Alberti, Leone Battista
Baif, Lazare de
Baliani, Giovanni Battista
Benedetti, Giovanni Battista
Borelli, Giovanni Alfonso
Cicero, M. Tullius
Foscarini, Paolo Antonio
Guevara, Giovanni di
Jordanus de Nemore
Marci of Kronland, Johannes Marcus
Monantheuil, Henri de
Monte, Guidobaldo del
Schreck, Johann Terrenz
Stelliola, Niccolò Antonio
Wolff, Christian von
Born on 24.9.1501 in Pavia, died on 21.9.1576 in Rome, Italian physician, mathematician, physicist, philosopher
Cardano came from one of the oldest and most famous families of Milan and was raised from the age of four in Milan, in the house of his father, Facius Cardanus, who was a lawyer and also knew a great deal about mathematics and medicine. At the age of 21 Cardano went to Pavia to complete his studies. Shortly thereafter he is said to have instructed Euclid’s geometry at the secondary school there. In 1524 he went to Padua, where he was awarded the doctor of medicine one year later. In the small town of Saccolongo near Padua he began working as a doctor and started a family. When he became professor for mathematics in Milan in 1534, he also worked there as a doctor and became a member of the Collegium medicum in 1539. Soon he was the most famous doctor in Milan, but did not enjoy good relations with his colleagues, as is evident from his first two books De malo recentiorum medicorum medendi usu (Venice 1536) and Contradicentium medicorum libri II (Lyon 1538). In these works Cardano criticizes the methods used by his contemporaries and the unsystematic and contradictory description of illnesses since antiquity. During the year 1544 he held medical lectures in Pavia, but returned to Milan shortly thereafter. In 1547 he received from the Danish king the esteemed offer of a professorship at the university in Copenhagen, which he turned down because of the Danish climate and the predominant religion there. From the Archbishop and Primate of Scotland, Hamilton, who suffered from asthma, Cardano was called to Scotland in 1552. He traveled to Scotland via France and about ten months later, after the archbishop had been treated successfully, returned richly rewarded to Milan via London, the Netherlands and Germany. After his return from Scotland Cardano remained in Milan until October 1559 and then went to Pavia as professor of medicine. From Pavia he accepted a professorship for medicine in Bologna in 1562, where he instructed until 1570. In this year he was thrown into jail for alleged heresy and was barred from writing and teaching. Once the charges were proven to be unfounded, Cardano was granted full freedom again in September 1571 and lived the rest of his life in Rome, where he received a pension from the pope, but did not hold any public office. Cardano wrote a vast number of works, not all of which were of major scientific importance; this frequently earned him a reputation as a scribbler. As he explains himself in his autobiography, he loved to provoke his contemporaries and carry out conflicts with them. Apparently Cardano was a very difficult character who had to suffer many cruel blows of fate in his private life as well.
The two works De subtilitate libri XXI (1550) and De rerum varietate (1557), a supplementary volume to De subtilitate, are an encyclopedia of the natural science of the time, but are not a systematic treatment, but rather a jumble of texts on a wide range of subjects, including cosmology, mechanics, machine construction, demons, etc. They are formulated in a very unclear Latin and even contradict each other in part. Cardano was a proponent of hylozoism, according to which the world is full of matter possessing a spiritual component.
In medicine he attempted to break with Galenic and Hippocratic traditions and to give medicine a foundation independent of these traditions, whereby he attempted to pair it with practical medical treatment as a theoretical discipline. He left the field of medicine with many important observations on pathology, teratology and infectious diseases. Never lacking in self-confidence, he asserted that a great physician was born only once every thousand years, and that he was the seventh since the creation of the world.
In mechanics Cardano was a great admirer of Archimedes. He studied the lever and the inclined plane in a new manner for his age and described many mechanical devices such as the Cardanic suspension, which was already known in antiquity and attributed by Cardano to a Jannello Turriano from Cremona. He also introduced another device named after him, but invented before him, the cardanic joint. His explanation of the path of a trajectory is somewhere between that of the advocates of an impetus theory and that of the defenders of Aristotelian ideas. Cardano believes that at the beginning of movement, the propelled bodies are moved by the impetus of propulsion, but thereafter are accelerated by the movement of the air. Particularly notable is his opinion that the path of a projected body initially is a diagonally climbing straight line, while the subsequent declining stretch of the trajectory has the shape of a parabola. Cardano is also especially convinced that there are no incessant, continuous movements other than celestial movements. He made important observations in hydrodynamics, recognizing, for instance, that water in a system of pipes never climbs to the level from which it started but only up to a lower level, and that the longer the system of pipes, the lower this level. He also rejects Aristotle’s “horror vacui,” because he believes that the corresponding phenomena can be explained by a power of dilution. He concerned himself with the measurement of rates of flow and determined that these are proportional to the diameter of the pipes and the speed of the flowing water. He further observed that the upper strata of a flowing body of water move more quickly than the lower strata. He was also the first to attempt to determine experimentally the ratio between the density of air and the density of water.
Cardano made particularly outstanding contributions to the development of algebra, in which his name lives on in what is known as the cardanic formula for the resolution of cubic equations, although this formula was not found by Cardano, but rather by N. Tartaglia’s pupil S. del Ferro and then later also by Tartaglia himself. Once Cardano learned that Tartaglia had such a formula, he persuaded Tartaglia to hand over this formula through cunning and promises of confidentiality. Despite all his promises, in 1545 he made it known to the general public, along with other important algebraic results, in his book Ars magna sive de regulis algebraicis, which led to a vigorous conflict between Tartaglia and Cardano. Cardano succeeded in resolving a number of new cases for which Tartaglia had not yet found a solution; moreover, Cardano attempted to formulate a general procedure rather than just observing special cases, which was standard practice until that time. He also described the solution procedure given by L. Ferrari for fourth-degree algebraic equations and considered for the first time negative and imaginary roots. For all of this Cardano is generally held to be the founder of the theory of algebraic equations.
Cardano’s interest in various games of chance inspired him to write Liber de ludo aleae, in which he makes the first recorded attempt to formulate the laws of probability. However, because this book was first published as part of Opera omnia in 1663, it did not become known until after the relevant works of the year 1654 by Fermat and Pascal. Cardano appears to have been one of the first to attempt to apply algebra in physics, but had little success in this endeavor because most of the physical values were not available.