# CARDANO VIETA PDF

Methods for solving cubic equations appear in The Nine Chapters on the Mathematical Art , a Chinese mathematical text compiled around the 2nd century BC and commented on by Liu Hui in the 3rd century. Some others like T. In an early paper, he discovered that a cubic equation can have more than one solution and stated that it cannot be solved using compass and straightedge constructions. He also found a geometric solution.

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Methods for solving cubic equations appear in The Nine Chapters on the Mathematical Art , a Chinese mathematical text compiled around the 2nd century BC and commented on by Liu Hui in the 3rd century.

Some others like T. In an early paper, he discovered that a cubic equation can have more than one solution and stated that it cannot be solved using compass and straightedge constructions. He also found a geometric solution. He used what would later be known as the " Ruffini - Horner method" to numerically approximate the root of a cubic equation. He also used the concepts of maxima and minima of curves in order to solve cubic equations which may not have positive solutions.

In fact, all cubic equations can be reduced to this form if we allow m and n to be negative, but negative numbers were not known to him at that time. Del Ferro kept his achievement secret until just before his death, when he told his student Antonio Fior about it.

He was soon challenged by Fior, which led to a famous contest between the two. Each contestant had to put up a certain amount of money and to propose a number of problems for his rival to solve. Whoever solved more problems within 30 days would get all the money. Later, Tartaglia was persuaded by Gerolamo Cardano — to reveal his secret for solving cubic equations. In , Tartaglia did so only on the condition that Cardano would never reveal it and that if he did write a book about cubics, he would give Tartaglia time to publish.

Nevertheless, this led to a challenge to Cardano from Tartaglia, which Cardano denied. Ferrari did better than Tartaglia in the competition, and Tartaglia lost both his prestige and his income. He even included a calculation with these complex numbers in Ars Magna, but he did not really understand it.

Rafael Bombelli studied this issue in detail [21] and is therefore often considered as the discoverer of complex numbers. Such an equation a.