![]() ![]() ![]() He also acknowledges that it was Ferrari who found a way of solving quartic equations. Cardano acknowledges that Tartaglia gave him the formula for solving a type of cubic equations and that the same formula had been discovered by Scipione del Ferro. ![]() The book, which is divided into forty chapters, contains the first published algebraic solution to cubic and quartic equations. Then Cardano became aware of the fact that Scipione del Ferro had discovered Tartaglia's formula before Tartaglia himself, a discovery that prompted him to publish these results. Furthermore, his student Lodovico Ferrari found a way of solving quartic equations, but Ferrari's method depended upon Tartaglia's, since it involved the use of an auxiliary cubic equation. Cardano submerged himself in mathematics during the next several years working on how to extend Tartaglia's formula to other types of cubics. After some reluctance, Tartaglia did so, but he asked Cardano not to share the information until he published it. That same year, he asked Tartaglia to explain to him his method for solving cubic equations. In 1539, Cardano, then a lecturer in mathematics at the Piatti Foundation in Milan, published his first mathematical book, Pratica Arithmeticæ et mensurandi singularis ( The Practice of Arithmetic and Simple Mensuration). However, he chose to keep his method secret. ![]() In 1535 Niccolò Fontana Tartaglia became famous for having solved cubics of the form x 3 + ax = b (with a, b > 0). The first editions of these three books were published within a two-year span (1543–1545). It is considered one of the three greatest scientific treatises of the early Renaissance, together with Copernicus' De revolutionibus orbium coelestium and Vesalius' De humani corporis fabrica. There was a second edition in Cardano's lifetime, published in 1570. It was first published in 1545 under the title Artis Magnae, Sive de Regulis Algebraicis Liber Unus ( Book number one about The Great Art, or The Rules of Algebra). The Ars Magna ( The Great Art, 1545) is an important Latin-language book on algebra written by Gerolamo Cardano. ![]()
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