Due protagonisti bolognesi dell'algebra rinascimentale: Ludovico Ferrari e Rafael Bombelli

Gavagna, Veronica

Matematica, cultura e società, Série 1, Tome 7 (2022) no. 3, pp. 249-265

Résumé

Two important anniversaries for the history of Renaissance algebra occur in 2022: 500 years since the birth of Ludovico Ferrari and 450 years since the publication of Rafael Bombelli's L'Algebra. Pupil of Girolamo Cardano, Ludovico Ferrari was the protagonist with Niccolò Tartaglia in one of the most famous challenges in the history of mathematics, in which he defended his master against the accusation that he had betrayed the pact of secrecy on the solving procedure of the third-degree equation by publishing it in Ars Magna (1545). This work, which also contained the resolution of the fourth-degree equation found by Ferrari, represented a crucial milestone in the development of algebra, but its dissemination was hampered by the “obscure saying” of its author. A profound admirer of algebra – which he said was first among mathematics – Rafael Bombelli of Bologna therefore set out to make the discipline accessible and “reduce it to perfect order,” partly in light of his study of Diophantine's Arithmetic, which influenced him to the point of rewriting part of his work. In L'Algebra Bombelli overcame the stumbling block on which Cardano and Ferrari had run aground – the nature of the square roots of negative numbers – by inventing the new signs “più di meno” and “meno di meno” and thus giving meaning to the solving formula of the third-degree equation even in the hostile irreducible case.