¡ß Cubic and Quartic Equations
Probably the most spectacular mathematical achievement of the sixteenth century
was the dicovery, by Italian mathematicians, of the algebraic solution of
cubic and quartic equations. The story of this discovery, when told in its most
colorful version, rivals any page ever written by Benvenuto Cellini. Briefly
told, the facts seem to be these. Avout 1515, Scipione del Ferro (1465-1526), a
professor of mathematics at the University of Bologna, solved algebraically the
cubic equation + mx = n, probably basing his work on earlier
Arabic sources. He did not publish his result but revealed the secret to his pupil Antonio Fior.
Now about 1535, Nicolo Fontana of Brescia, commonly referred to as Tartaglia (the stammerer)
because of a childhood injury that affected his speech, claimed to have discovered an algebraic solution of the cubic equation
+ p = n. Believing this claim was a bluff, Fior challinged Targaglia to a
public contest of solving cubic equations, whereupon the latter exerted himself
and only a few days before the contest found an algebraic solution for cubics
lacking a quadratic term. Entering the contest equipped to solve two types of
cubic equations, whereas Fior could solve but one type, Tartaglia triumphed
completely. Later Girolamo Cardano, an unprincipled genius who taught
mathematics and practiced medicine in Milan, upon giving a solemn pledge of
secredy, wheedled the key to the cubic form Tartaglia. In 1545, Cardano
published his Ars magna, a great Latin treatise on algebra, at Neuremberg,
Germany, and in it appeared Tartaglia's solution of the cubic. Tartaglia's vehement
protests were met by Ludovico Ferrari, Cardano's most capable pupil, who
argued that Cardano had received his information from del Ferro through a third party and accused Tartaglia
of plagiarism from the same source. There ensued an acrimonious dispute from which Tartaglia was perhaps lucky to
escape alive.
Since the actors in the above drama seem not always to have had the
highest regard for truth, one finds a number of variations in the details of the
plot.
It was not long after the cubic had been solved that an algebraic solution
was discovered for the general quartic (or biquadratic) equation. In 1540, the
Italian mathematician Zuanne de Tonini da Coi proposed a problem to Cardano that
led to quartic equation. Although Cardano was
unable to solvce the equation, his pupil Ferrari succeeded, and Cardano had the
pleasure of publishing this solution also in his Ars magna.
The repersentative mathematics of the 16th century is algebra
originated in Arabia but it developed in Europe because commerce
and calculation throve in there. Italian merchants and bankers, especially,
needed now to calculate accurately.
Astronomy contribute to the development of mathematics and
'mathematician' meant 'astronomer' for some time.
Nicolas Corpernicus (1473~1543), Polander, was the most
distinguished astronomer who contributed so much to the development of mathematics.
His theory about universe brought the improvement of trigonometry. He himself wrote a thesis on trigonometry.
