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Gerolamo Cardano

b. Pavia, Italy 24 September 1501
d. Rome, Italy 21 September 1576.

Cardano began university studies in 1520 at Pavia and completed them in 1526 at Padua where he earned a doctorate in medicine. He immediately put his degree to use.

In 1534 he began teaching mathematics in Milan while still practicing medicine. His skills as a physician were so great that nine years later he acquired the chair of medicine at the University of Pavia. There he taught almost continuously until 1560. He then purchased the chair of medicine at the University of Bologna in 1562.

Cardano ran afoul of the Inquisition and was imprisoned by them in 1570 on charges of heresy because he had cast the horoscope of Jesus Christ. He recanted and upon his release from prison went to Rome. There he obtained the favor of Pope Pius V who gave him a lifetime annuity.

In 1539, his work, Practica arithmetice et mensurandi singularis, was published. In this work, Cardano gave his solution to the problem of points and leveled a severe criticism of Pacioli. The relevant texts are these:

These texts from the Pratica are available in Latin and English with facing columns. 

Cardano was among other things a passionate gambler. In his later years he wrote Liber de ludo aleae (A book on games of chance) which is a handbook for gamblers. This work was published posthumously in 1663 among his collected works. It is unlikely the work had much influence since Huygens had published his De ratiociniis in 1657 and it became the foundation of subsequent studies.

A translation into English may be found in Cardano: the gambling scholar by Oysten Ore. Princeton Univ. Press, New Jersey, 1953. It has been reprinted by Dover Publications.