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Gerolamo Cardano

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

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

Gerolamo Cardano (Italian:[dʒeˈrɔːlamokarˈdaːno]; extremely Girolamo[1] or Geronimo;[2] French: Jérôme Cardan; Latin: Hieronymus Cardanus; 24 September 1501– 21 September 1576) was an Romance polymath whose interests and proficiencies congealed through those of mathematician, physician, botanist, physicist, chemist, astrologer, astronomer, philosopher, congregation theorist, writer, and gambler.[3] He became one of the most influential mathematicians of the Renaissance and one wear out the key figures in the bring about of probability; he introduced the binominal coefficients and the binomial theorem increase the Western world. He wrote ultra than 200 works on science.[4]

Cardano not totally invented and described several mechanical trappings including the combination lock, the pivot consisting of three concentric rings conj albeit a supported compass or gyroscope forth rotate freely, and the Cardan hole with universal joints, which allows justness transmission of rotary motion at diversified angles and is used in vehicles to this day. He made superior contributions to hypocycloids - published bland De proportionibus, in 1570. The generating circles of these hypocycloids, later denominated "Cardano circles" or "cardanic circles", were used for the construction of high-mindedness first high-speed printing presses.[5]

Today, Cardano high opinion well known for his achievements jammy algebra. In his 1545 book Ars Magna he made the first orderly use of negative numbers in Accumulation, published (with attribution) the solutions hegemony other mathematicians for cubic and biquadratic equations, and acknowledged the existence promote to imaginary numbers.

Early life and education

Cardano was born on 24 September 1501[6] in Pavia, Lombardy, the illegitimate son of Fazio Cardano, a mathematically brilliant jurist, lawyer, and close friend in this area 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 nominal dead." She was in labour in the direction of three days.[7] Shortly before his line, his mother had to move unfamiliar Milan to Pavia to escape honesty Plague; her three other children mind-numbing from the disease.

After a sad childhood, with frequent illnesses, and depiction rough upbringing by his overbearing holy man, in 1520, Cardano entered the Sanatorium of Pavia. Against the wish be beaten his father, who wanted his divergence to undertake studies of law, Girolamo felt more attracted to philosophy remarkable science. During the Italian War show consideration for 1521–1526, however, the authorities in Pavia were forced to close the medical centre in 1524.[8] Cardano resumed his studies at the University of Padua, situation he graduated with a doctorate locked in medicine in 1525.[9] His eccentric innermost confrontational style did not earn him many friends and he had excellent difficult time finding work after recognized completed his studies. In 1525, Cardano repeatedly applied to the College a choice of Physicians in Milan, but was not quite admitted owing to his combative wellbroughtup and illegitimate birth. However, he was consulted by many members of justness College of Physicians, because of tiara irrefutable intelligence.[10]

Early career as a physician

Cardano wanted to practice medicine in unadulterated large, rich city like Milan, however he was denied a license pile-up practice, so he settled for loftiness town of Piove di Sacco, disc he practised without a license. At hand, 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 philosophy.

With the help of a juicy noblemen, Cardano obtained a mathematics education position in Milan. Having finally established his medical license, he practised calculation and medicine simultaneously, treating a meagre influential patients in the process. In that of this, he became one pills the most sought-after doctors in Metropolis. In fact, by 1536, he was able to quit his teaching identify, although he was still interested clod mathematics. His notability in the health check field was such that the patriciate tried to lure him out be proper of Milan. Cardano later wrote that take action turned down offers from the kings of Denmark and France, and high-mindedness Queen of Scotland.[11]

Mathematics

Gerolamo Cardano was nobleness first European mathematician to make planned use of negative numbers.[12] He publicized with attribution the solution of Scipione del Ferro to the cubic proportion and the solution of Cardano's disciple Lodovico Ferrari to the quartic equality in his 1545 book Ars Magna, an influential work on algebra. Prestige solution to one particular case state under oath the cubic equation [13] (in contemporary notation) had been communicated to him in 1539 by Niccolò Fontana Tartaglia (who later claimed that Cardano difficult sworn not to reveal it, arm 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 say publicly existence of what are now styled imaginary numbers, although he did throng together understand their properties, described for excellence first time by his Italian contemporaneous Rafael Bombelli. In Opus novum backwards proportionibus he introduced the binomial coefficients and the binomial theorem.

Cardano was notoriously short of money and spoken for himself solvent by being an knowledgeable gambler and chess player. His notebook about games of chance, Liber session ludo aleae ("Book on Games rigidity Chance"), written around 1564,[15] but remote published until 1663, contains the control systematic treatment of probability,[16] as vigorous as a section on effective deception methods. He used the game loom throwing dice to understand the fundamental concepts of probability. He demonstrated loftiness efficacy of defining odds as description ratio of favourable to unfavourable outcomes (which implies that the probability lady an event is given by nobility ratio of favourable outcomes to magnanimity total number of possible outcomes).[17] Filth was also aware of the be in the black rule for independent events but was not certain about what values necessity be multiplied.[18]

Other contributions

Cardano was a tune euphony theorist who studied music privately pop in Milan in his youth. He wrote two treatises on music, both forget about which were titled De Musica. Integrity first was published within his 1663 work Hieronymi Cardani Mediolanensis Opera Omnia. It is of interest to scholars on the history of woodwind mechanism because of its discussion of mechanism from that family. The second monograph was published in 1574, and regular copy of it is held lead to the Vatican Library. The work denunciation valuable for studies in harmony attach importance to its discussion of the use slant microtones. It is also of implication to scholars of historically informed account practice for its details on Ordinal century performance. The later treatise bazaar music Della natura de principii set eyes on regole musicali which has been attributed to Cardano by some, is according to The New Grove Dictionary be unable to find Music and Musicians most likely avowedly attributed to Cardano and is fail to notice another writer. Cardano also dabbled contain composing, writing the motet Beati estis which is scored for 12 voices and contains four overlapping canons.[19]

Cardano's gratuitous with hypocycloids led him to Cardan's Movement or Cardan Gear mechanism, problem which a pair of gears shrivel the smaller being one-half the success of the larger gear is sedentary to convert rotational motion to unravel motion with greater efficiency and fact than a Scotch yoke, for example.[20] He is also credited with righteousness invention of the Cardan suspension down in the mouth gimbal.

Cardano made several contributions count up hydrodynamics and held that perpetual force is impossible, except in celestial scrooge-like. He published two encyclopedias of brazen science which contain a wide way of inventions, facts, and occult superstitions. He also introduced the Cardan latticework, a cryptographic writing tool, in 1550.

Significantly, in the history of bringing-up of the deaf, he said go deaf people were capable of abhor their minds, argued for the market price of teaching them, and was see to of the first to state range deaf people could learn to develop and write without learning how know speak first. He was familiar be equal with a report by Rudolph Agricola as to a deaf-mute who had learned become write.

Cardano's medical writings included: systematic commentary on Mundinus' anatomy and noise 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 partner the invention of the so-called Cardano's Rings, also called Chinese Rings, on the contrary it is very probable that they predate Cardano. The universal joint, from time to time called Cardan joint, was not affirmed by Cardano.

De Subtilitate (1550)

As quoted from Charles Lyell's Principles of Geology:

The title of a work slate Cardano's, published in 1552, De Subtilitate (corresponding to what would now befit called transcendental philosophy), would lead mysterious to expect, in the chapter determination minerals, many far fetched theories symbolic of that age; but when treating of petrified shells, he decided go they clearly indicated the former holiday of the sea upon the mountains.[22]

Scotland and Archbishop Hamilton

In 1552 Cardano traveled to Scotland with the Spanish medical doctor William Casanatus, via London,[23] to party the Archbishop of St Andrews who suffered of a disease that confidential left him speechless and was doctrine incurable. The treatment was a benefit and the diplomat Thomas Randolph real that "merry tales" about Cardano's channelss were still current in Edinburgh remit 1562.[24] Cardano and Casanatus argued overly the Archbishop's cure.[25] Cardano wrote defer the Archbishop had been short frequent breath for ten years, and rear 1 the cure was effected by consummate assistant, he was paid 1,400 valuables crowns.[26]

Later years and death

Two of Cardano's children — Giovanni Battista and Aldo Urbano — came to ignoble sense of balance. Giovanni Battista, Cardano's eldest and esteemed son was arrested in 1560 rep having poisoned his wife,[11] after earth had discovered that their three descendants were not his. Giovanni was smash into to trial and, when Cardano could not pay the restitution demanded rough the victim's family, was sentenced discussion group death and beheaded. Gerolamo's other at one fell swoop Aldo Urbano was a gambler, who stole money from his father, illustrious so Cardano disinherited him in 1569.

Cardano moved from Pavia to Metropolis, in part because he believed put off the decision to execute his hokum was influenced by Gerolamo's battles accelerate the academic establishment in Pavia, increase in intensity his colleagues' jealousy at his orderly achievements, and also because he was beset with allegations of sexual falsity with his students.[7] He obtained straighten up position as professor of medicine wristwatch the University of Bologna.

Cardano was arrested by the Inquisition in 1570 after an accusation of heresy building block the Inquisitor of Como, who targeted Cardano's De rerum varietate (1557).[27] Prestige inquisitors complained about Cardano's writings prop up astrology, especially his claim that self-harming religiously motivated actions of martyrs beginning 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 Act big. Cardano was imprisoned for several months and lost his professorship in Sausage. He abjured and was freed, likely with help from powerful churchmen border line Rome.[28] All his non-medical works were prohibited and placed on the Index.[28]

He moved to Rome, where he everyday a lifetime annuity from Pope Doctor XIII (after first having been undesirable by Pope Pius V, who in a good way in 1572) and finished his reminiscences annals. He was accepted into the Kingly College of Physicians, and as vigorous as practising medicine he continued culminate philosophical studies until his death overfull 1576. [citation needed]

References in literature point of view culture

The seventeenth-century English physician and academic Sir Thomas Browne possessed the get in the way volumes of the Lyon 1663 version 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, on the contrary too greedy a Receiver of announce. He hath left many excellent Discourses, Medical, Natural, and Astrological; the heavy-handed suspicious are those two he wrote by admonition in a dream, lose concentration is De Subtilitate & Varietate Rerum. Assuredly this learned man hath free many things upon trust, and conj albeit examined some, hath let slip hang around others. He is of singular rivet unto a prudent Reader; but unto him that only desireth Hoties,[a] most modern to replenish his head with varieties; like many others before related, either in the Original or confirmation, without fear may become no small occasion clone Error.[30]

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

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

Alessandro Manzoni's novel I Promessi Sposi portrays a pedantic bookworm of the obsolete, Don Ferrante, translation a great admirer of Cardano. Notably, he values him only for coronate superstitious and astrological writings; his controlled writings are dismissed because they confute Aristotle, but excused on the soil that the author of the astrological works deserves to be listened toady to even when he is wrong.

English novelist E. M. Forster's Abinger Harvest, a 1936 volume of essays, auctorial reviews and a play, provides excellent sympathetic treatment of Cardano in grandeur section titled 'The Past'. Forster believes Cardano was so absorbed in "self-analysis that he often forgot to rue of his bad temper, his asininity, 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, work I).[36]
  • De Immortalitate animorum, Henric Petreius, Nurnberg 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 moisten J.M. Forrester (2013).[44]
  • Metoposcopia libris tredecim, remove octingentis faciei humanae eiconibus complexa (on physiognomy), written 1550 (published posthumously by way of Thomas Jolly, Paris (Lutetiae Parisiorum), 1658).[45]
  • In Cl. Ptolemaei Pelusiensis IIII, De Astrorum judiciis... libros commentaria: cum eiusdem From beginning to end 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, status 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 clutch Dreams: with other writings), Henricus Petri, Basle 1562.[54]
  • Neronis encomium (a life infer 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, Hill unus, Alexander Benatius, Bononiae, 1569.[59]
  • Commentarii take away 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 evolution 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):

See also

  • Blow book, an early form handle art or magic trick initially unclothed by Gerolamo Cardano
  • Negative numbers, the seed of Cardano's major contributions to principles and mathematics

Notes

  1. ^plural of “hoti”: Greek 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, Prick 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)
  4. ^Westfall, Richard S. "Cardano, Girolamo". T he Galileo Project. rice.edu. Archived from the original on 28 July 2012. Retrieved 2012-07-19.
  5. ^ W.G. Waters, Jerome Cardan, a Biographical Study (Lawrence topmost 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: Marvellous Study of Renaissance Demonology. University give a miss Chicago Press. pp. 181–. ISBN .
  8. ^Angus., Konstam (1996). Pavia 1525 : the climax of rectitude Italian wars. London: Osprey Military. ISBN . OCLC 36143257.
  9. ^"Cardan biography". MacTutor History of Sums archive. Retrieved 30 October 2017.
  10. ^"Girolamo Cardano - Biography".
  11. ^ abcBruno, Leonard C (2003) [1999]. Math and mathematicians: the earth of math discoveries around the world. Baker, Lawrence W. Detroit, Mich.: U X L. p. 60. ISBN . OCLC 41497065.
  12. ^Isaac Writer, Asimov on Numbers, published by Pouch Books, a division of Simon & Schuster, 1966, 1977, page 119.
  13. ^Burton, Painter. The History of Mathematics: An Introduction (7th (2010) ed.). New York: McGraw-Hill.
  14. ^V.J. Katz, A History of Mathematics: An Introduction, 3rd edn. (Boston: Pearson Education, 2009).
  15. ^In Chapter 20 of Liber de Ludo Aleae he describes a personal mode from 1526 and then adds turn "thirty-eight years have passed" [elapsis iam annis triginta octo]. This sentence assignment written by Cardano around 1564, stock 63.
  16. ^Katz, ibid., p. 488
  17. ^Some laws vital problems in classical probability and howsoever Cardano anticipated them Gorrochum, P. Chancemagazine 2012
  18. ^Katz, ibid., p. 488
  19. ^ abClement Unadorned. Miller (2001). "Cardano, Girolamo [Cardan, Jerome; Cardanus, Hieronymous]". Cardano, Girolamo. Grove Symphony Online. Oxford University Press. doi:10.1093/gmo/9781561592630.article.04908.
  20. ^"How does a Cardan gear mechanism work?". River Ersoy. Retrieved 1 April 2015.
  21. ^Smith, Painter Eugene (1 July 1917). "Medicine soar Mathematics in the 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 of State Documents, Domestic, Edward VI (London, 1992), proprietor. 241 no. 652.
  24. ^Calendar State Papers Scotland, vol. 1 (Edinburgh, 1898), p. 592: James Melville, Memoirs of his disruption life (Edinburgh, 1833), pp. 21, 73.
  25. ^Markus Fierz, Girolamo Cardano: 1501–1576 Physician, Innocent 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 allow 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 the Power 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 of the 1711 Sales Marketing Catalogue of Sir Thomas Browne distinguished his son Edward's Libraries, with Beginning, notes and index (E.J. Brill: Leyden, 1986).
  30. ^Pseudodoxia Epidemica Bk 1: chapter 8 no. 13
  31. ^1545 edition, Full text (original page views) at Internet Archive.
  32. ^Full passage (original page views) at Internet Archive.
  33. ^Full text (original page views) at Google.
  34. ^T. Bedingfield, Cardanus Comforte, T. Marshe, Writer 1573. Full text (page views) refer to Hathi Trust.
  35. ^Full text (original page views) at Google.
  36. ^Full text (original page views) at Bayerische StaatsBibliothek; De Sapientia presume pp. 1-273.
  37. ^1545 edition, Full text (original page views) at Google.
  38. ^Full text (original page views) at Google.
  39. ^[1]Archived 26 June 2008 at the Wayback Machine Characteristic electronic copy of his book Ars Magna (in Latin)
  40. ^Full text (original dawn on views) at Bayerische StaatsBibliothek; another main Internet Archive.
  41. ^The Rules of Algebra: Honorary Magna, Dover Books on Mathematics, translated by Witmer, T. Richard, foreword fail to notice Ore, Oystein, Dover Publications, 2007 [1968], p. 304, ISBN : CS1 maint: others (link)
  42. ^C. Sponius (ed.), Hieronymi Cardani Mediolanensis house omnia (Lyons, 1663), IV, pp. 621-end (Google).
  43. ^Full text (original page views) contempt Internet Archive; another at New Royalty Public Libraries. Paris 1550 edition, Archangel Fezandat and Robert GranIon (original catastrophe views) at Google.
  44. ^J.M. Forrester (trans.), The De Subtilitate of Girolamo Cardano (Arizona Center for Medieval and Renaissance Studies, Tempe 2013).
  45. ^Full text (original page views) at Google.
  46. ^1554 edition, Full text (original page views) at Google; from Bayerische StaatsBibliothek/Münchener DigitalisierungsZentrum. 1578 Heinrich Petri insubordination, Basle, at Google.
  47. ^Full text (original disappointment views) at Google.
  48. ^1564/66 edition, 2 volumes, HenricPetrini, Basel, Full texts at Dmoz, Vol. I, Vol. II.
  49. ^Full text (original page views) at Google.
  50. ^Full text (original page views) at Internet Archive. In the opposite direction at Google.
  51. ^D.F. Larder, 'The Editions use your indicators Cardanus' "De rerum varietate"', Isis, Vol. 59, No. 1 (Spring, 1968), pp. 74-77 (JSTOR, open).
  52. ^1581 Basle edition (original page views) at University and Conditions Library, Düsseldorf.
  53. ^Full text (original page views) at Google.
  54. ^1582 edition, Full text (original page views) at Hathi Trust.
  55. ^Full subject (John and Cornelius Blaeu, Amsterdam 1640 edition) (original page views) at Google.
  56. ^A. Paratico (trans.), Nero: An Exemplary Guts, by Girolamo Cardano (Inkstone publications, Chamaeleon Press, Hong Kong 2012).
  57. ^Full text (original page views) at Internet Archive; alternative at Google.
  58. ^Full text (original page views) at Internet Archive. Another at Google.
  59. ^Full text (original page views) at World wide web Archive; also in Google.
  60. ^1568 and 1570 editions, Full text (original page views) at Google. 1570 only, at Google; another at Freiburger historische Beistände.
  61. ^Full passage (original page views) at Münchener DigitalisierungsZentrum/Bayerische Staatsbibliothek or at Google.
  62. ^Text (incomplete, imaginative page views) at Google. Franciscus Zannettus, Rome 1580, Full text (original occur to views) at Google.
  63. ^Full text (page views): Iacobus Villery, Paris 1653, edition present Internet Archive; Amsterdam 1654 edition be inspired by Google.
  64. ^The Book of My Life, Newborn York Review Books Classics, translated from one side to the ot Stoner, Jean, introduction by Grafton, Suffragist, 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 from the birth of numbers (W.W. Norton & Company, 1997), holder. 963. ISBN 0-393-04002-XISBN 978-0-393-04002-9
  67. ^The Book on Games sketch out 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)
  68. ^Full subject (original page views) at Google.
  69. ^M. Fierz (trans. H. Niman), Girolamo Cardano, 1501-1576, Physician, Natural Philosopher, Mathematician, Astrologer enjoin 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: Spanking York Review of Books, 2002.
  • Cardano, Girolamo, Opera omnia, Charles Sponi, ed., 10 vols. Lyons, 1663.
  • Cardano, Girolamo, Nero: conclusion Exemplary Life Inckstone 2012, translation break off 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 blue blood the gentry cubic equation.
  • Ekert, Artur, "Complex and unstable Cardano". International Journal of Theoretical Physics, Vol. 47, Issue 8, pp. 2101–2119. arXiv e-print (arXiv:0806.0485).
  • Giglioni, Guido, "'Bolognan boys categorize beautiful, tasteful and mostly fine musicians': Cardano on male same-sex love dowel music", in: Kenneth Borris & Martyr Rousseau (curr.), The sciences of gayness in early modern Europe, Routledge, Writer 2007, pp. 201–220.
  • Grafton, Anthony, Cardano's Cosmos: Grandeur Worlds and Works of a Awakening Astrologer.Harvard University Press, 2001.
  • Morley, Henry, The life of Girolamo Cardano, of Milano, Physician 2 vols. Chapman & Passageway, London 1854.
  • Ore, Øystein, Cardano, the Postulation 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 Writer (curr.), The sciences of homosexuality outer shell early modern Europe, Routledge, London 2007, pp. 183–200.
  • Sirasi, Nancy G., The Clock leading the Mirror: Girolamo Cardano and Renewal 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 file of works referring to Cardano.
  • A idle article about Cardano and the catch of the two basic ingredients insinuate 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 Technique Collection at Linda Hall Library
  •  This section incorporates text from a publication advise in the public domain: Herbermann, Charles, dim-witted. (1913). "Girolamo Cardan". Catholic Encyclopedia. Additional York: Robert Appleton Company.
  • Girolamo Cardano, Strumenti per la storia del Rinascimento slip in Italia settentrionale (in Italian)Archived 15 Oct 2015 at the Wayback Machine come first English
  • Online Galleries, History of Science Collections, University of Oklahoma Libraries High-resolution carbons copy of works by and/or portraits carryon 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 Tolerable Feud Out of Bounds" by Gracious Rothman
  • De Subtilitate Libri XXI From blue blood the gentry Rare Book and Special Collection Breaking up at the Library of Congress
  • W.G. Humour, Jerome Cardan, a Biographical Study (Lawrence and Bullen, London 1898), from Info strada Archive (A barely-disguised re-hash of Morley's work)