Page:A History of Mathematics (1893).djvu/163

 This is Tartaglia's solution of $$\scriptstyle{x^3+mx=n}$$. On the 13th of February, he found a similar solution for $$\scriptstyle{x^3=mx+n}$$. The contest began on the 22d. Each contestant proposed thirty problems. The one who could solve the greatest number within fifty days should be the victor. Tartaglia solved the thirty problems proposed by Floridas in two hours; Floridas could not solve any of Tartaglia's. From now on, Tartaglia studied cubic equations with a will. In 1541 he discovered a general solution for the cubic $$\scriptstyle{x^3 \pm px^2=\pm q}$$, by transforming it into the form $$\scriptstyle{x^3 \pm mx=\pm n}$$. The news of Tartaglia's victory spread all over Italy. Tartaglia was entreated to make known his method, but he declined to do so, saying that after his completion of the translation from the Greek of Euclid and Archimedes, he would publish a large algebra containing his method. But a scholar from Milan, named Hieronimo Cardano (1501-1576), after many solicitations, and after giving the most solemn and sacred promises of secrecy, succeeded in obtaining from Tartaglia a knowledge of his rules.

At this time Cardan was writing his Ars Magna, and he knew no better way to crown his work than by inserting the much sought for rules for solving cubics. Thus Cardan broke his most solemn vows, and published in 1545 in his Ars Magna Tartaglia's solution of cubics. Tartaglia became desperate. His most cherished hope, of giving to the world an immortal work which should be the monument of his deep learning and power for original research, was suddenly destroyed; for the crown intended for his work had been snatched away. His first step was to write a history of his invention; but, to completely annihilate his enemies, he challenged Cardan and his pupil Lodovico Ferrari to a contest: each party should propose thirty-one questions to be solved by the other within fifteen days. Tartaglia solved most questions in seven days, but the other party did not send in their solution before the expiration