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The Ars Magna (The Great Art, 1545) is an important Latin-language book on algebra written by Gerolamo Cardano. 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). There was a second edition in Cardano's lifetime, published in 1570.
Thus the resolution of the equation may be finished exactly as with Cardano's method, with and in place of u and . In the case of the depressed cubic, one has x 0 = 1 3 ( s 1 + s 2 ) {\displaystyle x_{0}={\tfrac {1}{3}}(s_{1}+s_{2})} and s 1 s 2 = − 3 p , {\displaystyle s_{1}s_{2}=-3p,} while in Cardano's method we have set x 0 = u + v ...
Gerolamo Cardano (Italian: [dʒeˈrɔːlamo karˈdaːno]; also Girolamo [1] or Geronimo; [2] French: Jérôme Cardan; Latin: Hieronymus Cardanus; 24 September 1501– 21 September 1576) was an Italian polymath whose interests and proficiencies ranged through those of mathematician, physician, biologist, physicist, chemist, astrologer, astronomer, philosopher, music theorist, writer, and ...
Cardano suggested drafting the text three times in order to smooth any irregularities that might indicate the hidden words. The recipient of the message must possess an identical grille. Copies of grilles are cut from an original template, but many different patterns could be made for one-to-one correspondence.
Gerolamo Cardano published them in his 1545 book Ars Magna, together with a solution for the quartic equations, discovered by his student Lodovico Ferrari. In 1572 Rafael Bombelli published his L'Algebra in which he showed how to deal with the imaginary quantities that could appear in Cardano's formula for solving cubic equations.
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Casus irreducibilis (from Latin 'the irreducible case') is the name given by mathematicians of the 16th century to cubic equations that cannot be solved in terms of real radicals, that is to those equations such that the computation of the solutions cannot be reduced the the computation of square and cube roots.
However, in 1925, manuscripts were discovered by Bortolotti which contained del Ferro's method and made Bortolotti suspect that del Ferro had solved both cases. Cardano , in his book Ars Magna (published in 1545) states that it was del Ferro who was the first to solve the cubic equation and that the solution he gives is del Ferro's method.