The calculation of an artillery projectile's trajectory is familiar to anyone who has taken an introductory course in physics - the cannonball's path can be found using

Isaac Newton's laws of motion. However, more than a century before Newton formulated a complete science of mechanics, and even before

Galileo's early experiments, the first person known to describe cannon trajectories mathematically was self-taught Italian mathematician Niccolo Fontana, known as "Tartaglia."

Fontana was born in Brescia, Italy in 1499 to poor, uneducated parents. His father died while Niccolo was still a child, and his mother could not afford to send him to school. She eventually scraped together enough money for fifteen days' tuition, after which time he took the opportunity to steal his textbook and taught himself to read and write.

In 1512, the French army sacked Brescia. The thirteen year old boy was horribly wounded in his face by an enemy soldier's saber, and left for dead. His mother, lacking any medical knowledge, cleaned his wounds by licking them, as a dog would. Though he survived, he was left with huge scars which he later concealed with a long beard, and a speech impediment that brought him his adopted surname: Tartaglia, "The Stammerer."

Lacking any prestige or noble family background, Tartaglia earned his living teaching mathematics and science to local pupils. His early research, collected in his 1537 volume *Nova Scientia,* described the motion of free-falling bodies, in particular the application of greatest interest to war-torn Italy: cannonball trajectories. The book further discussed methods of accurately measuring the guns' angles of elevation, as well as surveying techniques to determine their range. In a later (1546) work, *Questi et Inventioni Diverse,* he went into greater detail about the shapes of artillery trajectories; his descriptions, while lacking Newton's rigor, were accurate for practical purposes.

Tartaglia is best known today for his solutions of cubic equations. Early in the 16th century, a university professor named del Ferro discovered a formula for solving a specific case of cubic equation. He kept it secret, and gave it to his student Fior before he died. Tartaglia later derived a general formula, with which he defeated Fior in a 1535 contest. Being a poor schoolteacher, he wanted to use his still undivulged knowledge to bargain his way into a higher-paying position. Well-known mathematician Giuseppe Cardano managed to obtain Tartaglia's secret on the condition that he not publish it. Cardano broke his word, and Tartaglia, demanding revenge, engaged Cardano's student Ferrari in a fierce debate, lost, and returned home despondent and impoverished.

In addition to his own original studies, Tartaglia took the role of the "Renaissance man," translating ancient texts into the vernacular. He is credited with the first Italian editions of Euclid's *Elements,* as well as various of Archimedes' works.