Niccoló Tartaglia, (c. 1499-1557)

1554-1557 --- Engraving  --- Image by © CORBIS

Italian mathematician and “father of ballistic science.” He was nearly killed by French troops who lacerated his cheeks and jaw with deep saber cuts when they captured his home city of Brescia in 1512, during the Italian Wars (1494-1559). His reputation as a mathematician came with victory in a contest to solve cubic equations algebraically. He made a great impact on military affairs when he published a paper on the application of mathematics to artillery fire in which he outlined a scientific understanding of ballistics and published the first-ever firing tables. He is best remembered for “Tartaglia’s theorem,” which proved that the trajectory of a projectile is always a curved line, rather than the straight line-to-target that the naked eye perceived. He thereby proved that the maximum range of a cannonball at any speed is obtained by firing at an elevation of 458. Before that artillerists falsely believed that their cannonballs flew in a straight line after leaving the barrel, an error which often led gunners to fire short or position the guns dangerously close to the enemy. Tartaglia also invented the gunner’s quadrant by which a master gunner calculated and set the elevation of the barrel to meet the desired range according to a preset table divided into degrees, and indicated by a plumb line. Finally, he calculated maximum effective ranges for several known artillery types. For all that, he worried about the moral effects of applying science to the art of war, once destroying his manuscript on projectiles to prevent its application in war. However, when Italy was threatened by the Ottomans he set aside his scruples and published Nuova Scientia (1537), which was followed by other works on military science in the 1540s.


Curve balistiche di Tartaglia in una edizione del 1600.

Uttenhofer.Circinus Geometricus.1626.gunners quadrant

gunner’s quadrant

A right-angled instrument held in the mouth of a gun as it was raised, until a plumb line showed the correct muzzle elevation for the estimated range to target. It may have been invented by Niccolo` Tartaglia.


A major battle was not arguably decided by guns until Cerignola in 1503. And it was not until Marignano in 1515 that Swiss squares, dominant for 200 years, were decisively broken by pistol wielding cavalry and still more, by point-blank cannonades into their ranks. It was at Marignano that gunpowder weapon superiority was finally proven, and even then it was a close-run thing with guts as much as guns deciding the issue. After Marignano older weapons systems survived on the battlefield for many decades. This is best explained by cultural rather than technological factors: the old ways were still favored by the conservative warrior nobility whose exceptional status on and off the field of battle was threatened by the leveling power of musketry.


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