Evangelista Torricelli
Galileo's last student — invented the barometer, discovered atmospheric pressure, and wrote the first projectile tables.
Biography
Evangelista Torricelli was born in Faenza in 1608 and orphaned young. A Jesuit uncle arranged for him to study mathematics under Benedetto Castelli, one of Galileo's former pupils, and by the late 1630s Torricelli was working through Galileo's Two New Sciences and writing mathematical commentaries that eventually reached Galileo himself. In October 1641 he moved to Arcetri to serve as Galileo's assistant, secretary, and amanuensis during the old man's final, blind months. Galileo died three months later, and Torricelli was appointed to succeed him as court mathematician to the Grand Duke of Tuscany.
His most famous experiment came in 1643. Using a glass tube sealed at one end and filled with mercury, Torricelli inverted it into a dish and showed that the mercury column settled to roughly 76 centimetres above the reservoir. Above the column, in the closed top of the tube, was a region of empty space — the first sustained vacuum produced deliberately in the laboratory. The column's height measured the weight of the atmosphere pressing down on the open dish. He had invented the barometer and demonstrated atmospheric pressure in one stroke. The unit of pressure one millimetre of mercury is still called a torr in his honour.
His Opera Geometrica (1644) ran to several hundred pages of geometry, mechanics, and fluid statics. Two results stand out. First, Torricelli's law on fluid efflux: a liquid draining from a small hole in a tank leaves with the same speed it would have acquired by falling freely from the liquid's surface, v = √(2gh). Second, his systematic study of projectile trajectories: extending Galileo's parabolic theory, he compiled the first serious tables of ranges for different launch speeds and angles, and proved that the family of all parabolic trajectories at a given speed is bounded above by another parabola — the 'safety parabola' or enveloping curve, outside which no shot can reach no matter how you aim. It was the first enveloping curve in the history of mathematics.
Torricelli also contributed to the early calculus of indivisibles, deriving the volume of the hyperbolic solid now called Gabriel's horn — a surface of revolution with finite volume but infinite surface area, the first rigorous paradox of infinity in integration. He died abruptly of typhoid fever in October 1647, aged thirty-nine. His collected papers were published posthumously and remained an important reference for Pascal, Huygens, and Newton.
Contributions
- 01invented the mercury barometer and demonstrated atmospheric pressure (1643)
- 02produced the first sustained laboratory vacuum (the 'Torricellian vacuum')
- 03formulated Torricelli's law: v = √(2gh) for fluid efflux from a tank
- 04compiled the first systematic projectile range tables (Opera Geometrica, 1644)
- 05discovered the safety parabola — the enveloping curve of projectile trajectories
- 06early work on the method of indivisibles and the volume of Gabriel's horn
Major works
A three-part treatise covering conic sections, the motion of projectiles, and the geometry of solids. Extended Galileo's parabolic theory of trajectories, introduced the safety parabola, and presented Torricelli's law on the efflux of liquids.
The earliest of Torricelli's major works on mechanics, completed before he joined Galileo in Arcetri. Works through the kinematics of falling bodies and lays the foundations for the later projectile-range analysis.
Posthumous collection of academic lectures covering wind, sound, the vacuum, and the nature of pressure. Contains the clearest contemporary exposition of the barometric experiment.