# Babylonian and Muslim Algebra, Cubic Equations, Tartaglia

## Babylonian and Muslim Algebra

By 2000 B.C. the Babylonians had a well-developed algebra which was capable of solving quadratic equations by using a general formula as well as completing the square. This Babylonian algebra and the one developed by the Muslims in the eighth through 12th centuries A.D. were based on words rather than the symbolic type which arose in the 16th century A.D. in Europe and is now used. The very name of the subject, algebra, comes from the title of al-Khowarizmi’s book on the subject, Hisab al-jabr wal-mugabalah, the science of reunion and opposition. In its everyday usage, al-jabr meant “reuniter of broken bones” or “bonesetter.” The Muslim mathematician Omar Khayyam (better known today as a poet and author of The Rubricat) even developed geometric algorithms (another word with a Muslim origin) for solving some cubic and quartic equations.

## Cubic Equations

The next big advance in algebra did not occur until the 16th century, primarily in Italy. In the early 1500s, del Ferro, a professor at the University of Bologna, discovered how to solve equations of the form x3 + Ax = B and passed his secret technique on to his student Fior. About 1535, Tartaglia claimed that he could solve cubics of the form x3 + Ax2 = B . Fior thought that Tartaglia was bluffing and challenged him to a public problem-solving duel. In the meantime, Tartaglia discovered how to solve Fior’s types of problems and soundly defeated Fior in the mathematical duel. In the 1540’s, Cardano baited the secret techniques from Tartaglia but promised to keep them secret. Cardano then published them in his algebra book, Ars Magna , and a bitter dispute arose. Cardano’s student Ferrari discovered how to solve general quartic equations and that also appeared in Ars Magna.

## Tartaglia (Nicolo of Brescia)

Tartaglia was born into a poor family in Brescia about the year 1499, and he had the misfortune to be present in 1512 when the French captured the city. Tartaglia and his father fled to the sanctuary of the cathedral during the battle, but the soldiers also attacked there and massacred those inside. Tartaglia’s father was killed, and Tartaglia got a split skull and a saber cut through his jaw and palate. His mother later found him barely alive, and did the only thing she could think of for medical help. She remembered that dogs lick their wounds, so she did the same for Tartaglia. He lived, but from then on he had a speech impediment and was nicknamed Tartaglia, the stammerer. His mother managed to save enough money to send him to school for only 15 days, his only formal schooling, but he made the best of it — he stole the textbook and later taught himself to read and write from it. He eventually taught science and mathematics in Italy, and died in 1557 in Venice.

DTH

Last Updated September 19, 2022