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Gerolamo Cardano (; also Girolamo or Geronimo; french: link=no, Jérôme Cardan; la, Hieronymus Cardanus; 24 September 1501– 21 September 1576) was an Italian
polymath A polymath ( el, πολυμαθής, , "having learned much"; la, homo universalis, "universal human") is an individual whose knowledge spans a substantial number of subjects, known to draw on complex bodies of knowledge to solve specific pro ...

polymath
, whose interests and proficiencies ranged through those of mathematician,
physician A physician (American English), medical practitioner (English in the Commonwealth of Nations, Commonwealth English), medical doctor, or simply doctor, is a health professional who practices medicine, which is concerned with promoting, mai ...

physician
,
biologist A biologist is a scientist who conducts research in biology. Biologists are interested in studying life on Earth, whether it is an individual Cell (biology), cell, a multicellular organism, or a Community (ecology), community of Biological inter ...
,
physicist A physicist is a scientist who specializes in the field of physics, which encompasses the interactions of matter and energy at all length and time scales in the physical universe. Physicists generally are interested in the root or ultimate caus ...

physicist
,
chemist A chemist (from Greek ''chēm(ía)'' alchemy; replacing ''chymist'' from Medieval Latin ''alchemist'') is a scientist trained in the study of chemistry. Chemists study the composition of matter and its properties. Chemists carefully describe th ...

chemist
,
astrologer Astrology is a range of Divination, divinatory practices, recognized as pseudoscientific since the 18th century, that claim to discern information about human affairs and terrestrial events by studying the apparent positions of Celestial o ...

astrologer
,
astronomer An astronomer is a scientist in the field of astronomy who focuses their studies on a specific question or field outside the scope of Earth. They observe astronomical objects such as stars, planets, natural satellite, moons, comets and galaxy, g ...

astronomer
, philosopher, writer, and
gambler Gambling (also known as betting or gaming) is the wagering of something of Value (economics), value ("the stakes") on a Event (probability theory), random event with the intent of winning something else of value, where instances of strategy (ga ...
. He was one of the most influential mathematicians of the
Renaissance The Renaissance ( , ) , from , with the same meanings. is a Periodization, period in History of Europe, European history marking the transition from the Middle Ages to modernity and covering the 15th and 16th centuries, characterized by an e ...

Renaissance
, and was one of the key figures in the foundation of
probability Probability is the branch of mathematics concerning numerical descriptions of how likely an Event (probability theory), event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and ...

probability
and the earliest introducer of the
binomial coefficients In mathematics, the binomial coefficients are the positive integers that occur as coefficients in the binomial theorem. Commonly, a binomial coefficient is indexed by a pair of integers and is written \tbinom. It is the coefficient of the ter ...
and the
binomial theorem In elementary algebra, the binomial theorem (or binomial expansion) describes the algebraic expansion of powers of a binomial. According to the theorem, it is possible to expand the polynomial into a sum involving terms of the form , where th ...
in the Western world. He wrote more than 200 works on science. Cardano partially invented and described several mechanical devices including the
combination lock A combination lock is a type of locking device in which a sequence In mathematics, a sequence is an enumerated collection of mathematical object, objects in which repetitions are allowed and order theory, order matters. Like a Set (mathemati ...
, the
gimbal A gimbal is a pivoted support that permits rotation of an object about an axis. A set of three gimbals, one mounted on the other with orthogonal pivot axes, may be used to allow an object mounted on the innermost gimbal to remain independent of ...

gimbal
consisting of three concentric rings allowing a supported
compass A compass is a device that shows the cardinal directions used for navigation and geographic orientation. It commonly consists of a magnetized needle or other element, such as a compass card or compass rose, which can pivot to align itself with ...

compass
or
gyroscope A gyroscope (from Ancient Greek γῦρος ''gŷros'', "round" and σκοπέω ''skopéō'', "to look") is a device used for measuring or maintaining Orientation (geometry), orientation and angular velocity. It is a spinning wheel or disc in ...

gyroscope
to rotate freely, and the
Cardan shaft A drive shaft, driveshaft, driving shaft, tailshaft (Australian English), propeller shaft (prop shaft), or Cardan shaft (after Girolamo Cardano) is a component for transmitting mechanical power (physics), power and torque and rotation, usually ...
with
universal joint A universal joint (also called a universal coupling or U-joint) is a joint (mechanics), joint or coupling connecting rigid shaft (mechanical engineering), shafts whose wikt:axis#Noun, axes are inclined to each other. It is commonly used in shaft ...

universal joint
s, which allows the transmission of rotary motion at various angles and is used in vehicles to this day. He made significant contributions to
hypocycloid In geometry, a hypocycloid is a special plane curve generated by the trace of a fixed point on a small circle that rolls within a larger circle. As the radius of the larger circle is increased, the hypocycloid becomes more like the cycloid cr ...

hypocycloid
s, published in ''De proportionibus'', in 1570. The generating circles of these hypocycloids were later named Cardano circles or cardanic circles and were used for the construction of the first high-speed
printing presses A printing press is a mechanical device for applying pressure to an ink Ink is a gel, Sol (colloid), sol, or Solution (chemistry), solution that contains at least one colorant, such as a dye or pigment, and is used to color a surface to p ...
. Today, he is well known for his achievements in
algebra Algebra () is one of the areas of mathematics, broad areas of mathematics. Roughly speaking, algebra is the study of mathematical symbols and the rules for manipulating these symbols in formulas; it is a unifying thread of almost all of mathem ...

algebra
. In his 1545 book '' Ars Magna'', he made the first systematic use of negative numbers in Europe, published with attribution the solutions of other mathematicians for the cubic and
quartic equation In mathematics, a quartic equation is one which can be expressed as a ''quartic function'' equaling zero. The general form of a quartic equation is :ax^4+bx^3+cx^2+dx+e=0 \, where ''a'' ≠ 0. The quartic is the highest order polynomi ...
s, and acknowledged the existence of
imaginary number An imaginary number is a real number multiplied by the imaginary unit , is usually used in engineering contexts where has other meanings (such as electrical current) which is defined by its property . The square (algebra), square of an imagina ...
s.


Early life and education

Cardano was born on 24 September 1501 in
Pavia Pavia (, , , ; la, Ticinum; Medieval Latin: ) is a town and comune of south-western Lombardy in northern Italy, south of Milan on the lower Ticino river near its confluence with the Po River, Po. It has a population of c. 73,086. The city was ...

Pavia
, Lombardy, the
illegitimate Legitimacy, in traditional Western common law, is the status of a child born to parents who are legally marriage, married to each other, and of a child Fertilisation, conceived before the parents obtain a legal divorce. Conversely, ''illegitim ...
child of Fazio Cardano, a mathematically gifted
jurist A jurist is a person with expert knowledge of law; someone who analyses and comments on law. This person is usually a specialist legal scholar, mostly (but not always) with a formal qualification in law and often a legal practitioner. In the U ...
, lawyer, and close friend of
Leonardo da Vinci Leonardo di ser Piero da Vinci (15 April 14522 May 1519) was an Italian polymath of the High Renaissance who was active as a painter, Drawing, draughtsman, engineer, scientist, theorist, sculptor, and architect. While his fame initially res ...

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. Shortly before his birth, his mother had to move from
Milan Milan ( , , Lombard language, Lombard: ; it, Milano ) is a city in northern Italy, capital of Lombardy, and the List of cities in Italy, second-most populous city proper in Italy after Rome. The city proper has a population of about 1.4  ...

Milan
to
Pavia Pavia (, , , ; la, Ticinum; Medieval Latin: ) is a town and comune of south-western Lombardy in northern Italy, south of Milan on the lower Ticino river near its confluence with the Po River, Po. It has a population of c. 73,086. The city was ...

Pavia
to escape the
Plague
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 1520, Cardano entered the
University of Pavia The University of Pavia ( it, Università degli Studi di Pavia, UNIPV or ''Università di Pavia''; la, Alma Ticinus, Ticinensis Universitas) is a university located in Pavia, Lombardy, Italy. There was evidence of teaching as early as 1361, makin ...
against the wish of his father, who wanted his son to undertake studies of law, but Girolamo felt more attracted to philosophy and science. During the
Italian War of 1521–1526 The Italian War of 1521–1526, sometimes known as the Four Years' War, (french: Sixième guerre d'Italie) was a part of the Italian Wars The Italian Wars, also known as the Habsburg–Valois Wars, were a series of conflicts covering the ...
, however, the authorities in Pavia were forced to close the university in 1524. Cardano resumed his studies at the
University of Padua The University of Padua ( it, Università degli Studi di Padova, UNIPD) is an Italian university located in the city of Padua, region of Veneto, northern Italy. The University of Padua was founded in 1222 by a group of students and teachers from B ...
, where he graduated with a doctorate in medicine in 1525. His eccentric and confrontational style did not earn him many friends and he had a difficult time finding work after his studies had ended. 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.


Early career as a physician

Cardano wanted to practice medicine in a large, rich city like
Milan Milan ( , , Lombard language, Lombard: ; it, Milano ) is a city in northern Italy, capital of Lombardy, and the List of cities in Italy, second-most populous city proper in Italy after Rome. The city proper has a population of about 1.4  ...

Milan
, but he was denied a license to practice, so he settled for the town of Piove di Sacco, where he practiced 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). Cardano later wrote that those were the happiest days of his life. With the help of a few noblemen, Cardano obtained a teaching position in mathematics in Milan. Having finally received his medical license, he practiced 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.


Mathematics

Gerolamo Cardano was the first European mathematician to make systematic use of negative numbers. He published with attribution the solution of Scipione del Ferro to the
cubic equation In algebra Algebra () is one of the areas of mathematics, broad areas of mathematics. Roughly speaking, algebra is the study of mathematical symbols and the rules for manipulating these symbols in formulas; it is a unifying thread of alm ...
and the solution of Cardano's student
Lodovico Ferrari Lodovico de Ferrari (2 February 1522 – 5 October 1565) was an Italian mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are ...
to the
quartic equation In mathematics, a quartic equation is one which can be expressed as a ''quartic function'' equaling zero. The general form of a quartic equation is :ax^4+bx^3+cx^2+dx+e=0 \, where ''a'' ≠ 0. The quartic is the highest order polynomi ...
in his 1545 book '' Ars Magna'', an influential work on algebra. The solution to one particular case of the cubic equation ax^3+bx+c=0 (in modern notation) had been communicated to him in 1539 by
Niccolò Fontana Tartaglia Niccolò Fontana Tartaglia (; 1499/1500 – 13 December 1557) was an Italian mathematician, engineer (designing fortifications), a surveyor (of topography, seeking the best means of defense or offense) and a bookkeeper from the then Republi ...
(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, but del Ferro's solution predated Tartaglia's. In his exposition, he acknowledged the existence of what are now called
imaginary number An imaginary number is a real number multiplied by the imaginary unit , is usually used in engineering contexts where has other meanings (such as electrical current) which is defined by its property . The square (algebra), square of an imagina ...
s, 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 coefficient In mathematics, the binomial coefficients are the positive integers that occur as coefficients in the binomial theorem. Commonly, a binomial coefficient is indexed by a pair of integers and is written \tbinom. It is the coefficient of the ter ...
s and the
binomial theorem In elementary algebra, the binomial theorem (or binomial expansion) describes the algebraic expansion of powers of a binomial. According to the theorem, it is possible to expand the polynomial into a sum involving terms of the form , where th ...
. Cardano was notoriously short of money and kept himself solvent by being an accomplished gambler and
chess Chess is a board game between two Player (game), players. It is sometimes called international chess or Western chess to distinguish it from chess variant, related games, such as xiangqi (Chinese chess) and shogi (Japanese chess). The current ...

chess
player. His book about games of chance, ''Liber de ludo aleae'' ("Book on Games of Chance"), written around 1564,In Chapter 20 of ''Liber de Ludo Aleae'' he describes a personal experience from 1526 and then adds that "thirty-eight years have passed" lapsis iam annis triginta octo This sentence is written by Cardano around 1564, age 63. but not published until 1663, contains the first systematic treatment of
probability Probability is the branch of mathematics concerning numerical descriptions of how likely an Event (probability theory), event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and ...

probability
, 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 Odds provide a measure of the likelihood of a particular outcome. They are calculated as the ratio of the number of events that produce that outcome to the number that do not. Odds are commonly used in gambling and statistics. Odds also have ...
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). He was also aware of the multiplication rule for independent events but was not certain about what values should be multiplied.


Other contributions

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 converting rotational motion to linear motion with greater efficiency and precision than a
Scotch yoke The Scotch Yoke (also known as slotted link mechanism) is a reciprocating motion mechanism, converting the linear motion of a slider into rotation around a fixed axis, rotational motion, or vice versa. The piston or other reciprocating part is di ...
, for example. He is also credited with the invention of the Cardan suspension or
gimbal A gimbal is a pivoted support that permits rotation of an object about an axis. A set of three gimbals, one mounted on the other with orthogonal pivot axes, may be used to allow an object mounted on the innermost gimbal to remain independent of ...

gimbal
. Cardano made several contributions to hydrodynamics and held that
perpetual motion Perpetual motion is the motion of bodies that continues forever in an unperturbed system. A perpetual motion machine is a hypothetical machine that can do work infinitely without an external energy source. This kind of machine is impossible, a ...
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 1550. 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 Aelius Galenus or Claudius Galenus ( el, Κλαύδιος Γαληνός; September 129 – c. AD 216), often Anglicization, Anglicized as Galen () or Galen of Pergamon, was a Ancient Greeks, Greek physician, surgeon and Philosophy, philosopher i ...
'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''. 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 A universal joint (also called a universal coupling or U-joint) is a joint (mechanics), joint or coupling connecting rigid shaft (mechanical engineering), shafts whose wikt:axis#Noun, axes are inclined to each other. It is commonly used in shaft ...

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


''De Subtilitate'' (1550)

As quoted from
Charles Lyell Sir Charles Lyell, 1st Baronet, (14 November 1797 – 22 February 1875) was a Scottish geologist who demonstrated the power of known natural causes in explaining the earth's history. He is best known as the author of ''Principles of Geolo ...

Charles Lyell
's ''
Principles of Geology ''Principles of Geology: Being an Attempt to Explain the Former Changes of the Earth's Surface, by Reference to Causes Now in Operation'' is a book by the Scottish geologist Charles Lyell that was first published in 3 volumes from 1830–1833. Ly ...
'':
The title of a work of Cardano's, published in 1552, ''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.


Later years and death

In 1553 Cardano traveled to Scotland to treat the
Archbishop of St Andrews The Bishop of St. Andrews ( gd, Easbaig Chill Rìmhinn, sco, Beeshop o Saunt Andras) was the ecclesiastical head of the Diocese of St Andrews in the Catholic Church and then, from 14 August 1472, as Archbishop of St Andrews ( gd, Àrd-easbaig ...
who suffered of a disease that had left him speechless and was thought incurable The treatment was a success and the diplomat Thomas Randolph recorded that "merry tales" about Cardano's methods were still current in Edinburgh in 1562. 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. Two of Cardano's children — Giovanni Battista and Aldo Urbano — came to ignoble ends. Giovanni Battista, Cardano's eldest and favorite son was arrested in 1560 for having poisoned his wife, 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 . Cardano's other son Aldo Urbano was a gambler, who stole money from his father, and so Gerolamo 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. He obtained a position as professor of medicine at the
University of Bologna The University of Bologna ( it, Alma Mater Studiorum – Università di Bologna, UNIBO) is a Public university, public research university in Bologna, Italy. Founded in 1088 by an organised guild of students (''studiorum''), it is the List of old ...
. Cardano was arrested by the
Inquisition The Inquisition was a group of institutions within the Catholic Church whose aim was to combat Christian heresy, heresy, conducting trials of suspected heretics. Studies of the records have found that the overwhelming majority of sentences consi ...

Inquisition
in 1570 after an accusation of heresy by the Inquisitor of Como, who targeted Cardano's ''De rerum varietate'' (1557). The inquisitors complained about Cardano's writings on
astrology Astrology is a range of Divination, divinatory practices, recognized as pseudoscientific since the 18th century, that claim to discern information about human affairs and terrestrial events by studying the apparent positions of Celestial o ...
, especially his claim that self-harming religiously motivated actions of martyrs and heretics were caused by the stars. In his 1543 book ''De Supplemento Almanach,'' a commentary on the astrological work '' Tetrabiblos'' by
Ptolemy Claudius Ptolemy (; grc-gre, wikt:Πτολεμαῖος, Πτολεμαῖος, ; la, Claudius Ptolemaeus; AD) was a mathematician, astronomer, astrologer, geographer, and music theorist, who wrote about a dozen scientific Treatise, treatis ...
, Cardano had also published a horoscope of
Jesus Jesus, likely from he, יֵשׁוּעַ, translit=Yēšūaʿ, label=Hebrew/Aramaic ( AD 30 or 33), also referred to as Jesus Christ or Jesus of Nazareth (among other Names and titles of Jesus in the New Testament, names and titles), was ...

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. All his non-medical works were prohibited and placed on the
Index Index (or its plural form indices) may refer to: Arts, entertainment, and media Fictional entities * Index (''A Certain Magical Index''), a character in the light novel series ''A Certain Magical Index'' * The Index, an item on a Halo megastru ...
. He moved to Rome, where he received a lifetime annuity from
Pope Gregory XIII Pope Gregory XIII ( la, Gregorius XIII; it, Gregorio XIII; 7 January 1502 – 10 April 1585), born Ugo Boncompagni, was head of the Catholic Church and ruler of the Papal States from 13 May 1572 to his death in April 1585. He is best known for ...

Pope Gregory XIII
(after first having been rejected by
Pope Pius V Pope Pius V ( it, Pio V; 17 January 1504 – 1 May 1572), born Antonio Ghislieri (from 1518 called Michele Ghislieri, Dominican Order, O.P.), was head of the Catholic Church and ruler of the Papal States from 8 January 1566 to his death in M ...

Pope Pius V
, who died in 1572) and finished his autobiography. He was accepted in the Royal College of Physicians, and as well as practising medicine he continued his philosophical studies until his death in 1576.


References in literature and culture

The seventeenth-century English physician and philosopher Sir
Thomas Browne Sir Thomas Browne (; 19 October 160519 October 1682) was an English polymath and author of varied works which reveal his wide learning in diverse fields including science and medicine, religion and the esoteric. His writings display a deep curi ...
possessed the ten volumes of the Leyden 1663 edition of the complete works of Cardan in his library. 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, 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."
Richard Hinckley Allen tells of an amusing reference made by Samuel Butler in his book ''
Hudibras ''Hudibras'' is a vigorous satire, satirical poem, written in a mock-heroic style by Samuel Butler (poet), Samuel Butler (1613–1680), and published in three parts in 1663, 1664 and 1678. The action is set in the last years of the Interregnum (En ...
'': 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 Alessandro Francesco Tommaso Antonio Manzoni (, , ; 7 March 1785 – 22 May 1873) was an Italian poet, novelist and philosopher. He is famous for the novel '' The Betrothed'' (orig. it, I promessi sposi) (1827), generally ranked among the maste ...

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 Aristotle (; grc-gre, Ἀριστοτέλης ''Aristotélēs'', ; 384–322 BC) was a Greek philosopher and polymath during the Classical Greece, Classical period in Ancient Greece. Taught by Plato, he was the founder of the Peripatet ...

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 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). The blockchain Cardano is named after him. Neil Patrick Harris, on the Introduction card included with the limited edition standard playing card deck that he designed for, and is distributed by Theory 11 (2021), writes, "This is going to be a challenge. Just as a spider spends its web, I've taken a page out of Cardano's book and created a puzzle. Look upon photos and inside in this deck. You can do this - just look closely at the cards. Good luck! -NPH"


Works

* ''De malo recentiorum medicorum medendi usu libellus'', Hieronymus Scotus, Venice, 1536 (on medicine). * ''Practica arithmetice et mensurandi singularis'' (on mathematics), Io. Antoninus Castellioneus/Bernadino Caluscho, Milan, 1539. * ''De Consolatione, Libri tres'', Hieronymus Scotus, Venice, 1542. ** Translation into English by T. Bedingfield (1573). * ''Libelli duo: De Supplemento Almanach; De Restitutione temporum et motuum coelestium; Item Geniturae LXVII insignes casibus et fortuna, cum expositione'', Iohan. Petreius, Norimbergae, 1543. * ''De Sapientia, Libri quinque'', Iohan. Petreius, Norimbergae, 1544 (with ''De Consolatione'' reprint and ''De Libris Propriis'', book I). * ''De Immortalitate animorum'', Henric Petreius, Nuremberg 1544/Sebastianus Gryphius, Lyons, 1545. * ''Contradicentium medicorum'' (on medicine), Hieronymus Scotus, Venetijs, 1545. * '' Artis magnae, sive de regulis algebraicis'' (on algebra: also known as ''Ars magna''), Iohan. Petreius, Nuremberg, 1545. ** Translation into English by D. Witmer (1968). * ''Della Natura de Principii e Regole Musicale'', ca 1546 (on music theory: in Italian): posthumously published. * ''De Subtilitate rerum'' (on natural phenomena), Johann Petreius, Nuremberg, 1550 . ** Translation into English by J.M. Forrester (2013). * '' Metoposcopia libris tredecim, et octingentis faciei humanae eiconibus complexa'' (on physiognomy), written 1550 (published posthumously by Thomas Jolly, Paris (Lutetiae Parisiorum), 1658). * ''In Cl. Ptolemaei Pelusiensis IIII, De Astrorum judiciis... libros commentaria: cum eiusdem De Genituris libro'', Henrichus Petri, Basle, 1554. * ''Geniturarum Exemplar'' (''De Genituris liber'', separate printing), Theobaldus Paganus, Lyons, 1555. * ''Ars Curandi Parva'' (written c. 1556). * ''De Libris propriis'' (about the books he has written, and his successes in medical work), Gulielmus Rouillius, Leiden, 1557. * ''De Rerum varietate, Libri XVII'' (on natural phenomena); (Revised edition), Matthaeus Vincentius, Avignon 1558. Also Basle, Henricus Petri, 1559. * ''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. * ''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. * ''Neronis encomium'' (a life of
Nero Nero Claudius Caesar Augustus Germanicus ( ; born Lucius Domitius Ahenobarbus; 15 December AD 37 – 9 June AD 68), was the fifth Roman emperor and final emperor of the Julio-Claudian dynasty, reigning from AD 54 unti ...

Nero
), Basle, 1562. ** Translation into English by A. Paratico (2012). * ''De Providentia ex anni constitutione,'' Alexander Benaccius, Bononiae, 1563. * ''De Methodo medendi,'' Paris, In Aedibus Rouillii, 1565. * ''De Causis, signis ac locis morborum, Liber unus'', Alexander Benatius, Bononiae, 1569. * ''Commentarii in Hippocratis Coi Prognostica, Opus Divinum; Commentarii De Aere, aquis et locis opus'', Henric Petrina Officina, Basel, 1568/1570. * ''Opus novum, De Proportionibus numerorum, motuum, ponderum, sonorum, aliarumque rerum mensurandarum. Item de aliza regula'', Henric Petrina, Basel, 1570. * ''Opus novum, cunctis De Sanitate tuenda, Libri quattuor'', Sebastian HenricPetri, Basle, 1569. * ''De Vita propria'', 1576 (autobiography). ** Translation into English by J. Stoner (2002). * ''Liber De Ludo aleae'' ("On Casting the "; on probability): posthumously published. ** Translation into English by S.H. Gould (1961). * ''Proxeneta, seu De Prudentia Civili'' (posthumously published: Paulus Marceau, Geneva, 1630).


''Collected Works''

A chronological key to this edition is supplied by M. Fierz.M. Fierz (trans. H. Niman), ''Girolamo Cardano, 1501-1576, Physician, Natural Philosopher, Mathematician, Astrologer and Interpreter of Dreams'' (Birkhäuser, Boston/Basel/Stuttgart 1983)
pp. 32-33
(Google).
* ''Hieronymi Cardani Mediolanensis Opera Omnia, cura Carolii Sponii'' (Lugduni, Ioannis Antonii Huguetan and Marci Antonii Ravaud, 1663) (10 volumes, Latin): **Volume 1: Philologica, Logica, Moralia
Internet Archive
another a
Google
another a
Google
**Volume 2: Moralia Quaedam et Physica
Google
**Volume 3: Physica
Google
**Volume 4: Arithmetica, Geometrica, Musica
Google
**Volume 5: Astronomica, Astrologica, Onirocritica
Internet Archive
another a
Google
**Volume 6: Medicinalium I
Google
**Volume 7: Medicinalium II
Google
**Volume 8: Medicinalium III
Google
**Volume 9: Medicinalium IV
Google
**Volume 10: Opuscula Miscellanea
Google


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


References


Sources

* 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:
New York Review of Books New is an adjective referring to something recently made, discovered, or created. New or NEW may refer to: Music * New, singer of K-pop group The Boyz (South Korean band), The Boyz Albums and EPs * New (album), ''New'' (album), by Paul McCartn ...
, 2002. * Cardano, Girolamo, ''Opera omnia'', Charles Sponi, ed., 10 vols. Lyons, 1663. * Cardano, Girolamo, ''Nero: an Exemplary Life'' Inckstone 2012, translation in English of the ''Neronis Encomium''. * Dunham, William, ''Journey through Genius'', Chapter 6, 1990,
John Wiley and Sons John Wiley & Sons, Inc., commonly known as Wiley (), is an American Multinational corporation, multinational publishing company founded in 1807 that focuses on academic publishing and instructional materials. The company produces books, Academi ...
. . 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. 2101–2119. arXiv e-print
arXiv:0806.0485
. * 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. * Grafton, Anthony,
Cardano's Cosmos: The Worlds and Works of a Renaissance Astrologer.
'
Harvard University Press Harvard University Press (HUP) is a publishing house established on January 13, 1913, as a division of Harvard University, and focused on academic publishing. It is a member of the Association of American University Presses. After the retirem ...
, 2001. * Morley, Henry, ''The life of Girolamo Cardano, of Milan, Physician'' 2 vols.
Chapman & Hall Chapman & Hall is an Imprint (trade name), imprint owned by CRC Press, originally founded as a United Kingdom, British publishing house in London in the first half of the 19th century by Edward Chapman (publisher), Edward Chapman and William 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 Princeton University Press is an independent Academic publishing, publisher with close connections to Princeton University. Its mission is to disseminate scholarship within academia and society at large. The press was founded by Whitney Darrow, ...

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
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.
*
History of Science Collection
at
Linda Hall Library The Linda Hall Library is a privately Financial endowment, endowed American library of science, engineering and technology located in Kansas City, Missouri, Kansas City, Missouri, sitting "majestically on a urban arboretum." It is the "largest i ...
* *
Girolamo Cardano, Strumenti per la storia del Rinascimento in Italia settentrionale (in Italian)
an
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. * E. M. Forster, Forster, E.M. 'Cardan' in ''Abinger Harvest'' (1936). Middlesex, UK: Penguin Books Ltd. pp. 208–221. *
"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 1898), fro
Internet Archive
(A barely-disguised re-hash of Morley's work) {{DEFAULTSORT:Cardano, Gerolamo 1501 births 1576 deaths 16th-century Latin-language writers 16th-century Italian mathematicians 16th-century Italian physicians Italian astrologers 16th-century astrologers 16th-century Italian inventors Physicians from Pavia University of Pavia alumni Scientists from Pavia