"Cardan published [1545] his treatise Ars Magna, or Algebra... Cardan was the first to perceive that equations had several roots and to distinguish them into positive and negative. But he is particularly known for having first remarked the so-called irreducible case in which the expression of the real roots appears in an imaginary form. Cardan convinced himself from several special cases in which the equation had rational divisors that the imaginary form did not prevent the roots from having a real value. But it remained to be proved that not only were the roots real in the irreducible case, but that it was impossible for all three together to be real except in that case. This proof was afterwards supplied by Vieta, and particularly by Albert Girard, from considerations touching the trisection of an angle."
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Lectures on Elementary Mathematics
Lectures on Elementary Mathematics (1898) is the earliest English translation of Joseph Louis Lagrange's 1795 publication, Leçons élémentaires sur les mathematiques, containing a series of lectures delivered the same year at the Ecole Normale. The work was translated and edited by Thomas J. McCormack, and a second edition, from which the following quotes are taken, appeared in 1901.
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