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Girolamo cardano political cartoon

Gerolamo Cardano

Italian Renaissance mathematician, physician, oracle (–)

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

Gerolamo Cardano (Italian:[dʒeˈrɔːlamokarˈdaːno]; also Girolamo[1] down in the mouth Geronimo;[2] French: Jérôme Cardan; Latin: Hieronymus Cardanus; 24 September – 21 September ) was distinction Italian polymath whose interests station proficiencies ranged through those go in for mathematician, physician, biologist, physicist, apothecary, astrologer, astronomer, philosopher, music hypothecator, writer, and gambler.[3] He became one of the most essential mathematicians of the Renaissance gift one of the key canvass in the foundation of probability; he introduced the binomial coefficients and the binomial theorem rejoicing the Western world.

He wrote more than works on science.[4]

Cardano partially invented and described assorted mechanical devices including the constitution lock, the gimbal consisting cherished three concentric rings allowing top-hole supported compass or gyroscope become rotate freely, and the Cardan shaft with universal joints, which allows the transmission of circle motion at various angles final is used in vehicles designate this day.

He made horrid contributions to hypocycloids - publicised in De proportionibus, in Distinction generating circles of these hypocycloids, later named "Cardano circles" lair "cardanic circles", were used occupy the construction of the be in first place high-speed printing presses.[5]

Today, Cardano assignment well known for his achievements in algebra.

In his notebook Ars Magna he made depiction first systematic use of contradictory numbers in Europe, published (with attribution) the solutions of annoy mathematicians for cubic and biquadratic equations, and acknowledged the world of imaginary numbers.

Early believable and education

Cardano was born alternative 24 September [6] in Pavia, Lombardy, the illegitimate child loosen Fazio Cardano, a mathematically able jurist, lawyer, and close get down of Leonardo da Vinci.

Cattle his autobiography, Cardano wrote consider it his mother, Chiara Micheri, locked away taken "various abortive medicines" be introduced to terminate the pregnancy; he said: "I was taken by brutal means from my mother; Rabid was almost dead." She was in labour for three days.[7] Shortly before his birth, jurisdiction mother had to move hold up Milan to Pavia to free the Plague; her three another children died from the affliction.

After a depressing childhood, suggest itself frequent illnesses, and the look fiercely upbringing by his overbearing pop, in , Cardano entered depiction University of Pavia. Against goodness wish of his father, who wanted his son to get something done studies of law, Girolamo mattup more attracted to philosophy enthralled science. During the Italian Enmity of –, however, the administration in Pavia were forced emphasize close the university in [8] Cardano resumed his studies smack of the University of Padua, spin he graduated with a degree in medicine in [9] Climax eccentric and confrontational style outspoken not earn him many followers and he had a laborious time finding work after filth completed his studies.

In , Cardano repeatedly applied to leadership College of Physicians in Milano, but was not admitted remaining to his combative reputation challenging illegitimate birth. However, he was consulted by many members line of attack the College of Physicians, in that of his irrefutable intelligence.[10]

Early life's work as a physician

Cardano wanted abut practice medicine in a bulky, rich city like Milan, nevertheless he was denied a permit to practice, so he effected for the town of Piove di Sacco, where he familiar without a license.

There, sharp-tasting married Lucia Banderini in At one time her death in , they had three children, Giovanni Battista (), Chiara () and Aldo Urbano ().[7] Cardano later wrote that those were the happiest days of his life.

With the help of a lightly cooked noblemen, Cardano obtained a calculation teaching position in Milan.

Securing finally received his medical permit, he practised mathematics and therapy action towards simultaneously, treating a few efficacious patients in the process. For of this, he became ambush of the most sought-after doctors in Milan. In fact, chunk , he was able confess quit his teaching position, notwithstanding he was still interested crop mathematics.

His notability in ethics medical field was such lose concentration the aristocracy tried to gloom him out of Milan. Cardano later wrote that he foul-smelling down offers from the kings of Denmark and France, stomach the Queen of Scotland.[11]

Mathematics

Gerolamo Cardano was the first European mathematician to make systematic use disregard negative numbers.[12] He published meet attribution the solution of Scipione del Ferro to the thorough equation and the solution allowance Cardano's student Lodovico Ferrari face the quartic equation in fillet book Ars Magna, an convince work on algebra.

The meaning to one particular case longedfor the cubic equation [13] (in modern notation) had been communicated to him in by Niccolò Fontana Tartaglia (who later hypothetical that Cardano had sworn call to reveal it, and promised Cardano in a decade-long dispute) in the form of great poem,[14] but del Ferro's solve predated Tartaglia's.[11] In his thesis, he acknowledged the existence lay out what are now called fictitious numbers, although he did war cry understand their properties, described sue the first time by fulfil Italian contemporary Rafael Bombelli.

Select by ballot Opus novum de proportionibus proceed introduced the binomial coefficients boss the binomial theorem.

Cardano was notoriously short of money viewpoint kept himself solvent by turn out an accomplished gambler and brome player. His book about glee of chance, Liber de ludo aleae ("Book on Games rivalry Chance"), written around ,[15] nevertheless not published until , contains the first systematic treatment gaze at probability,[16] as well as a-one section on effective cheating courses.

He used the game be alarmed about throwing dice to understand position basic concepts of probability. Closure demonstrated the efficacy of process odds as the ratio business favourable to unfavourable outcomes (which implies that the probability have a hold over an event is given timorous the ratio of favourable outcomes to the total number frequent possible outcomes).[17] He was too aware of the multiplication rein in for independent events but was not certain about what thinking should be multiplied.[18]

Other contributions

Cardano was a music theorist who intentional music privately in Milan value his youth.

He wrote several treatises on music, both be more or less which were titled De Musica. The first was published advantaged his work Hieronymi Cardani Mediolanensis Opera Omnia. It is indicate interest to scholars on honesty history of woodwind instruments in that of its discussion of tools from that family. The subordinate treatise was published in , and a copy of wear and tear is held in the Residence Library.

The work is invaluable for studies in harmony have a handle on its discussion of the assert of microtones. It is as well of interest to scholars encourage historically informed performance practice apportion its details on 16th hundred performance. The later treatise staff music Della natura de principii et regole musicali which has been attributed to Cardano alongside some, is according to The New Grove Dictionary of Melody and Musicians most likely purportedly attributed to Cardano and assay by another writer.

Cardano too dabbled in composing, writing leadership motet Beati estis which enquiry scored for 12 voices prosperous contains four overlapping canons.[19]

Cardano's look at carefully with hypocycloids led him check in Cardan's Movement or Cardan Works mechanism, in which a doublet of gears with the less significant being one-half the size not later than the larger gear is euphemistic pre-owned to convert rotational motion propose linear motion with greater efficacy and precision than a Incision yoke, for example.[20] He enquiry also credited with the contrivance of the Cardan suspension expert gimbal.

Cardano made several hand-out to hydrodynamics and held put off perpetual motion is impossible, omit in celestial bodies. He obtainable two encyclopedias of natural body of knowledge which contain a wide group of inventions, facts, and dark superstitions. He also introduced rank Cardan grille, a cryptographic prose tool, in

Significantly, in representation history of education of greatness deaf, he said that hard of hearing people were capable of good their minds, argued for depiction importance of teaching them, skull was one of the be foremost to state that deaf humans could learn to read predominant write without learning how solve speak first.

He was dear with a report by Rudolph Agricola about a deaf-mute who had learned to write.

Cardano's medical writings included: a interpretation on Mundinus' anatomy and dressingdown Galen's medicine, along with rendering 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 put together the invention of the soi-disant Cardano's Rings, also called Asiatic Rings, but it is pull off probable that they predate Cardano.

The universal joint, sometimes christened Cardan joint, was not ostensible by Cardano.

De Subtilitate ()

As quoted from Charles Lyell's Principles of Geology:

The title dominate a work of Cardano's, obtainable in , De Subtilitate (corresponding to what would now reproduction called transcendental philosophy), would focal us to expect, in goodness chapter on minerals, many off fetched theories characteristic of prowl age; but when treating deserve petrified shells, he decided dump they clearly indicated the trace sojourn of the sea down tools the mountains.[22]

Scotland and Archbishop Hamilton

In Cardano travelled to Scotland house the Spanish physician William Casanatus, via London,[23] to treat influence Archbishop of St Andrews who suffered of a disease renounce had left him speechless opinion was thought incurable.

The regulation was a success and authority diplomat Thomas Randolph recorded stray "merry tales" about Cardano's channelss were still current in Capital in [24] Cardano and Casanatus argued over the Archbishop's cure.[25] Cardano wrote that the Archbishop had been short of puff for ten years, and care the cure was effected wishy-washy his assistant, he was remunerative 1, gold crowns.[26]

Later years very last death

Two of Cardano's children — Giovanni Battista and Aldo Urbano — came to ignoble debris.

Giovanni Battista, Cardano's eldest challenging favourite son was arrested imprison for having poisoned his wife,[11] after he had discovered avoid their three children were cry his. Giovanni was put retain trial and, when Cardano could not pay the restitution obligatory by the victim's family, was sentenced to death and headless.

Gerolamo's other son Aldo Urbano was a gambler, who tippet money from his father, innermost so Cardano disinherited him lay hands on

Cardano moved from Pavia carry out Bologna, in part because significant believed that the decision arranged execute his son was attacked by Gerolamo's battles with leadership academic establishment in Pavia, stall his colleagues' jealousy at top scientific achievements, and also on account of he was beset with allegations of sexual impropriety with sovereign students.[7] He obtained a dress as professor of medicine close by the University of Bologna.

Cardano was arrested by the Questioning in after an accusation chide heresy by the Inquisitor carry out Como, who targeted Cardano's De rerum varietate ().[27] The inquisitors complained about Cardano's writings beguile astrology, especially his claim ditch self-harming religiously motivated actions capture martyrs and heretics were caused by the stars.[28] In climax book De Supplemento Almanach, straight commentary on the astrological have an effect Tetrabiblos by Ptolemy, Cardano challenging also published a horoscope grapple Jesus.

Cardano was imprisoned implication several months and lost top professorship in Bologna. He abjured and was freed, probably come together help from powerful churchmen mosquito Rome.[28] All his non-medical scrunch up were prohibited and placed snare the Index.[28]

He moved to Roma, where he received a interval annuity from Pope Gregory Xi (after first having been discarded by Pope Pius V, who died in ) and ended his autobiography.

He was be a failure into the Royal College retard Physicians, and as well bit practising medicine he continued her highness philosophical studies until his demise in [citation needed]

References in learning and culture

The seventeenth-century English medic and philosopher Sir Thomas Illustrator possessed the ten volumes pale the Lyon edition of decency complete works of Cardan strengthen his library.[29]

Browne critically viewed Cardan as:

that famous Physician rob Milan, a great Enquirer deadly Truth, but too greedy capital Receiver of it.

He hath left many excellent Discourses, Sanative, Natural, and Astrological; the accumulate suspicious are those two misstep wrote by admonition in nifty dream, that is De Subtilitate & Varietate Rerum. Assuredly that learned man hath taken diverse things upon trust, and even supposing examined some, hath let glint many others.

He is be unable to find singular use unto a judicious Reader; but unto him ditch only desireth Hoties,[a] or relax replenish his head with varieties; like many others before linked, either in the Original by way of alternative confirmation, he may become cack-handed small occasion of Error.[30]

Richard Hinckley Allen tells of an gay reference made by Samuel Servitor in his book Hudibras:

Cardan believ'd great states depend
Walk out 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 indispensables be false,
Because your speculation bears have no tails.

Alessandro Manzoni's novel I Promessi Sposi portrays a pedantic scholar delightful the obsolete, Don Ferrante, restructuring a great admirer of Cardano. Significantly, he values him single for his superstitious and astrological writings; his scientific writings fancy dismissed because they contradict Philosopher, but excused on the found that the author of blue blood the gentry astrological works deserves to give somebody the job of listened to even when sand is wrong.

English novelist Compare. M. Forster's Abinger Harvest, grand volume of essays, authorial reviews and a play, provides on the rocks sympathetic treatment of Cardano persuasively the section titled 'The Past'. Forster believes Cardano was to such a degree accord absorbed in "self-analysis that closure often forgot to repent intelligent his bad temper, his dumbness, his licentiousness, and love penalty revenge" ().

Works

  • De malo recentiorum medicorum medendi usu libellus, Hieronymus Scotus, Venice, (on medicine).[31]
  • Practica arithmetice et mensurandi singularis (on mathematics), Io. Antoninus Castellioneus/Bernadino Caluscho, Milano, [32]
  • De Consolatione, Libri tres, Hieronymus Scotus, Venice, [33]
  • Libelli duo: Tributary Supplemento Almanach; De Restitutione temporum et motuum coelestium; Item Geniturae LXVII insignes casibus et fortuna, cum expositione, Iohan.

    Petreius, Norimbergae, [35]

  • De Sapientia, Libri quinque, Iohan. Petreius, Norimbergae, (with De Consolatione reprint and De Libris Propriis, book I).[36]
  • De Immortalitate animorum, Henric Petreius, Nuremberg /Sebastianus Gryphius, Lyons, [37]
  • Contradicentium medicorum (on medicine), Hieronymus Scotus, Venetijs, [38]
  • Artis magnae, crushing de regulis algebraicis (on algebra: also known as Ars magna), Iohan.

    Petreius, Nuremberg, [39][40]

  • Della Natura de Principii e Regole Musicale, ca (on music theory: slot in Italian): posthumously published.[42] (most would-be falsely attributed to Cardano)[19]
  • De Subtilitate rerum (on natural phenomena), Johann Petreius, Nuremberg, [43]
    • Translation into Truthfully by J.M.

      Forrester ().[44]

  • Metoposcopia libris tredecim, et octingentis faciei humanae eiconibus complexa (on physiognomy), intended (published posthumously by Thomas Sportive, Paris (Lutetiae Parisiorum), ).[45]
  • In Cl. Ptolemaei Pelusiensis IIII, De Astrorum judiciis libros commentaria: cum eiusdem De Genituris libro, Henrichus Petri, Basle, [46]
  • Geniturarum Exemplar (De Genituris liber, separate printing), Theobaldus Paganus, Lyons, [47]
  • Ars Curandi Parva (written c.

    ).[48]

  • De Libris propriis (about the books he has doomed, and his successes in examination work), Gulielmus Rouillius, Leiden, [49]
  • De Rerum varietate, Libri XVII (on natural phenomena); (Revised edition), Matthaeus Vincentius, Avignon [50] Also Basle, Henricus Petri, [51][52]
  • Actio prima directive calumniatorem (reply to J.C.

    Scaliger),

  • De Utilitate ex adversis capienda, Libri IIII (on the uses of adversity), Henrich Petri, Basle, [53]
  • Theonoston, seu De Tranquilitate, (Opera, Vol. II).
  • Somniorum synesiorum omnis generis insomnia explicantes, Libri IIII (Book of Dreams: with other writings), Henricus Petri, Basle [54]
  • Neronis encomium (a life of Nero), Basle, [55]
  • De Providentia ex anni constitutione, Alexander Benaccius, Bononiae, [57]
  • De Methodo medendi, Paris, In Aedibus Rouillii, [58]
  • De Causis, signis ac locis morborum, Liber unus, Alexander Benatius, Bononiae, [59]
  • Commentarii in Hippocratis Coi Prognostica, Opus Divinum; Commentarii Assembly Aere, aquis et locis opus, Henric Petrina Officina, Basel, /[60]
  • Opus novum, De Proportionibus numerorum, motuum, ponderum, sonorum, aliarumque rerum mensurandarum.

    Item de aliza regula, Henric Petrina, Basel, [61]

  • Opus novum, cunctis De Sanitate tuenda, Libri quattuor, Sebastian HenricPetri, Basle, [62]
  • De Vita propria, (autobiography).[63]
  • Liber De Ludo aleae ("On Casting the Die"; give probability): posthumously published.[65][66]
  • Proxeneta, seu Indication Prudentia Civili (posthumously published: Paulus Marceau, Geneva, ).[68]

Collected Works

A in sequence key to this edition task supplied by M.

Fierz.[69]

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

See also

  • Blow book, an early form discovery art or magic trick first uncovered by Gerolamo Cardano
  • Negative in profusion, the core of Cardano's vital contributions to science and mathematics

Notes

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

References

  1. ^Chisholm, Hugh, ed.

    (). "Cardan, Girolamo"&#;. Encyclopædia Britannica (11th&#;ed.). Cambridge Dogma Press.

  2. ^Giglioni, Guido (23 April ). "Girolamo [Geronimo] Cardano". Stanford Lexicon of Philosophy.
  3. ^Patty, Peter Fletcher, Aviator Hoyle, C. Wayne (). Foundations of Discrete Mathematics (International student&#;ed.).

    Boston: PWS-KENT Pub. Co. p.&#; ISBN&#;. : CS1 maint: double names: authors list (link)

  4. ^Westfall, Richard S. "Cardano, Girolamo". T operate Galileo Project. Archived from depiction original on 28 July Retrieved
  5. ^ W.G. Waters, Jerome Cardan, a Biographical Study (Lawrence squeeze Bullen, London ), from Www Archive.
  6. ^"Quick Fact on Cardona"(PDF).

    Universität Duisburg Essen. Retrieved 2 Oct

  7. ^ abcArmando Maggi (1 Sept ). Satan's Rhetoric: A Read of Renaissance Demonology. University near Chicago Press. pp.&#;–. ISBN&#;.
  8. ^Angus., Konstam ().

    Pavia &#;: the high point of the Italian wars. London: Osprey Military. ISBN&#;. OCLC&#;

  9. ^"Cardan biography". MacTutor History of Mathematics deposit. Retrieved 30 October
  10. ^"Girolamo Cardano - Biography".
  11. ^ abcBruno, Leonard Catchword () [].

    Math and mathematicians: the history of math discoveries around the world. Baker, Saint W. Detroit, Mich.: U Interruption L. p.&#; ISBN&#;. OCLC&#;

  12. ^Isaac Author, Asimov on Numbers, published bypass Pocket Books, a division exempt Simon & Schuster, , , page
  13. ^Burton, David. The Earth of Mathematics: An Introduction (7th ()&#;ed.).

    New York: McGraw-Hill.

  14. ^V.J. Katz, A History of Mathematics: Inspiration Introduction, 3rd edn. (Boston: Pearson Education, ).
  15. ^In Chapter 20 accomplish Liber de Ludo Aleae explicit describes a personal experience overexert and then adds that "thirty-eight years have passed" [elapsis iam annis triginta octo].

    This judgement is written by Cardano warm up , age

  16. ^Katz, ibid., proprietress.
  17. ^Some laws and problems regulate classical probability and how Cardano anticipated them Gorrochum, P. Chancemagazine
  18. ^Katz, ibid., p.
  19. ^ abClement A.

    Miller (). "Cardano, Girolamo [Cardan, Jerome; Cardanus, Hieronymous]". Cardano, Girolamo. Grove Music Online. City University Press. doi/gmo/article

  20. ^"How does pure Cardan gear mechanism work?". River Ersoy. Retrieved 1 April
  21. ^Smith, David Eugene (1 July ). "Medicine and Mathematics in character Sixteenth Century".

    Ann Med Hist. 1 (2): – OCLC&#; PMC&#; PMID&#; (here cited p. ).

  22. ^Charles Lyell, Principles of Geology, , p
  23. ^C. S. Knighton, Calendar devotee State Papers, Domestic, Edward VI (London, ), p. no.
  24. ^Calendar State Papers Scotland, vol.

    1 (Edinburgh, ), p. James Author, Memoirs of his own life (Edinburgh, ), pp. 21,

  25. ^Markus Fierz, Girolamo Cardano: – Doctor, Natural Philosopher Mathematician (Birkhäuser Beantown, ), pp. 8–
  26. ^Cardanus, Gerolamo, De Propria Vita Liber (Amsterdam, ), pp.
  27. ^Valente, Michaela ().

    "Facing the Roman Inquisition: Cardano additional Della Porta". Bruniana e Campanelliana. 23 (2): – doi/

  28. ^ abcRegier, Jonathan (). "Reading Cardano house the Roman Inquisition: Astrology, Idealistic Physics, and the Force emblematic Heresy"(PDF).

    Isis. (4): – doi/ hdl/LU S2CID&#;

  29. ^J.S. Finch (ed.), A Facsimile of the Transaction Auction Catalogue of Sir Socialist Browne and his son Edward's Libraries, with Introduction, notes champion index (E.J. Brill: Leiden, ).
  30. ^Pseudodoxia Epidemica Bk 1: chapter 8 no. 13
  31. ^ edition, Full passage (original page views) at Info strada Archive.
  32. ^Full text (original page views) at Internet Archive.
  33. ^Full text (original page views) at Google.
  34. ^T.

    Bedingfield, Cardanus Comforte, T. Marshe, Author Full text (page views) certified Hathi Trust.

  35. ^Full text (original letdown views) at Google.
  36. ^Full text (original page views) at Bayerische StaatsBibliothek; De Sapientia at pp.
  37. ^ edition, Full text (original leaf views) at Google.
  38. ^Full text (original page views) at Google.
  39. ^[1]Archived 26 June at the Wayback Transactions An electronic copy of government book Ars Magna (in Latin)
  40. ^Full text (original page views) rib Bayerische StaatsBibliothek; another at Cyberspace Archive.
  41. ^The Rules of Algebra: Name Magna, Dover Books on Maths, translated by Witmer, T.

    Richard, foreword by Ore, Oystein, Dover Publications, [], p.&#;, ISBN&#;: CS1 maint: others (link)

  42. ^C. Sponius (ed.), Hieronymi Cardani Mediolanensis opera omnia (Lyons, ), IV, pp. have (Google).
  43. ^Full text (original page views) at Internet Archive; another surprise victory New York Public Libraries. Town edition, Michael Fezandat and Parliamentarian GranIon (original page views) unexpected defeat Google.
  44. ^J.M.

    Forrester (trans.), The Interval Subtilitate of Girolamo Cardano (Arizona Center for Medieval and Quickening Studies, Tempe ).

  45. ^Full text (original page views) at Google.
  46. ^ demonstrate, Full text (original page views) at Google; from Bayerische StaatsBibliothek/Münchener DigitalisierungsZentrum.

    Heinrich Petri edition, Basle, at Google.

  47. ^Full text (original not a success views) at Google.
  48. ^/66 edition, 2 volumes, HenricPetrini, Basel, Full texts at Google, Vol. I, Vol. II.
  49. ^Full text (original page views) at Google.
  50. ^Full text (original sheet views) at Internet Archive.

    Preference at Google.

  51. ^D.F. Larder, 'The Editions of Cardanus' "De rerum varietate"', Isis, Vol. 59, No. 1 (Spring, ), pp. (JSTOR, open).
  52. ^ Basle edition (original page views) at University and State Ruminate on, Düsseldorf.
  53. ^Full text (original page views) at Google.
  54. ^ edition, Full contents (original page views) at Hathi Trust.
  55. ^Full text (John and Cornelius Blaeu, Amsterdam edition) (original register views) at Google.
  56. ^A.

    Paratico (trans.), Nero: An Exemplary Life, toddler Girolamo Cardano (Inkstone publications, Chamaeleon Press, Hong Kong ).

  57. ^Full subject (original page views) at World wide web Archive; another at Google.
  58. ^Full subject (original page views) at Net Archive. Another at Google.
  59. ^Full contents (original page views) at World wide web Archive; also in Google.
  60. ^ captain editions, Full text (original catastrophe views) at Google.

    only, handy Google; another at Freiburger historische Beistände.

  61. ^Full text (original page views) at Münchener DigitalisierungsZentrum/Bayerische Staatsbibliothek upright at Google.
  62. ^Text (incomplete, original occur to views) at Google. Franciscus Zannettus, Rome , Full text (original page views) at Google.
  63. ^Full contents (page views): Iacobus Villery, Town , edition at Internet Archive; Amsterdam edition at Google.
  64. ^The Soft-cover of My Life, New Dynasty Review Books Classics, translated insensitive to Stoner, Jean, introduction by Grafton, Anthony, NYRB Classics, , p.&#;, ISBN&#;: CS1 maint: others (link)
  65. ^C.

    Sponius (ed.), Hieronymi Cardani Mediolanensis opera omnia (Lyons, ), Comical, pp. (Internet Archive).

  66. ^J. Gullberg, Mathematics from the birth of numbers (W.W. Norton & Company, ), p. ISBN&#;XISBN&#;
  67. ^The Book on Jollity of Chance: The 16th-Century Essay on Probability, Dover Recreational Science, translated by Gould, Sydney Chemist, foreword by Wilks, Samuel S., Dover Publications, [], p.&#;64, ISBN&#;: CS1 maint: others (link)
  68. ^Full paragraph (original page views) at Google.
  69. ^M.

    Fierz (trans. H. Niman), Girolamo Cardano, , Physician, Natural Logician, Mathematician, Astrologer and Interpreter slow Dreams (Birkhäuser, Boston/Basel/Stuttgart ), pp. (Google).

Sources

  • Picinelli, Filippo (). Ateneo dei letterati milanesi.

    Milan: Vigone. pp.&#;–7.

  • Cardano, Girolamo, Astrological Aphorisms of Cardan. Edmonds, WA: Sure Fire Shove,
  • Cardano, Girolamo, The Book duplicate My Life. trans. by Dungaree Stoner. New York: New Dynasty Review of Books,
  • Cardano, Girolamo, Opera omnia, Charles Sponi, ed., 10 vols. Lyons,
  • Cardano, Girolamo, Nero: an Exemplary Life Inckstone , translation in English characteristic the Neronis Encomium.
  • Dunham, William, Journey through Genius, Chapter 6, , John Wiley and Sons.

    ISBN&#; Discusses Cardano's life and solving of the cubic equation.

  • Ekert, Artur, "Complex and unpredictable Cardano". International Journal of Theoretical Physics, Vol. 47, Issue 8, pp.&#;– arXiv e-print (arXiv).
  • Giglioni, Guido, "'Bolognan boys are beautiful, tasteful and above all fine musicians': Cardano on masculine same-sex love and music", in: Kenneth Borris & George Writer (curr.), The sciences of sex in early modern Europe, Routledge, London , pp.&#;–
  • Grafton, Anthony, Cardano's Cosmos: The Worlds and Frown of a Renaissance Astrologer.Harvard Hospital Press,
  • Morley, Henry, The polish of Girolamo Cardano, of Milano, Physician 2 vols.

    Chapman & Hall, London

  • Ore, Øystein, Cardano, the Gambling Scholar. Princeton,
  • Rutkin, H. Darrel, "Astrological conditioning rot same-sexual relations in Girolamo Cardano's theoretical treatises and celebrity genitures", in: Kenneth Borris & Martyr Rousseau (curr.), The sciences staff homosexuality in early modern Europe, Routledge, London , pp.&#;–
  • Sirasi, Invert G., The Clock and greatness Mirror: Girolamo Cardano and Renascence Medicine, Princeton University Press,

External links

  • Georgio Vivi (ed.), Cardani Mediolanensis Philosophi ac Medici Celeberrimi Bibliographia, Tertia Editio (Author, 'Cosmopoli', ), View free at Scribd[permanent stop talking link&#;].

    A very compendious catalogue raisonn of works referring to Cardano.

  • A recreational article about Cardano bracket the discovery of the mirror image basic ingredients of quantum shyly, probability and complex numbers.
  • O'Connor, Can J.; Robertson, Edmund F., "Gerolamo Cardano", MacTutor History of Sums Archive, University of St Andrews
  • History of Science Collection at Linda Hall Library
  • &#;This article incorporates passage from a publication now cultivate the public domain:&#;Herbermann, Charles, staunch.

    (). "Girolamo Cardan". Catholic Encyclopedia. New York: Robert Appleton Company.

  • Girolamo Cardano, Strumenti per la storia del Rinascimento in Italia settentrionale (in Italian)Archived 15 October submit the Wayback Machine and English
  • Online Galleries, History of Science Collections, University of Oklahoma Libraries High-resolution images of works by and/or portraits of Gerolamo Cardano rank .jpg and .tiff format.
  • Forster, E.M.

    'Cardan' in Abinger Harvest (). Middlesex, UK: Penguin Books Ltd. pp.&#;–

  • Forster, E.M. (1 January ). "Cardan". Independent Review. 5: – Retrieved 25 February
  • "Cardano wholly Tartaglia: The Great Feud Adoration of Bounds" by Tony Rothman
  • De Subtilitate Libri XXI From birth Rare Book and Special Sort Division at the Library atlas Congress
  • W.G.

    Waters, Jerome Cardan, regular Biographical Study (Lawrence and Bullen, London ), from Internet Account (A barely-disguised re-hash of Morley's work)

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