Huffman Pittsburg State University Renaissance man Gerolamo Cardano was a physician, mathematician, gambler, and writer. It was actually the tenth in a series of volumes Cardano wrote for a work he called Opus Perfectum, or The Perfect Work. In fact, there are places in the book where he gave credit to the originator of a particular method e. The first paragraph, as translated by T.
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Huffman Pittsburg State University Renaissance man Gerolamo Cardano was a physician, mathematician, gambler, and writer. It was actually the tenth in a series of volumes Cardano wrote for a work he called Opus Perfectum, or The Perfect Work. In fact, there are places in the book where he gave credit to the originator of a particular method e.
The first paragraph, as translated by T. He [Tartaglia] gave it to me in response to my entreaties, though withholding the demonstration. Armed with this assistance, I sought out its demonstration in [various] forms. This was very difficult. My version follows. Thus, it took four different cases to include all possible quadratic equations. In English, these three cases are a number equal to a square and a linear term, a number and a linear term equal to a square, and a number and a square equal to a linear term.
The case of a number equal to a square term was mentioned on the previous page. A possible activity in a high school or college algebra class would be to have students write these cases in modern notation and investigate why Cardano had these, and only these, four cases for quadratic equations.
Using his techniques, Cardano encountered a square root of a negative integer while solving a certain quadratic equation. Specifically, the problem was to find two numbers whose sum is 10 and product In the Witmer translation p. The image folio 66 below shows the corresponding page from Ars Magna. Swetz and Victor J. Katz in Convergence. A complete digital scan of Ars Magna, call number QA References Branson, William B. Helfgott, Harald, and Michel Helfgott.
Smith, David Eugene. A Source Book in Mathematics. Dover, Swetz, Frank J. Witmer, T. Richard, trans. Ars Magna or the Rules of Algebra. MIT Press, Reprint, Dover,
Mathematical Treasure: Cardano's Ars Magna
However, he chose to keep his method secret. That same year, he asked Tartaglia to explain to him his method for solving cubic equations. After some reluctance, Tartaglia did so, but he asked Cardano not to share the information until he published it. Contents[ edit ] The book, which is divided into forty chapters, contains the first published algebraic solution to cubic and 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. He also acknowledges that it was Ferrari who found a way of solving quartic equations. In Ars Magna the concept of multiple root appears for the first time chapter I.
“Ars Magna”, de Girolano Cardano, e os desdobramentos da história da matemática
Gerolamo Cardano: biografía, aportes, inventos