Niccolo Tartaglia, born Niccolo Fontana in Brescia about 1500, was raised in poverty by his mother. His father was killed in the French occupation of the town in 1512, and it was then that Niccolo received a saber cut which was supposed to have been the cause of his stammering for the rest of his life. Because of this disability, he gave himself the nickname of Tartaglia, the "stutterer".
He was a self-taught engineer, surveyor, and bookkeeper and is said to have used tombstones as slates because he was too poor to buy writing materials. As he grew to manhood, he demonstrated definite mathematical abilities, and he established himself as a teacher of mathematics in Venice in 1534.
Tartaglia's pioneer work on ballistics and falling bodies, Nova scientia (1537; New Science) represents an original attempt to establish theories for knowledge which had previously been known empirically. Leonardo da Vinci had studied the science of ballistics earlier, but his work was not nearly so comprehensive. In his analysis of the dynamics of moving bodies, Tartaglia differentiated types of motion. Thus, a freely falling body possesses a natural motion if it is an "evenly heavy" body; by this phrase it was understood that the object was made of dense material and was of a form which would not develop much air resistance. Such bodies fall at an accelerated rate, and each has its maximum velocity at the moment of impact with the earth. The natural motion of descent varies with the distance traveled by the body.
The other case is that of the violent motion characteristic of a projectile. Tartaglia opposed the prevailing view that a projectile was subject to an initial acceleration and claimed that a violently propelled body starts to lose velocity as soon as it is detached from the propelling force. In his diagram of an evenly heavy body in violent motion, the first phase is a straight line upward at an angle, the second a curve, and the third a straight vertical line representing the body in a state of natural motion. He claimed that the curved part of the trajectory was the result of the body's own weight, but he recognized that this was theory inconsistent with his description of the first phase of violent motion. To save his theory, Tartaglia suggested that the whole path was actually curved but that the curvature was so slight as to be imperceptible.
In his discussions of violent motion, it is obvious that Tartaglia was still in harmony with the earlier "impetus" school of physics, which held that a quantity of force was impressed into a body when it was put in motion. Motion ceased when this force was exhausted, and a body in flight had its motion changed from violent to natural at that point.
In his second book on the subject, Quesiti et inventioni diverse (1546; Diverse Problems and Inventions), Tartaglia made some important modifications in the theories he had expounded in Nova scientia. He stated that a body could possess violent and natural motion at the same time and that the only motion which could occur as a straight line was purely vertical. Thus, in the case of a cannonball, unless the cannon was fired straight upward, the projectile was bound to have a curved path. Artillerymen, who based their conclusions on field observations, insisted that this was not so and that the force of propulsion of a shot guaranteed that it would move in a straight line for part of its flight. Some mathematicians agreed, but Tartaglia insisted that under the influences of violent and natural motion not even the smallest part of a missile's trajectory could be rectilinear.
In convincing his opponents, Tartaglia was less than successful, and they would accept only the triple-phase trajectory of his earlier work. Not until Galileo gave his mathematical proofs did scientists realize that all projectile motions are parabolic and hence trace a curved path.
Tartaglia is perhaps best known today for his conflicts with Gerolamo Cardano. Cardano cajoled Tartaglia into revealing his solution to the cubic equations by promising not to publish them. Tartaglia divulged the secrets of the solutions of three different forms of the cubic equation in verse. Several years later, Cardano happened to see unpublished work by Scipione del Ferro who independently came up with the same solution as Tartaglia. As the unpublished work was dated before Tartaglia's, Cardano decided his promise could be broken and included Tartaglia's solution in his next publication. Even though Cardano credited his discovery, Tartaglia was extremely upset and a famous public challenge match resulted between himself and Cardano's student, Ludovico Ferrari. Widespread stories that Tartaglia devoted the rest of his life to ruining Cardano, however, appear to be completely fabricated. Mathematical historians now credit both Cardano and Tartaglia with the formula to solve cubic equations, referring to it as the "Cardano–Tartaglia formula".
