Gerolamo Cardano (; also Girolamo or Geronimo; ; ; 24 September 1501– 21 September 1576) was an Italian
polymath
A polymath or polyhistor is an individual whose knowledge spans many different subjects, known to draw on complex bodies of knowledge to solve specific problems. Polymaths often prefer a specific context in which to explain their knowledge, ...
whose interests and proficiencies ranged through those of mathematician,
physician
A physician, medical practitioner (British English), medical doctor, or simply doctor is a health professional who practices medicine, which is concerned with promoting, maintaining or restoring health through the Medical education, study, Med ...
,
biologist,
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 cau ...
,
chemist
A chemist (from Greek ''chēm(ía)'' alchemy; replacing ''chymist'' from Medieval Latin ''alchemist'') is a graduated scientist trained in the study of chemistry, or an officially enrolled student in the field. Chemists study the composition of ...
,
astrologer
Astrology is a range of Divination, divinatory practices, recognized as pseudoscientific since the 18th century, that propose that information about human affairs and terrestrial events may be discerned by studying the apparent positions ...
,
astronomer
An astronomer is a scientist in the field of astronomy who focuses on a specific question or field outside the scope of Earth. Astronomers observe astronomical objects, such as stars, planets, natural satellite, moons, comets and galaxy, galax ...
,
philosopher
Philosophy ('love of wisdom' in Ancient Greek) is a systematic study of general and fundamental questions concerning topics like existence, reason, knowledge, Value (ethics and social sciences), value, mind, and language. It is a rational an ...
,
music theorist,
writer
A writer is a person who uses written words in different writing styles, genres and techniques to communicate ideas, to inspire feelings and emotions, or to entertain. Writers may develop different forms of writing such as novels, short sto ...
, and
gambler. He became one of the most influential mathematicians of the
Renaissance
The Renaissance ( , ) is a Periodization, period of history and a European cultural movement covering the 15th and 16th centuries. It marked the transition from the Middle Ages to modernity and was characterized by an effort to revive and sur ...
and one of the key figures in the foundation of
probability
Probability is a branch of mathematics and statistics concerning events and numerical descriptions of how likely they are to occur. The probability of an event is a number between 0 and 1; the larger the probability, the more likely an e ...
; he introduced 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 te ...
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, the power expands into a polynomial with terms of the form , where the exponents and a ...
in the Western world. He wrote more than 200 works on science.
Cardano partially invented and described several mechanical devices including the
combination lock, the
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 No ...
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 ...
to rotate freely, and the
Cardan shaft
Cardan may refer to:
* Gerolamo Cardano or Jerome Cardan (1501–1576), Renaissance mathematician, physician, astrologer, and gambler
* Cornelius Castoriadis (1922–1997), Greek-French philosopher who used the pseudonym Paul Cardan
* Cardan, Giro ...
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 1570. 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.
Today, Cardano is well known for his achievements in
algebra
Algebra is a branch of mathematics that deals with abstract systems, known as algebraic structures, and the manipulation of expressions within those systems. It is a generalization of arithmetic that introduces variables and algebraic ope ...
. 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
cubic
Cubic may refer to:
Science and mathematics
* Cube (algebra), "cubic" measurement
* Cube, a three-dimensional solid object bounded by six square faces, facets or sides, with three meeting at each vertex
** Cubic crystal system, a crystal system w ...
and
quartic equations, and acknowledged the existence of
imaginary number
An imaginary number is the product of a real number and 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 im ...
s.
Early life and education
Cardano was born on 24 September 1501 in
Pavia
Pavia ( , ; ; ; ; ) is a town and comune of south-western Lombardy, in Northern Italy, south of Milan on the lower Ticino (river), Ticino near its confluence with the Po (river), Po. It has a population of c. 73,086.
The city was a major polit ...
, Lombardy, the
illegitimate child of
Fazio Cardano, a mathematically gifted
jurist
A jurist is a person with expert knowledge of law; someone who analyzes and comments on law. This person is usually a specialist legal scholar, mostly (but not always) with a formal education in law (a law degree) and often a Lawyer, legal prac ...
, lawyer, and close friend of
Leonardo da Vinci
Leonardo di ser Piero da Vinci (15 April 1452 - 2 May 1519) was an Italian polymath of the High Renaissance who was active as a painter, draughtsman, engineer, scientist, theorist, sculptor, and architect. While his fame initially rested o ...
. 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 ( , , ; ) is a city in northern Italy, regional capital of Lombardy, the largest city in Italy by urban area and the List of cities in Italy, second-most-populous city proper in Italy after Rome. The city proper has a population of nea ...
to
Pavia
Pavia ( , ; ; ; ; ) is a town and comune of south-western Lombardy, in Northern Italy, south of Milan on the lower Ticino (river), Ticino near its confluence with the Po (river), Po. It has a population of c. 73,086.
The city was a major polit ...
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 1520, Cardano entered the
University of Pavia
The University of Pavia (, UNIPV or ''Università di Pavia''; ) is a university located in Pavia, Lombardy, Italy. There was evidence of teaching as early as 1361, making it one of the List of oldest universities in continuous operation, oldest un ...
. 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 1521–1526
The Italian War of 1521–1526, sometimes known as the Four Years' War, () was a part of the Italian Wars. The war pitted Francis I of France and the Republic of Venice against the Holy Roman Emperor Charles V, Holy Roman Emperor, Charles V ...
, however, the authorities in Pavia were forced to close the university in 1524. Cardano resumed his studies at the
University of Padua, 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 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.
Early career as a physician
Cardano wanted to practice medicine in a large, rich city like
Milan
Milan ( , , ; ) is a city in northern Italy, regional capital of Lombardy, the largest city in Italy by urban area and the List of cities in Italy, second-most-populous city proper in Italy after Rome. The city proper has a population of nea ...
, 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 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 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.
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, a cubic equation in one variable is an equation of the form
ax^3+bx^2+cx+d=0
in which is not zero.
The solutions of this equation are called roots of the cubic function defined by the left-hand side of the equation. If all of th ...
and the solution of Cardano's student
Lodovico Ferrari to the
quartic equation in his 1545 book ''
Ars Magna'', an influential work on algebra. The solution to one particular case of the cubic equation
(in modern notation) had been communicated to him in 1539 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, 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 the product of a real number and 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 im ...
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 t ...
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, the power expands into a polynomial with terms of the form , where the exponents and a ...
.
Cardano was chronically short of money and kept himself solvent by being an accomplished gambler and
chess
Chess is a board game for two players. It is an abstract strategy game that involves Perfect information, no hidden information and no elements of game of chance, chance. It is played on a square chessboard, board consisting of 64 squares arran ...
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 a branch of mathematics and statistics concerning events and numerical descriptions of how likely they are to occur. The probability of an event is a number between 0 and 1; the larger the probability, the more likely an e ...
, 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
In probability theory, odds provide a measure of the probability of a particular outcome. Odds are commonly used in gambling and statistics. For example for an event that is 40% probable, one could say that the odds are or
When gambling, o ...
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 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 1663 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 1574, and a copy of it is held in the
Vatican Library
The Vatican Apostolic Library (, ), more commonly known as the Vatican Library or informally as the Vat, is the library of the Holy See, located in Vatican City, and is the city-state's national library. It was formally established in 1475, alth ...
. The work is valuable for studies in
harmony
In music, harmony is the concept of combining different sounds in order to create new, distinct musical ideas. Theories of harmony seek to describe or explain the effects created by distinct pitches or tones coinciding with one another; harm ...
for its discussion of the use of
microtones. It is also of interest to scholars of
historically informed performance
Historically informed performance (also referred to as period performance, authentic performance, or HIP) is an approach to the performance of Western classical music, classical music which aims to be faithful to the approach, manner and style of ...
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
''The New Grove Dictionary of Music and Musicians'' is an encyclopedic dictionary of music and musicians. Along with the German-language '' Die Musik in Geschichte und Gegenwart'', it is one of the largest reference works on the history and t ...
'' 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.
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. 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 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 (; September 129 – AD), often Anglicization, anglicized as Galen () or Galen of Pergamon, was a Ancient Rome, Roman and Greeks, Greek physician, surgeon, and Philosophy, philosopher. Considered to be one o ...
'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, sometimes called ''Cardan joint'', was not described by Cardano.
''De Subtilitate'' (1550)
As quoted from
Charles Lyell's ''
Principles of Geology'':
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.
Scotland and Archbishop Hamilton
In 1552 Cardano travelled to Scotland with the Spanish physician William Casanatus, via London, to treat the
Archbishop of St Andrews 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 and Casanatus argued over the Archbishop's cure. 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.
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 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
beheaded. 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.
He obtained a position as professor of medicine at the
University of Bologna
The University of Bologna (, abbreviated Unibo) is a Public university, public research university in Bologna, Italy. Teaching began around 1088, with the university becoming organised as guilds of students () by the late 12th century. It is the ...
.
Cardano was arrested by the
Inquisition
The Inquisition was a Catholic Inquisitorial system#History, judicial procedure where the Ecclesiastical court, ecclesiastical judges could initiate, investigate and try cases in their jurisdiction. Popularly it became the name for various med ...
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 propose that information about human affairs and terrestrial events may be discerned by studying the apparent positions ...
, 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 (; , ; ; – 160s/170s AD) was a Greco-Roman mathematician, astronomer, astrologer, geographer, and music theorist who wrote about a dozen scientific treatises, three of which were important to later Byzantine science, Byzant ...
, Cardano had also published a horoscope of
Jesus
Jesus (AD 30 or 33), also referred to as Jesus Christ, Jesus of Nazareth, and many Names and titles of Jesus in the New Testament, other names and titles, was a 1st-century Jewish preacher and religious leader. He is the Jesus in Chris ...
. 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 (: indexes or 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 the Halo Array in the ...
.
He moved to Rome, where he received a lifetime
annuity
In investment, an annuity is a series of payments made at equal intervals based on a contract with a lump sum of money. Insurance companies are common annuity providers and are used by clients for things like retirement or death benefits. Examples ...
from
Pope Gregory XIII
Pope Gregory XIII (, , born Ugo Boncompagni; 7 January 1502 – 10 April 1585) 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 commissioning and being the namesake ...
(after first having been rejected by
Pope 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.
References in literature and culture
The seventeenth-century English physician and philosopher Sir
Thomas Browne possessed the ten volumes of the Lyon 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'':
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 (Manzoni novel), The Betrothed'' (orig. ) (1827), generally ranked among ...
'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 (; 384–322 BC) was an Ancient Greek philosophy, Ancient Greek philosopher and polymath. His writings cover a broad range of subjects spanning the natural sciences, philosophy, linguistics, economics, politics, psychology, a ...
, 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).
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. (most likely falsely attributed to Cardano)
* ''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 a Roman emperor and the final emperor of the Julio-Claudian dynasty, reigning from AD 54 until his ...
), 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
Die"; 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, 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 publishing company that focuses on academic publishing and instructional materials. The company was founded in 1807 and produces books, journals, and encyclop ...
. . 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 an academic publishing house established on January 13, 1913, as a division of Harvard University. It is a member of the Association of University Presses. Its director since 2017 is George Andreou.
The pres ...
, 2001.
* 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
Princeton University Press is an independent 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, with the financial ...
, 1997.
External links
* Georgio Vivi (ed.), ''Cardani Mediolanensis Philosophi ac Medici Celeberrimi Bibliographia'', Tertia Editio (Author, 'Cosmopoli', 2018). A 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 Collectionat
Linda Hall Library
*
*
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.
*
Forster, E.M. 'Cardan' in ''Abinger Harvest'' (1936). Middlesex, UK:
Penguin Books
Penguin Books Limited is a Germany, German-owned English publishing, publishing house. It was co-founded in 1935 by Allen Lane with his brothers Richard and John, as a line of the publishers the Bodley Head, only becoming a separate company the ...
Ltd. pp. 208–221.
*
"Cardano v Tartaglia: The Great Feud Out of Bounds"by Tony Rothman
De Subtilitate Libri XXIFrom the Rare Book and Special Collection Division at the
Library of Congress
The Library of Congress (LOC) is a research library in Washington, D.C., serving as the library and research service for the United States Congress and the ''de facto'' national library of the United States. It also administers Copyright law o ...
* 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 writers in Latin
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
Italian music theorists