Cardano partially invented and described several mechanical devices including thecombination lock, thegimbal consisting of three concentric rings allowing a supportedcompass orgyroscope to rotate freely, and theCardan shaft withuniversal joints, which allows the transmission of rotary motion at various angles and is used in vehicles to this day. He made significant contributions tohypocycloids - published inDe proportionibus, in 1570. The generating circles of these hypocycloids, later named "Cardano circles" or "cardanic circles", were used for the construction of the first high-speedprinting presses.[5]
Today, Cardano is well known for his achievements inalgebra. In his 1545 bookArs Magna he made the first systematic use ofnegative numbers in Europe, published (with attribution) the solutions of other mathematicians forcubic andquartic equations, and acknowledged the existence ofimaginary numbers.
Cardano was born on 24 September 1501[6] inPavia, Lombardy, theillegitimate child ofFazio Cardano, a mathematically giftedjurist, lawyer, and close friend ofLeonardo 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 fromMilan toPavia to escape thePlague; her three other children died from the disease.
After a depressing childhood, with frequent illnesses, and the rough upbringing by his overbearing father, in 1520, Cardano entered theUniversity 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 theItalian War of 1521–1526, however, the authorities in Pavia were forced to close the university in 1524.[8] Cardano resumed his studies at theUniversity of Padua, where he graduated with a doctorate in medicine in 1525.[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 1525, 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]
Cardano wanted to practice medicine in a large, rich city likeMilan, but he was denied a license to practice, so he settled for the town ofPiove di Sacco, where he practised without a license. There, 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 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 1536, he was able to quit his teaching position, although he was still interested in mathematics. 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]
Portrait of Cardano on display at the School of Mathematics and Statistics,University of St Andrews
Gerolamo Cardano was the first European mathematician to make systematic use of negative numbers.[12] He published with attribution the solution ofScipione del Ferro to thecubic equation and the solution of Cardano's studentLodovico Ferrari to thequartic equation in his 1545 bookArs 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 1539 byNiccolò 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 calledimaginary numbers, although he did not understand their properties, described for the first time by his Italian contemporaryRafael Bombelli. InOpus novum de proportionibus he introduced thebinomial coefficients and thebinomial theorem.
Cardano was chronically short of money and kept himself solvent by being an accomplished gambler andchess player. His book about games of chance,Liber de ludo aleae ("Book on Games of Chance"), written around 1564,[15] but not published until 1663, contains the first systematic treatment ofprobability,[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 definingodds as the ratio of favourable to unfavourable outcomes (which implies that the probability of anevent 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]
"Oneiron" ("Dream"), reverse of the medallion of Cardano byLeone Leoni, 1550–51
Cardano was amusic theorist who studied music privately in Milan in his youth. He wrote two treatises on music, both of which were titledDe Musica. The first was published within his 1663 workHieronymi Cardani Mediolanensis Opera Omnia. It is of interest to scholars on the history ofwoodwind instruments because of its discussion of instruments from that family. The second treatise was published in 1574, and a copy of it is held in theVatican Library. The work is valuable for studies inharmony for its discussion of the use ofmicrotones. It is also of interest to scholars ofhistorically informed performance practice for its details on 16th century performance. The later treatise of musicDella natura de principii et regole musicali which has been attributed to Cardano by some, is according toThe New Grove Dictionary of Music and Musicians most likely falsely attributed to Cardano and is by another writer. Cardano also dabbled in composing, writing themotet Beati estis which is scored for 12 voices and contains four overlappingcanons.[19]
Cardano's work with hypocycloids led him toCardan'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 aScotch yoke, for example.[20] He is also credited with the invention of the Cardan suspension orgimbal.
Cardano made several contributions to hydrodynamics and held thatperpetual 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 theCardan grille, a cryptographic writing tool, in 1550.
Significantly, in the history ofeducation 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 byRudolph Agricola about a deaf-mute who had learned to write.
Cardano's medical writings included: a commentary onMundinus' anatomy and ofGalen's medicine, along with the treatiesDelle cause, dei segni e dei luoghi delle malattie,Picciola terapeutica,Degli abusi dei medici andDelle orine, libro quattro.[21]
Cardano has been credited with the invention of the so-calledCardano's Rings, also called Chinese Rings, but it is very probable that they predate Cardano. Theuniversal joint, sometimes calledCardan joint, was not described by Cardano.
The title of a work of Cardano's, published in 1552,De Subtilitate (corresponding to what would now be calledtranscendental 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]
Medallion portrait of Cardano aged 49 byLeone Leoni (1509–1590)
In 1552 Cardano travelled to Scotland with the Spanish physician William Casanatus, via London,[23] to treat theArchbishop of St Andrews who suffered of a disease that had left him speechless and was thought incurable. The treatment was a success and the diplomatThomas Randolph recorded that "merry tales" about Cardano's methods were still current in Edinburgh in 1562.[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 1,400 gold crowns.[26]
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 1560 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 andbeheaded.[27] Gerolamo's other son Aldo Urbano was a gambler, who stole money from his father, and so Cardano disinherited him in 1569.
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 theUniversity of Bologna.
Cardano was arrested by theInquisition in 1570 after an accusation of heresy by the Inquisitor of Como, who targeted Cardano'sDe rerum varietate (1557).[28] The inquisitors complained about Cardano's writings onastrology, especially his claim that self-harming religiously motivated actions of martyrs and heretics were caused by the stars.[29] In his 1543 bookDe Supplemento Almanach, a commentary on the astrological workTetrabiblos byPtolemy, Cardano had also published a horoscope ofJesus. 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.[29] All his non-medical works were prohibited and placed on theIndex.[29]
He moved to Rome, where he received a lifetimeannuity fromPope Gregory XIII (after first having been rejected byPope Pius V, who died in 1572) and finished his autobiography. He was accepted into the Royal College of Physicians, and as well as practising medicine he continued his philosophical studies until his death in 1576.[30]
The seventeenth-century English physician and philosopher SirThomas Browne possessed the ten volumes of the Lyon 1663 edition of the complete works of Cardan inhis library.[31]
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 isDe 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.[32]
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 novelI 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 contradictAristotle, but excused on the ground that the author of the astrological works deserves to be listened to even when he is wrong.
English novelistE. M. Forster'sAbinger Harvest, a 1936 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" (212).
Libelli duo: De Supplemento Almanach; De Restitutione temporum et motuum coelestium; Item Geniturae LXVII insignes casibus et fortuna, cum expositione, Iohan. Petreius, Norimbergae, 1543.[37]
De Sapientia, Libri quinque, Iohan. Petreius, Norimbergae, 1544 (withDe Consolatione reprint andDe Libris Propriis, book I).[38]
De Immortalitate animorum, Henric Petreius, Nuremberg 1544/Sebastianus Gryphius, Lyons, 1545.[39]
Contradicentium medicorum (on medicine), Hieronymus Scotus, Venetijs, 1545.[40]
Della Natura de Principii e Regole Musicale, ca 1546 (on music theory: in Italian): posthumously published.[44] (most likely falsely attributed to Cardano)[19]
De Subtilitate rerum (on natural phenomena),Johann Petreius, Nuremberg, 1550.[45]
Translation into English by J.M. Forrester (2013).[46]
Metoposcopia libris tredecim, et octingentis faciei humanae eiconibus complexa (on physiognomy), written 1550 (published posthumously by Thomas Jolly, Paris (Lutetiae Parisiorum), 1658).[47]
In Cl. Ptolemaei Pelusiensis IIII, De Astrorum judiciis... libros commentaria: cum eiusdem De Genituris libro, Henrichus Petri, Basle, 1554.[48]
Geniturarum Exemplar (De Genituris liber, separate printing), Theobaldus Paganus, Lyons, 1555.[49]
De Libris propriis (about the books he has written, and his successes in medical work), Gulielmus Rouillius, Leiden, 1557.[51]
De Rerum varietate, Libri XVII (on natural phenomena); (Revised edition), Matthaeus Vincentius, Avignon 1558.[52] Also Basle, Henricus Petri, 1559.[53][54]
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.[55]
Theonoston, seu De Tranquilitate, 1561. (Opera, Vol. II).
Somniorum synesiorum omnis generis insomnia explicantes, Libri IIII (Book of Dreams: with other writings), Henricus Petri, Basle 1562.[56]
Neronis encomium (a life ofNero), Basle, 1562.[57]
Translation into English by A. Paratico (2012).[58]
De Providentia ex anni constitutione, Alexander Benaccius, Bononiae, 1563.[59]
De Methodo medendi, Paris, In Aedibus Rouillii, 1565.[60]
De Causis, signis ac locis morborum, Liber unus, Alexander Benatius, Bononiae, 1569.[61]
Commentarii in Hippocratis Coi Prognostica, Opus Divinum; Commentarii De Aere, aquis et locis opus, Henric Petrina Officina, Basel, 1568/1570.[62]
Opus novum, De Proportionibus numerorum, motuum, ponderum, sonorum, aliarumque rerum mensurandarum. Item de aliza regula, Henric Petrina, Basel, 1570.[63]
Opus novum, cunctis De Sanitate tuenda, Libri quattuor, Sebastian HenricPetri, Basle, 1569.[64]
A chronological key to this edition is supplied by M. Fierz.[71]
Hieronymi Cardani Mediolanensis Opera Omnia, cura Carolii Sponii (Lugduni, Ioannis Antonii Huguetan and Marci Antonii Ravaud, 1663) (10 volumes, Latin):
^Patty, Peter Fletcher, Hughes Hoyle, C. Wayne (1991).Foundations of Discrete Mathematics (International student ed.). Boston: PWS-KENT Pub. Co. p. 207.ISBN0-534-92373-9.Cardano was a physician, astrologer, and mathematician.... [He] supported his wife and three children by gambling and casting horoscopes.{{cite book}}: CS1 maint: multiple names: authors list (link)
^Westfall, Richard S."Cardano, Girolamo".T he Galileo Project. rice.edu. Archived fromthe original on 28 July 2012. Retrieved2012-07-19.
^W.G. Waters,Jerome Cardan, a Biographical Study (Lawrence and Bullen, London 1898), fromInternet Archive.
^Burton, David.The History of Mathematics: An Introduction (7th (2010) ed.). New York:McGraw-Hill.
^V.J. Katz,A History of Mathematics: An Introduction, 3rd edn. (Boston: Pearson Education, 2009).
^In Chapter 20 ofLiber de Ludo Aleae he describes a personal experience from 1526 and then adds that "thirty-eight years have passed" [elapsis iam annis triginta octo]. This sentence is written by Cardano around 1564, age 63.
^J.S. Finch (ed.),A Facsimile of the 1711 Sales Auction Catalogue of Sir Thomas Browne and his son Edward's Libraries, with Introduction, notes and index (E.J. Brill: Leiden, 1986).
^Text (incomplete, original page views) atGoogle. Franciscus Zannettus, Rome 1580, Full text (original page views) atGoogle.
^Full text (page views): Iacobus Villery, Paris 1653, edition atInternet Archive; Amsterdam 1654 edition atGoogle.
^The Book of My Life, New York Review Books Classics, translated by Stoner, Jean, introduction by Grafton, Anthony, NYRB Classics, 2002, p. 320,ISBN978-1-59017-016-8{{citation}}: CS1 maint: others (link)
^C. Sponius (ed.),Hieronymi Cardani Mediolanensis opera omnia (Lyons, 1663), I,pp. 262-76 (Internet Archive).
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 2007, pp. 201–220.
Morley, Henry,The life of Girolamo Cardano, of Milan, Physician 2 vols.Chapman & Hall, London 1854.
Ore, Øystein,Cardano, the Gambling Scholar. Princeton, 1953.
Rutkin, H. Darrel, "Astrological conditioning of same-sexual relations 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 2007, pp. 183–200.
Sirasi, Nancy G.,The Clock and the Mirror: Girolamo Cardano and Renaissance Medicine,Princeton University Press, 1997.
Georgio Vivi (ed.),Cardani Mediolanensis Philosophi ac Medici Celeberrimi Bibliographia, Tertia Editio (Author, 'Cosmopoli', 2018). A bibliography of works referring to Cardano.
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