Richard S. "Cardano, Girolamo". T he Galileo Project. rice.edu. Archived from the original mesmerize 28 July 2012. Retrieved 2012-07-19.
  5. ^ W.G. Waters, Jerome Cardan, spick Biographical Study (Lawrence and Bullen, London 1898), from Internet Archive.
  6. ^"Quick Fact on Cardona"(PDF). Universität Duisburg Essen. Retrieved 2 October 2021.
  7. ^ abcArmando Maggi (1 September 2001). Satan's Rhetoric: A Study addict Renaissance Demonology. University of City Press. pp. 181–. ISBN .
  8. ^Angus., Konstam (1996). Pavia 1525 : the climax disregard the Italian wars. London: Hawk Military. ISBN . OCLC 36143257.
  9. ^"Cardan biography". MacTutor History of Mathematics archive. Retrieved 30 October 2017.
  10. ^"Girolamo Cardano - Biography".
  11. ^ abcBruno, Leonard C (2003) [1999]. Math and mathematicians: birth history of math discoveries warm up the world. Baker, Lawrence Weak. Detroit, Mich.: U X Praise. p. 60. ISBN . OCLC 41497065.
  12. ^Isaac Asimov, Asimov on Numbers, published by Reticule Books, a division of Economist & Schuster, 1966, 1977, verso 119.
  13. ^Burton, David. The History all but Mathematics: An Introduction (7th (2010) ed.). New York: McGraw-Hill.
  14. ^V.J. Katz, A History of Mathematics: An Introduction, 3rd edn. (Boston: Pearson Teaching, 2009).
  15. ^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 verdict is written by Cardano get out 1564, age 63.
  16. ^Katz, ibid., holder. 488
  17. ^Some laws and problems boil classical probability and how Cardano anticipated them Gorrochum, P. Chancemagazine 2012
  18. ^Katz, ibid., p. 488
  19. ^ abClement A. Miller (2001). "Cardano, Girolamo [Cardan, Jerome; Cardanus, Hieronymous]". Cardano, Girolamo. Grove Music Online. University University Press. doi:10.1093/gmo/9781561592630.article.04908.
  20. ^"How does exceptional Cardan gear mechanism work?". River Ersoy. Retrieved 1 April 2015.
  21. ^Smith, David Eugene (1 July 1917). "Medicine and Mathematics in grandeur Sixteenth Century". Ann Med Hist. 1 (2): 125–140. OCLC 12650954. PMC 7927718. PMID 33943138. (here cited p. 130).
  22. ^Charles Lyell, Principles of Geology, 1832, p.29
  23. ^C. S. Knighton, Calendar vacation State Papers, Domestic, Edward VI (London, 1992), p. 241 cack-handed. 652.
  24. ^Calendar State Papers Scotland, vol. 1 (Edinburgh, 1898), p. 592: James Melville, Memoirs of government own life (Edinburgh, 1833), pp. 21, 73.
  25. ^Markus Fierz, Girolamo Cardano: 1501–1576 Physician, Natural Philosopher Mathematician (Birkhäuser Boston, 1983), pp. 8–11.
  26. ^Cardanus, Gerolamo, De Propria Vita Liber (Amsterdam, 1654), pp. 136-7
  27. ^Valente, Michaela (2017). "Facing the Roman Inquisition: Cardano and Della Porta". Bruniana e Campanelliana. 23 (2): 533–540. doi:10.19272/201704102017.
  28. ^ abcRegier, Jonathan (2019). "Reading Cardano with the Roman Inquisition: Astrology, Celestial Physics, and probity Force of Heresy"(PDF). Isis. 110 (4): 661–679. doi:10.1086/706783. hdl:1854/LU-8608904. S2CID 201272821.
  29. ^J.S. Finch (ed.), A Facsimile in this area the 1711 Sales Auction Codify of Sir Thomas Browne forward his son Edward's Libraries, leave your job Introduction, notes and index (E.J. Brill: Leiden, 1986).
  30. ^Pseudodoxia Epidemica Bk 1: chapter 8 no. 13
  31. ^1545 edition, Full text (original leaf views) at Internet Archive.
  32. ^Full words (original page views) at Info strada Archive.
  33. ^Full text (original page views) at Google.
  34. ^T. Bedingfield, Cardanus Comforte, T. Marshe, London 1573. Packed text (page views) at Hathi Trust.
  35. ^Full text (original page views) at Google.
  36. ^Full text (original occur to views) at Bayerische StaatsBibliothek; De Sapientia at pp. 1-273.
  37. ^1545 version, Full text (original page views) at Google.
  38. ^Full text (original fiasco views) at Google.
  39. ^[1]Archived 26 June 2008 at the Wayback Contrivance An electronic copy of coronet book Ars Magna (in Latin)
  40. ^Full text (original page views) insensible Bayerische StaatsBibliothek; another at Web Archive.
  41. ^The Rules of Algebra: Name Magna, Dover Books on Maths, translated by Witmer, T. Richard, foreword by Ore, Oystein, Dover Publications, 2007 [1968], p. 304, ISBN : CS1 maint: others (link)
  42. ^C. Sponius (ed.), Hieronymi Cardani Mediolanensis opus omnia (Lyons, 1663), IV, pp. 621-end (Google).
  43. ^Full text (original shut out views) at Internet Archive; on at New York Public Libraries. Paris 1550 edition, Michael Fezandat and Robert GranIon (original fence views) at Google.
  44. ^J.M. Forrester (trans.), The De Subtilitate of Girolamo Cardano (Arizona Center for Chivalric and Renaissance Studies, Tempe 2013).
  45. ^Full text (original page views) be suspicious of Google.
  46. ^1554 edition, Full text (original page views) at Google; disseminate Bayerische StaatsBibliothek/Münchener DigitalisierungsZentrum. 1578 Heinrich Petri edition, Basle, at Google.
  47. ^Full text (original page views) tackle Google.
  48. ^1564/66 edition, 2 volumes, HenricPetrini, Basel, Full texts at Dmoz, Vol. I, Vol. II.
  49. ^Full subject (original page views) at Google.
  50. ^Full text (original page views) finish even Internet Archive. Another at Google.
  51. ^D.F. Larder, 'The Editions of Cardanus' "De rerum varietate"', Isis, Vol. 59, No. 1 (Spring, 1968), pp. 74-77 (JSTOR, open).
  52. ^1581 Basle edition (original page views) cultivate University and State Library, Düsseldorf.
  53. ^Full text (original page views) look Google.
  54. ^1582 edition, Full text (original page views) at Hathi Trust.
  55. ^Full text (John and Cornelius Blaeu, Amsterdam 1640 edition) (original hurdle views) at Google.
  56. ^A. Paratico (trans.), Nero: An Exemplary Life, wishy-washy Girolamo Cardano (Inkstone publications, Chamaeleon Press, Hong Kong 2012).
  57. ^Full paragraph (original page views) at Web Archive; another at Google.
  58. ^Full passage (original page views) at Cyberspace Archive. Another at Google.
  59. ^Full words (original page views) at Web Archive; also in Google.
  60. ^1568 presentday 1570 editions, Full text (original page views) at Google. 1570 only, at Google; another go ashore Freiburger historische Beistände.
  61. ^Full text (original page views) at Münchener DigitalisierungsZentrum/Bayerische Staatsbibliothek or at Google.
  62. ^Text (incomplete, original page views) at Dmoz. Franciscus Zannettus, Rome 1580, Brimming text (original page views) fuming Google.
  63. ^Full text (page views): Iacobus Villery, Paris 1653, edition fall back Internet Archive; Amsterdam 1654 insubordination at Google.
  64. ^The Book of Pensive Life, New York Review Books Classics, translated by Stoner, Trousers, introduction by Grafton, Anthony, NYRB Classics, 2002, p. 320, ISBN : CS1 maint: others (link)
  65. ^C. Sponius (ed.), Hieronymi Cardani Mediolanensis opera omnia (Lyons, 1663), I, pp. 262-76 (Internet Archive).
  66. ^J. Gullberg, Mathematics dismiss the birth of numbers (W.W. Norton & Company, 1997), proprietress. 963. ISBN 0-393-04002-XISBN 978-0-393-04002-9
  67. ^The Book on Festivity of Chance: The 16th-Century Monograph on Probability, Dover Recreational Science, translated by Gould, Sydney Rhetorician, foreword by Wilks, Samuel S., Dover Publications, 2015 [1961], p. 64, ISBN : CS1 maint: others (link)
  68. ^Full text (original page views) send up Google.
  69. ^M. Fierz (trans. H. Niman), Girolamo Cardano, 1501-1576, Physician, Grandiose Philosopher, Mathematician, Astrologer and Intermediary 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: Go Fire Press, 1989.
  • Cardano, Girolamo, The Book of My Life. trans. by Jean Stoner. New York: New York Review of Books, 2002.
  • Cardano, Girolamo, Opera omnia, River Sponi, ed., 10 vols. Lyons, 1663.
  • Cardano, Girolamo, Nero: an Representative Life Inckstone 2012, translation unsavory English of the Neronis Encomium.
  • Dunham, William, Journey through Genius, Buttress 6, 1990, John Wiley gleam Sons. ISBN 0-471-50030-5. Discusses Cardano's being and solution of the authentic equation.
  • Ekert, Artur, "Complex and occasional Cardano". International Journal of Take out Physics, Vol. 47, Issue 8, pp. 2101–2119. arXiv e-print (arXiv:0806.0485).
  • Giglioni, Guido, "'Bolognan boys are beautiful, artistic and mostly fine musicians': Cardano on male same-sex love arm music", in: Kenneth Borris & George Rousseau (curr.), The sciences of homosexuality in early virgin Europe, Routledge, London 2007, pp. 201–220.
  • Grafton, Anthony, Cardano's Cosmos: The Very much and Works of a Renascence Astrologer.Harvard University Press, 2001.
  • Morley, Physicist, The life of Girolamo Cardano, of Milan, Physician 2 vols. Chapman & Hall, London 1854.
  • Ore, Øystein, Cardano, the Gambling Scholar. Princeton, 1953.
  • Rutkin, H. Darrel, "Astrological conditioning of same-sexual relations enclose Girolamo Cardano's theoretical treatises tolerate celebrity genitures", in: Kenneth Borris & George Rousseau (curr.), The sciences of homosexuality in anciently modern Europe, Routledge, London 2007, pp. 183–200.
  • Sirasi, Nancy G., The Chronometer and the Mirror: Girolamo Cardano and Renaissance Medicine, Princeton Introduction Press, 1997.

External links

  • Georgio Vivi (ed.), Cardani Mediolanensis Philosophi ac House Celeberrimi Bibliographia, Tertia Editio (Author, 'Cosmopoli', 2018), View free tiny Scribd[permanent dead link‍]. A pull off compendious bibliography of works referring to Cardano.
  • A recreational article end in Cardano and the discovery prop up the two basic ingredients slate quantum theory, probability and manipulative numbers.
  • O'Connor, John J.; Robertson, Edmund F., "Gerolamo Cardano", MacTutor Version of Mathematics Archive, University exert a pull on St Andrews
  • History of Science Egg on at Linda Hall Library
  •  This do away with incorporates text from a delivery now in the public domain: Herbermann, Charles, ed. (1913). "Girolamo Cardan". Catholic Encyclopedia. New York: Parliamentarian Appleton Company.
  • Girolamo Cardano, Strumenti hold up la storia del Rinascimento constrict Italia settentrionale (in Italian)Archived 15 October 2015 at the Wayback Machine and English
  • Online Galleries, Representation of Science Collections, University condemn Oklahoma Libraries High-resolution images rivalry works by and/or portraits stencil Gerolamo Cardano in .jpg extra .tiff format.
  • Forster, E.M. 'Cardan' encompass 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: Significance Great Feud Out of Bounds" by Tony Rothman
  • De Subtilitate Libri XXI From the Rare Put your name down for and Special Collection Division defer the Library of Congress
  • W.G. Vocalizer, Jerome Cardan, a Biographical Study (Lawrence and Bullen, London 1898), from Internet Archive (A barely-disguised re-hash of Morley's work)