CARDANO, GIROLAMO (b. Pavia, Italy, 24 September 1501; d. Rome, Italy, 21 September 1576), medicine, mathematics, physics, philosophy.

    Cardano to write the Liber de ludo aleae, which he completed in his old age, perhaps during his stay at Bologna; it was published posthumously in the Opera omnia. The book represents the first attempt at a theory of probability based on the philosophical premise that, beyond mere luck, laws and rules govern any given case. The concept of probability was introduced, expressed as the ratio of favorable to possible cases; the law of large numbers was enunciated; the so-called “power law” (if p is the probability of an event, the probability that the event will be repeated n times is pn) was presented; and numerous problems relating to games of dice, cards, and knucklebones were solved. The book was published, however, subsequent to the first research into the theory of games developed in the correspondence between Fermat and Pascal in 1654; it had no influence on the later development of the field.

Cardano published two encyclopedias of natural science: De subtilitate libri XXI (1550) and De rerum varietate (1557), a supplement to De subtilitate. The two works, written in an elliptical and often obscure Latin, contain a little of everything: from cosmology to the construction of machines; from the usefulness of natural sciences to the evil influence of demons; from the laws of mechanics to cryptology. It is a mine of facts, both real and imaginary; of notes on the state of the sciences; of superstition, technology, alchemy, and various branches of the occult. The similarities between the scientific opinions expressed by Cardano in these two works and those of Leonardo da Vinci, at that time unpublished, has led some historians, particularly Pierre Duhem, to suppose that Cardano has used Leonardo's manuscript notes; others insist that the similarity is entirely coincidental. Be that as it may, Cardano must always be credited with having introduced new ideas that inspired new investigations. In the sixteenth century there were five editions of De rerum varietate and eight of De subtilitate, as well as seven editions of the French translation of the latter.

Cardano reduced the elements to three (air, earth, water), eliminating fire, which he considered a mode of existence of matter; and he reduced the four qualities to two (hot and moist). His magic was, above all, an attempt to interpret natural phenomena in terms of sympathy and antipathy.

In mechanics, Cardano was a fervent admirer of Archimedes. He studied the lever and the inclined plane in new ways and described many mechanical devices, among them “Cardano's suspension,” known in classical antiquity, which he attributed to a certain Jannello Turriano of Cremona. Cardano followed a middle road between the partisans of the theory of impetus and the supporters of the Aristotelian theory, who attributed the movement of projectiles to pushing by the air: he favored the idea that at the beginning of its trajectory the projectile was moved by the impetus of the firing mechanism but subsequently was accelerated by the movement of the air. Notable is his observation that the trajectory described by a projectile is not rectilinear at the center, but is a line “which imitates the form of a parabola.” Cardano's chief claim to fame, however, was his affirmation of the impossibility of perpetual motion, except in heavenly bodies.

Cardano's contributions to hydrodynamics are important: counter to contemporary belief, he observed that in a conduit of running water, the water does not rise to the level from which it started, but to a lower level that becomes lower as the length of the conduit increases. He also refuted the Aristotelian “abhorrence of a vacuum,” holding that the phenomena attributed to this abhorrence can be explained by the force of rarefaction. Cardano investigated the measurement of the capacity of streams and stated that the capacity is proportional to the area of the cross section and the velocity. He observed that a stream presses against its banks and, counter to contemporary opinion, he held that the upper levels of moving water move faster than the lower levels.

In his Opus novum de proportionibus, Cardano turned to problems of mechanics, with the principal aim of applying quantitative methods to the study of physics. His use of the concept of moment of a force in his study of the conditions of equilibrium in balance and his attempt to determine experimentally the relation between the densities of air and water are noteworthy. The value that he obtained, 1:50, is rough; but it is the first deduction to be based on the experimental method and on the hypothesis that the ratio of the distances traveled by bullets shot from the same ballistic instrument, through air and through water, is the inverse of the ratio between the densities of air and water.

Geology is indebted to Cardano for several theories: that the formation of mountains is often due to erosion by running water; that rise of the ocean floor is indicated by the presence of marine fossils in land that was once submerged; and the idea—then novel—that streams originate from rainwater, which runs back to the sea and evaporates from it, to fall back to earth as rain, in a perpetual cycle.

The many editions of Cardano's works and the citations of them by writers of the second half of the sixteenth century demonstrate their influence, especially