Girolamo cardano facts management

Gerolamo Cardano

Italian Renaissance mathematician, physician, astrologer (–)

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

Gerolamo Cardano (Italian:[dʒeˈrɔːlamokarˈdaːno]; also Girolamo[1] or Geronimo;[2] French: Jérôme Cardan; Latin: Hieronymus Cardanus; 24 September – 21 September ) was an Italian polymath whose interests and proficiencies ranged through those of mathematician, physician, biologist, physicist, chemist, astrologer, astronomer, philosopher, music theorist, writer, and gambler.[3] He became one of the most influential mathematicians of the Renaissance and one of the key figures in the foundation of probability; he introduced the binomial coefficients and the binomial theorem in the Western world.

He wrote more than works on science.[4]

Cardano partially invented and described several mechanical devices including the combination lock, the gimbal consisting of three concentric rings allowing a supported compass or gyroscope to rotate freely, and the Cardan shaft with universal joints, which allows the transmission of rotary motion at various angles and is used in vehicles to this day.

He made significant contributions to hypocycloids - published in De proportionibus, in The generating circles of these hypocycloids, later named "Cardano circles" or "cardanic circles", were used for the construction of the first high-speed printing presses.[5]

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

In his book Ars Magna he made the first systematic use of negative numbers in Europe, published (with attribution) the solutions of other mathematicians for cubic and quartic equations, and acknowledged the existence of imaginary numbers.

Early life and education

Cardano was born on 24 September [6] in Pavia, Lombardy, the illegitimate child of Fazio Cardano, a mathematically gifted jurist, lawyer, and close friend of Leonardo da Vinci.

In his autobiography, Cardano wrote that his mother, Chiara Micheri, had taken "various abortive medicines" to terminate the pregnancy; he said: "I was taken by violent means from my mother; I was almost dead." She was in labour for three days.[7] Shortly before his birth, his mother had to move from Milan to Pavia to escape the Plague; her three other children died from the disease.

After a depressing childhood, with frequent illnesses, and the rough upbringing by his overbearing father, in , Cardano entered the University of Pavia. Against the wish of his father, who wanted his son to undertake studies of law, Girolamo felt more attracted to philosophy and science. During the Italian War of –, however, the authorities in Pavia were forced to close the university in [8] Cardano resumed his studies at the University of Padua, where he graduated with a doctorate in medicine in [9] His eccentric and confrontational style did not earn him many friends and he had a difficult time finding work after he completed his studies.

In , Cardano repeatedly applied to the College of Physicians in Milan, but was not admitted owing to his combative reputation and illegitimate birth. However, he was consulted by many members of the College of Physicians, because of his irrefutable intelligence.[10]

Early career as a physician

Cardano wanted to practice medicine in a large, rich city like Milan, but he was denied a license to practice, so he settled for the town of Piove di Sacco, where he practised without a license.

There, he married Lucia Banderini in Before 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 few noblemen, Cardano obtained a mathematics teaching position in Milan.

Having finally received his medical license, he practised mathematics and medicine simultaneously, treating a few influential patients in the process. Because of this, he became one of the most sought-after doctors in Milan. In fact, by , he was able to quit his teaching position, although he was still interested in mathematics.

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    • His notability in the medical field was such that the aristocracy tried to lure him out of Milan. Cardano later wrote that he turned down offers from the kings of Denmark and France, and the Queen of Scotland.[11]

    Mathematics

    Gerolamo Cardano was the first European mathematician to make systematic use of negative numbers.[12] He published with attribution the solution of Scipione del Ferro to the cubic equation and the solution of Cardano's student Lodovico Ferrari to the quartic equation in his book Ars Magna, an influential work on algebra.

    The solution to one particular case of the cubic equation [13] (in modern notation) had been communicated to him in by Niccolò Fontana Tartaglia (who later claimed that Cardano had sworn not to reveal it, and 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 the existence of what are now called imaginary numbers, although he did not understand their properties, described for the first time by his Italian contemporary Rafael Bombelli.

    In Opus novum de proportionibus he introduced the binomial coefficients and the binomial theorem.

    Cardano was notoriously short of money and kept himself solvent by being an accomplished gambler and chess player. His book about games of chance, Liber de ludo aleae ("Book on Games of Chance"), written around ,[15] but not published until , contains the first systematic treatment of probability,[16] as well as a section on effective cheating methods.

    He used the game of throwing dice to understand the basic concepts of probability. He demonstrated the efficacy of defining odds as the ratio of favourable to unfavourable outcomes (which implies that the probability of an event is given by the ratio of favourable outcomes to the total number of possible outcomes).[17] He was also aware of the multiplication rule for independent events but was not certain about what values should be multiplied.[18]

    Other contributions

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

    He wrote two treatises on music, both of which were titled De Musica. The first was published within his work Hieronymi Cardani Mediolanensis Opera Omnia. It is of interest to scholars on the history of woodwind instruments because of its discussion of instruments from that family. The second treatise was published in , and a copy of it is held in the Vatican Library.

    The work is valuable for studies in harmony for its discussion of the use of microtones. It is also of interest to scholars of historically informed performance practice for its details on 16th century performance. The later treatise of music Della natura de principii et regole musicali which has been attributed to Cardano by some, is according to The New Grove Dictionary of Music and Musicians most likely falsely attributed to Cardano and is by another writer.

    Cardano also dabbled in composing, writing the motet Beati estis which is scored for 12 voices and contains four overlapping canons.[19]

    Cardano's work with hypocycloids led him to Cardan's Movement or Cardan Gear mechanism, in which a pair of gears with the smaller being one-half the size of the larger gear is used to convert rotational motion to linear motion with greater efficiency and precision than a Scotch yoke, for example.[20] He is also credited with the invention of the Cardan suspension or gimbal.

    Cardano made several contributions to hydrodynamics and held that perpetual motion is impossible, except in celestial bodies. He published two encyclopedias of natural science which contain a wide variety of inventions, facts, and occult superstitions. He also introduced the Cardan grille, a cryptographic writing tool, in

    Significantly, in the history of education of the deaf, he said that deaf people were capable of using their minds, argued for the importance of teaching them, and was one of the first to state that deaf people could learn to read and write without learning how to speak first.

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

    Cardano's medical writings included: a commentary on Mundinus' anatomy and of 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 with the invention of the so-called Cardano's Rings, also called Chinese Rings, but it is very probable that they predate Cardano.

    The universal joint, sometimes called Cardan joint, was not described by Cardano.

    De Subtilitate ()

    As quoted from Charles Lyell's Principles of Geology:

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

    Scotland and Archbishop Hamilton

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

    Girolamo cardano facts management company For, besides the fact that no animal, apart from the human being, knows that it is going to die, all non human animals bruta enjoy some happiness for the very fact that they exist, since they live as if they were to live forever, and therefore they participate in eternal bliss. Cardano made several contributions to hydrodynamics and held that perpetual motion is impossible, except in celestial bodies. For the lunar crater, see Cardanus crater. Sirasi, Nancy G.

    The treatment was a success and the diplomat Thomas Randolph recorded that "merry tales" about Cardano's methods were still current in Edinburgh in [24] Cardano and Casanatus argued over the Archbishop's cure.[25] Cardano wrote that the Archbishop had been short of breath for ten years, and after the cure was effected by his assistant, he was paid 1, 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 favourite son was arrested in for having poisoned his wife,[11] after he had discovered that their three children were not his. Giovanni was put to trial and, when Cardano could not pay the restitution demanded by the victim's family, was sentenced to death and beheaded. Gerolamo's other son Aldo Urbano was a gambler, who stole money from his father, and so Cardano disinherited him in

    Cardano moved from Pavia to Bologna, in part because he believed that the decision to execute his son was influenced by Gerolamo's battles with the academic establishment in Pavia, and his colleagues' jealousy at his scientific achievements, and also because he was beset with allegations of sexual impropriety with his students.[7] He obtained a position as professor of medicine at the University of Bologna.

    Cardano was arrested by the Inquisition in after an accusation of heresy by the Inquisitor of Como, who targeted Cardano's De rerum varietate ().[27] The inquisitors complained about Cardano's writings on astrology, especially his claim that self-harming religiously motivated actions of martyrs and heretics were caused by the stars.[28] In his book De Supplemento Almanach, a commentary on the astrological work Tetrabiblos by Ptolemy, Cardano had also published a horoscope of Jesus.

    Cardano was imprisoned for several months and lost his professorship in Bologna. He abjured and was freed, probably with help from powerful churchmen in Rome.[28] All his non-medical works were prohibited and placed on the Index.[28]

    He moved to Rome, where he received a lifetime annuity from Pope Gregory XIII (after first having been rejected by Pope Pius V, who died in ) and finished his autobiography.

    Girolamo cardano facts management system He wrote more than works on science. In his Opus novum de proportionibus , Cardano turned to problems of mechanics, with the principal aim of applying quantitative methods to the study of physics. Among the circumstances that affect our perception of want, penury prevents us from focusing on the improvement of our knowledge and level of awareness. In the sublunary world, the major operations of life and generation are performed by nature, understood as a source of teleological activity supervised by the intellect and the soul of the world De subtilitate , OO, III, a; ed.

    He was accepted into the Royal College of Physicians, and as well as practising medicine he continued his philosophical studies until his death in [citation needed]

    References in literature and culture

    The seventeenth-century English physician and philosopher Sir Thomas Browne possessed the ten volumes of the Lyon edition of the complete works of Cardan in his library.[29]

    Browne critically viewed Cardan as:

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

    He hath left many excellent Discourses, Medical, Natural, and Astrological; the most suspicious are those two he wrote by admonition in a dream, that is De Subtilitate & Varietate Rerum. Assuredly this learned man hath taken many things upon trust, and although examined some, hath let slip many others. He is of singular use unto a prudent Reader; but unto him that only desireth Hoties,[a] or to replenish his head with varieties; like many others before related, either in the Original or confirmation, he may become no small occasion of Error.[30]

    Richard Hinckley Allen tells of an amusing reference made by Samuel Butler in his book Hudibras:

    Cardan believ'd great states depend
    Upon 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 needs be false,
    Because your true bears have no tails.

    Alessandro Manzoni's novel I Promessi Sposi portrays a pedantic scholar of the obsolete, Don Ferrante, as a great admirer of Cardano. Significantly, he values him only for his superstitious and astrological writings; his scientific writings are dismissed because they contradict Aristotle, but excused on the ground that the author of the astrological works deserves to be listened to even when he is wrong.

    English novelist E. M. Forster's Abinger Harvest, a volume of essays, authorial 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 that he often forgot to repent of his bad temper, his stupidity, his licentiousness, and love of 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, Milan, [32]
    • De Consolatione, Libri tres, Hieronymus Scotus, Venice, [33]
    • Libelli duo: De 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, sive 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: in Italian): posthumously published.[42] (most likely falsely attributed to Cardano)[19]
    • De Subtilitate rerum (on natural phenomena), Johann Petreius, Nuremberg, [43]
      • Translation into English by J.M.

        Forrester ().[44]

    • Metoposcopia libris tredecim, et octingentis faciei humanae eiconibus complexa (on physiognomy), written (published posthumously by Thomas Jolly, 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 written, and his successes in medical 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 in 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 De 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"; on probability): posthumously published.[65][66]
    • Proxeneta, seu De Prudentia Civili (posthumously published: Paulus Marceau, Geneva, ).[68]

    Collected Works

    A chronological key to this edition is 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 of art or magic trick initially uncovered by Gerolamo Cardano
    • Negative numbers, the core of Cardano's major 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 University Press.

    2. ^Giglioni, Guido (23 April ). "Girolamo [Geronimo] Cardano". Stanford Encyclopedia of Philosophy.
    3. ^Patty, Peter Fletcher, Hughes Hoyle, C.

      Wayne (). Foundations of Discrete Mathematics (International student&#;ed.). Boston: PWS-KENT Pub. Co. p.&#; ISBN&#;. : CS1 maint: multiple names: authors list (link)

    4. ^Westfall, Richard S. "Cardano, Girolamo". T he Galileo Project. Archived from the original on 28 July Retrieved
    5. ^ W.G.

      Waters, Jerome Cardan, a Biographical Study (Lawrence and Bullen, London ), from Internet Archive.

    6. ^"Quick Fact on Cardona"(PDF). Universität Duisburg Essen. Retrieved 2 October
    7. ^ abcArmando Maggi (1 September ).

      Satan's Rhetoric: A Study of Renaissance Demonology. University of Chicago Press. pp.&#;–. ISBN&#;.

    8. ^Angus., Konstam (). Pavia &#;: the climax of the Italian wars. London: Osprey Military. ISBN&#;. OCLC&#;
    9. ^"Cardan biography". MacTutor History of Mathematics archive. Retrieved 30 October
    10. ^"Girolamo Cardano - Biography".
    11. ^ abcBruno, Leonard C () [].

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

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

      New York: McGraw-Hill.

    14. ^V.J. Katz, A History of Mathematics: An Introduction, 3rd edn. (Boston: Pearson Education, ).
    15. ^In Chapter 20 of Liber de Ludo Aleae he describes a personal experience from and then adds that "thirty-eight years have passed" [elapsis iam annis triginta octo]. This sentence is written by Cardano around , age
    16. ^Katz, ibid., p.

      Girolamo cardano facts management The De Subtilitate of Girolamo Cardano , ed. Cite this article Pick a style below, and copy the text for your bibliography. He demonstrated the efficacy of defining odds as the ratio of favourable to unfavourable outcomes which implies that the probability of an event is given by the ratio of favourable outcomes to the total number of possible outcomes. As an expression of unity and goodness, order is so pervasive that in fact accounts for even the most haphazard and disorderly aspects of reality.

    17. ^Some laws and problems in 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.

    20. Girolamo cardano imaginary numbers
    21. Girolamo cardano contributions to math
    22. When was girolamo cardano born
    23. Girolamo cardano interesting facts

      24. Oxford University Press. doi/gmo/article

    24. ^"How does a Cardan gear mechanism work?". Seyhan Ersoy. Retrieved 1 April
    25. ^Smith, David Eugene (1 July ). "Medicine and Mathematics in the Sixteenth Century".

      Facts tuition management: Among the universal causes of action, the most important are the stars, which act over the sublunary world through influences conveyed by light, heat and motion De uno , OO, I, , ; ed. English novelist E. Read Edit View history. The title of a work of Cardano's, published in , De Subtilitate corresponding to what would now be called transcendental philosophy , would lead us to expect, in the chapter on minerals, many far fetched theories characteristic of that age; but when treating of petrified shells, he decided that they clearly indicated the former sojourn of the sea upon the mountains.

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

    26. ^Charles Lyell, Principles of Geology, , p
    27. ^C. S. Knighton, Calendar of State Papers, Domestic, Edward VI (London, ), p. no.
    28. ^Calendar State Papers Scotland, vol. 1 (Edinburgh, ), p. James Melville, Memoirs of his own life (Edinburgh, ), pp.

      21,

    29. ^Markus Fierz, Girolamo Cardano: – Physician, Natural Philosopher Mathematician (Birkhäuser Boston, ), pp. 8–
    30. ^Cardanus, Gerolamo, De Propria Vita Liber (Amsterdam, ), pp.
    31. ^Valente, Michaela (). "Facing the Roman Inquisition: Cardano and Della Porta". Bruniana e Campanelliana.

      23 (2): – doi/

    32. ^ abcRegier, Jonathan (). "Reading Cardano with the Roman Inquisition: Astrology, Celestial Physics, and the Force of Heresy"(PDF). Isis. (4): – doi/ hdl/LU S2CID&#;
    33. ^J.S. Finch (ed.), A Facsimile of the Sales Auction Catalogue of Sir Thomas Browne and his son Edward's Libraries, with Introduction, notes and index (E.J.

      Brill: Leiden, ).

    34. ^Pseudodoxia Epidemica Bk 1: chapter 8 no. 13
    35. ^ edition, Full text (original page views) at Internet Archive.
    36. ^Full text (original page views) at Internet Archive.
    37. ^Full text (original page views) at Google.
    38. ^T. Bedingfield, Cardanus Comforte, T.

      Marshe, London Full text (page views) at Hathi Trust.

    39. ^Full text (original page views) at Google.
    40. ^Full text (original page views) at Bayerische StaatsBibliothek; De Sapientia at pp.
    41. ^ edition, Full text (original page views) at Google.
    42. ^Full text (original page views) at Google.
    43. ^[1]Archived 26 June at the Wayback Machine An electronic copy of his book Ars Magna (in Latin)
    44. ^Full text (original page views) at Bayerische StaatsBibliothek; another at Internet Archive.
    45. ^The Rules of Algebra: Ars Magna, Dover Books on Mathematics, translated by Witmer, T.

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

    46. ^C. Sponius (ed.), Hieronymi Cardani Mediolanensis opera omnia (Lyons, ), IV, pp. end (Google).
    47. ^Full text (original page views) at Internet Archive; another at New York Public Libraries. Paris edition, Michael Fezandat and Robert GranIon (original page views) at Google.
    48. ^J.M.

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

    49. ^Full text (original page views) at Google.
    50. ^ edition, Full text (original page views) at Google; from Bayerische StaatsBibliothek/Münchener DigitalisierungsZentrum.

      Heinrich Petri edition, Basle, at Google.

    51. ^Full text (original page views) at Google.
    52. ^/66 edition, 2 volumes, HenricPetrini, Basel, Full texts at Google, Vol. I, Vol. II.
    53. ^Full text (original page views) at Google.
    54. ^Full text (original page views) at Internet Archive. Another at Google.
    55. ^D.F.

      Larder, 'The Editions of Cardanus' "De rerum varietate"', Isis, Vol. 59, No. 1 (Spring, ), pp. (JSTOR, open).

    56. ^ Basle edition (original page views) at University and State Library, Düsseldorf.
    57. ^Full text (original page views) at Google.
    58. ^ edition, Full text (original page views) at Hathi Trust.
    59. ^Full text (John and Cornelius Blaeu, Amsterdam edition) (original page views) at Google.
    60. ^A.

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

    61. ^Full text (original page views) at Internet Archive; another at Google.
    62. ^Full text (original page views) at Internet Archive. Another at Google.
    63. ^Full text (original page views) at Internet Archive; also in Google.
    64. ^ and editions, Full text (original page views) at Google.

      only, at Google; another at Freiburger historische Beistände.

    65. ^Full text (original page views) at Münchener DigitalisierungsZentrum/Bayerische Staatsbibliothek or at Google.
    66. ^Text (incomplete, original page views) at Google. Franciscus Zannettus, Rome , Full text (original page views) at Google.
    67. ^Full text (page views): Iacobus Villery, Paris , edition at Internet Archive; Amsterdam edition at Google.
    68. ^The Book of My Life, New York Review Books Classics, translated by Stoner, Jean, introduction by Grafton, Anthony, NYRB Classics, , p.&#;, ISBN&#;: CS1 maint: others (link)
    69. ^C.

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

    70. ^J. Gullberg, Mathematics from the birth of numbers (W.W. Norton & Company, ), p. ISBN&#;XISBN&#;
    71. ^The Book on Games of Chance: The 16th-Century Treatise on Probability, Dover Recreational Math, translated by Gould, Sydney Henry, foreword by Wilks, Samuel S., Dover Publications, [], p.&#;64, ISBN&#;: CS1 maint: others (link)
    72. ^Full text (original page views) at Google.
    73. ^M.

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

    Sources

    • Picinelli, Filippo ().

      Facts management parent login Cardano reduced the elements to three air, earth, water , eliminating fire, which he considered a mode of existence of matter; and he reduced the four qualities to two hot and moist. At its deepest, the principle of unity and order coincides with God. Armando Torno, Milan: Philobiblon, Regarding the immortality of the soul, Cardano maintains that, in order to lead a meaningful existence and act accordingly, people need to know whether there is life after death and whether the nature of their afterlife will depend on the way they behaved in this world.

      Ateneo dei letterati milanesi. Milan: Vigone. pp.&#;–7.

    • Cardano, Girolamo, Astrological Aphorisms of Cardan. Edmonds, WA: Sure Fire Press,
    • Cardano, Girolamo, The Book of My Life. trans. by Jean Stoner. New York: New York Review of Books,
    • Cardano, Girolamo, Opera omnia, Charles Sponi, ed., 10 vols.

      Lyons,

    • Cardano, Girolamo, Nero: an Exemplary Life Inckstone , translation in English of the Neronis Encomium.
    • Dunham, William, Journey through Genius, Chapter 6, , John Wiley and Sons. ISBN&#; Discusses Cardano's life and solution 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 mostly fine musicians': Cardano on male same-sex love and music", in: Kenneth Borris & George Rousseau (curr.), The sciences of homosexuality in early modern Europe, Routledge, London , pp.&#;–
    • Grafton, Anthony, Cardano's Cosmos: The Worlds and Works of a Renaissance Astrologer.Harvard University Press,
    • Morley, Henry, The life of Girolamo Cardano, of Milan, Physician 2 vols.

      Chapman & Hall, London

    • Ore, Øystein, Cardano, the Gambling Scholar. Princeton,
    • Rutkin, H. Darrel, "Astrological conditioning of same-sexual relations in Girolamo Cardano's theoretical treatises and celebrity genitures", in: Kenneth Borris & George Rousseau (curr.), The sciences of homosexuality in early modern Europe, Routledge, London , pp.&#;–
    • Sirasi, Nancy G., The Clock and the Mirror: Girolamo Cardano and Renaissance 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 dead link&#;].

      A very compendious bibliography of works referring to Cardano.

    • A recreational article about Cardano and the discovery of the two basic ingredients of 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 Science Collection at Linda Hall Library
    • &#;This article incorporates text from a publication now in the public domain:&#;Herbermann, Charles, ed.

      (). "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 at 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 in .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 v Tartaglia: The Great Feud Out of Bounds" by Tony Rothman
    • De Subtilitate Libri XXI From the Rare Book and Special Collection Division at the Library of Congress
    • W.G.

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