16th Century Math
|Characteristic of The 16th Century Mathematics.|
|Arrangement of The Symbols|
|Cubic and Quartic Equations|
Characteristic of The Sixteenth-Century Mathematics
Mathematics in 1400's-1500's in spite of the Renaissance revival was not developed after seventeenth century or Greek. The only thing focused was a solving of an equation of the third and fourth degree and symbolizing algebra of France. Though mathematics had a small change in Renaissance, it had powerful energy. However, the most important meaning is to make a modern mathematics start and to estabish a tradition of European mathematics.
Arrangement of The Symbols
Renaissant algebra started with necessity for commerce and arrangement of algebraic symbols.
Equal Symbol(=) : This symbol appeared for the first time in
Division Symbol(،ہ): Swiss mathematician Johann Heinrich Rahn used this symbol for the first time in his book
Decimal Symbol : Simon Stevin (1546~1620), a former technician, introduced this symbol for the first time.
Inequality Symbol(>,<) : These two Symbols were shown in a book published 10 years after English mathematician Thomas Harriot(1560~1621).
Symbols of Multiplication(،؟) and Difference(،) : These symbols appeared in
symbol of Letters : French mathematician Francois Viete (1540~1603) used letters to distinguish 'the known quantity' from 'the unknown'.
Cubic and Quartic Equations
Probably the most spectacular mathematical achievement of the sixteenth century was the discovery, 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. About 1515, Scipione del Ferro (1465-1526), a professor of mathematics at the University of Bologna, solved algebraically the cubic equation 3 + 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 3 + p2 = 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.
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.