# Gerolamo Cardano

**Girolamo CardanoCardanoJerome CardanCardanusCardanCardano, GerolamoHieronymus Cardanuscardan suspensionCardano, GirolamoGeralomo Cardano**

Gerolamo (or Girolamo, or Geronimo ) Cardano (Jérôme Cardan; Hieronymus Cardanus; 24 September 1501 – 21 September 1576) was an Italian polymath, whose interests and proficiencies ranged from being a mathematician, physician, biologist, physicist, chemist, astrologer, astronomer, philosopher, writer, and gambler.wikipedia

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### Drive shaft

**propeller shaftdriveshaftshaft**

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.

A drive shaft, driveshaft, driving shaft, tailshaft (Australian English), propeller shaft (prop shaft), or Cardan shaft (after Girolamo Cardano) is a mechanical component for transmitting torque and rotation, usually used to connect other components of a drive train that cannot be connected directly because of distance or the need to allow for relative movement between them.

### Universal joint

**Cardan jointuniversal jointscardan**

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.

A universal joint (universal coupling, U-joint, Cardan joint, Spicer or Hardy Spicer joint, or Hooke's joint) is a joint or coupling connecting rigid rods whose axes are inclined to each other, and is commonly used in shafts that transmit rotary motion.

### Gimbal

**gimbalsCardan suspensiongimballed**

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.

The gimbal suspension used for mounting compasses and the like is sometimes called a Cardan suspension after Italian mathematician and physicist Gerolamo Cardano (1501–1576) who described it in detail.

### Probability

**probabilisticprobabilitieschance**

He was one of the most influential mathematicians of the Renaissance, and was one of the key figures in the foundation of probability and the earliest introducer of the binomial coefficients and the binomial theorem in the Western world.

The sixteenth century Italian polymath Gerolamo Cardano 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 ).

### Astrology

**astrologerastrologicalastrologers**

Gerolamo (or Girolamo, or Geronimo ) Cardano (Jérôme Cardan; Hieronymus Cardanus; 24 September 1501 – 21 September 1576) was an Italian polymath, whose interests and proficiencies ranged from being a mathematician, physician, biologist, physicist, chemist, astrologer, astronomer, philosopher, writer, and gambler.

Gerolamo Cardano cast the horoscope of king Edward VI of England, while John Dee was the personal astrologer to queen Elizabeth I of England.

### Hypocycloid

**hypocycloidal gearcyclical curvehypocycloid curve**

He made significant contributions to hypocycloids, published in De proportionibus, in 1570.

Girolamo Cardano was the first to describe these hypocycloids and their applications to high-speed printing.

### Quartic function

**quartic equationquarticquartic polynomial**

He made the first systematic use of negative numbers in Europe, published with attribution the solutions of other mathematicians for the cubic and quartic equations, and acknowledged the existence of imaginary numbers. He published with attribution the solution of Scipione del Ferro to the cubic equation and the solution of his student Lodovico Ferrari to the quartic equation in his 1545 book Ars Magna.

The solution of the quartic was published together with that of the cubic by Ferrari's mentor Gerolamo Cardano in the book Ars Magna.

### Combination lock

**combinationcombination lockscombination dial**

Gerolamo Cardano later described a combination lock in the 16th century.

### University of Pavia

**PaviaPavia UniversityUniversità di Pavia**

After a depressing childhood, with frequent illnesses, including impotence, and the rough upbringing by his overbearing father, in 1520, Cardano entered the University of Pavia against his father's wish, who wanted his son to undertake studies of law, but Girolamo felt more attracted to philosophy and science.

However, during the 16th century, after the university was re-opened, scholars and scientists such as Andrea Alciato and Gerolamo Cardano taught here.

### Imaginary number

**imaginaryimaginary numbersimaginary axis**

He made the first systematic use of negative numbers in Europe, published with attribution the solutions of other mathematicians for the cubic and quartic equations, and acknowledged the existence of imaginary numbers. 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.

The concept had appeared in print earlier, for instance in work by Gerolamo Cardano.

### Cubic equation

**cubicCardano's formulaCardano's method**

He made the first systematic use of negative numbers in Europe, published with attribution the solutions of other mathematicians for the cubic and quartic equations, and acknowledged the existence of imaginary numbers. He published with attribution the solution of Scipione del Ferro to the cubic equation and the solution of his student Lodovico Ferrari to the quartic equation in his 1545 book Ars Magna.

Later, Tartaglia was persuaded by Gerolamo Cardano (1501–1576) to reveal his secret for solving cubic equations.

### Ars Magna (Gerolamo Cardano)

**Ars MagnaArs Magna'' (Gerolamo Cardano)Artis magnae sive de regulis algebraicis**

He published with attribution the solution of Scipione del Ferro to the cubic equation and the solution of his student Lodovico Ferrari to the quartic equation in his 1545 book Ars Magna.

The Ars Magna ("The Great Art") is an important Latin-language book on algebra written by Gerolamo Cardano.

### Cardan grille

He also introduced the Cardan grille, a cryptographic writing tool, in 1550.

In 1550, Girolamo Cardano (1501–1576), known in French as Jérôme, proposed a simple grid for writing hidden messages.

### Odds

**4/15/13/1**

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 ).

The sixteenth-century polymath Cardano demonstrated the efficacy of defining odds as the ratio of favourable to unfavourable outcomes.

### Lodovico Ferrari

**Ludovico FerrariFerrariFerrari, Lodovico**

He published with attribution the solution of Scipione del Ferro to the cubic equation and the solution of his student Lodovico Ferrari to the quartic equation in his 1545 book Ars Magna.

Lodovico settled in Bologna, Italy, and he began his career as the servant of Gerolamo Cardano.

### Pavia

**Pavia, Italycomune di Paviahistory**

He was born in Pavia, Lombardy, the illegitimate child of Fazio Cardano, a mathematically gifted jurist, lawyer, and close personal friend of Leonardo da Vinci.

Among the illustrious scholars who studied or taught at the University of Pavia, the following are at least worth remembering: Carlo Goldoni, Gerolamo Cardano, Gerolamo Saccheri, Ugo Foscolo, Alessandro Volta the inventor of the battery, Lazzaro Spallanzani, Antonio Scarpa, Carlo Forlanini, the Nobel laureate biologist Camillo Golgi, the Nobel laureate chemist Giulio Natta and Emanuele Severino, one of the most important contemporary Italian philosophers.

### Rafael Bombelli

**Raphael BombelliBombelli, RafaelBombelli**

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.

As such, Bombelli was able to get solutions using Scipione del Ferro's rule, even in the irreducible case, where other mathematicians such as Cardano had given up.

### Negative number

**negativenegative numberssigned**

He made the first systematic use of negative numbers in Europe, published with attribution the solutions of other mathematicians for the cubic and quartic equations, and acknowledged the existence of imaginary numbers.

In 1545, Gerolamo Cardano, in his Ars Magna, provided the first satisfactory treatment of negative numbers in Europe.

### Niccolò Fontana Tartaglia

**Niccolò TartagliaTartagliaTartaglia's formula**

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 (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 Ferro's solution predated Fontana's.

Tartaglia is perhaps best known today for his conflicts with Gerolamo Cardano.

### Scipione del Ferro

**Scipione dal FerroDel Ferrodel Ferro, Scipione**

He published with attribution the solution of Scipione del Ferro to the cubic equation and the solution of his student Lodovico Ferrari to the quartic equation in his 1545 book Ars Magna.

In 1543, Gerolamo Cardano and Ludovico Ferrari (one of Cardano's students) travelled to Bologna to meet Nave and learn about his late father-in-law's notebook, where the solution to the depressed cubic equation appeared.

### Fazio Cardano

**Cardano, Fazio**

He was born in Pavia, Lombardy, the illegitimate child of Fazio Cardano, a mathematically gifted jurist, lawyer, and close personal friend of Leonardo da Vinci.

Fazio Cardano was the father of Gerolamo Cardano.

### Library of Sir Thomas Browne

**his librarylibrary**

The seventeenth-century English physician and philosopher Sir Thomas Browne possessed the ten volumes of the Leyden 1663 edition of the complete works of Cardan in his library.

### Blow book

The earliest known mention of the concept was by Gerolamo Cardano in 1550, who described the trick by mentioning "conjurors show different and always unlike pictures in one and the same book".

### Anthony Grafton

**Grafton, AnthonyAnthony T. GraftonAnthony Thomas Grafton**

His many books include a study of the scholarship and chronology of Renaissance scholar Joseph Scaliger (2 vols, 1983–1993), and, more recently, studies of Girolamo Cardano as an astrologer (1999) and Leon Battista Alberti (2000).

### Metoposcopy

**MetoposcopiaMetoposcopists**

Metoposcopy was developed by the 16th century Italian polymath Gerolamo Cardano, considered to be one of the foremost mathematicians of the Renaissance.