Evangelista Torricelli

Italian physicist and mathematician

• Born: October 15, 1608
• Birthplace: Faenza, Romagna, Papal States (now in Italy)
• Died: October 25, 1647
• Place of death: Florence, Tuscany (now in Italy)

In an attempt to solve the problem of raising water over ten meters, Torricelli decided to employ mercury, which is fourteen times as heavy as water. He succeeded, thus inventing the barometer.

Primary fields: Mathematics; physics

Primary invention: Barometer

Early Life

The eldest of three children, Evangelista Torricelli (eh-vahn-jeh-LEE-stah tohr-ih-CHEH-lee) was born to Gaspare Torricelli and Caterina Angetti in 1608 in Faenza, at the time part of the Papal States. Having been left fatherless at an early age, Torricelli was educated first by his paternal uncle Jacopo, a religious of the Order of the Camaldolesi, and in 1624 he entered the Jesuit College at Faenza, where he studied mathematics and philosophy until 1626. The following year, Torricelli transferred to the University of Rome to study under the Benedictine Benedetto Castelli, an illustrious water engineer and professor of mathematics, who had also been a student of Galileo at Pisa. Among Torricelli’s peers at Rome were other future well-known physicists and mathematicians such as Alfonso Borelli, Bonaventura Cavalieri, and Michelangelo Ricci. After completing his studies, Torricelli became Castelli’s secretary and held this post between 1626 and 1632.

Little is known of Torricelli’s activities in the period 1632 to 1641. During these years, he appears to have been secretary to Monsignor Giovanni Ciampolli, a friend of Galileo, who served as governor of a number of cities in Umbria and the Marches. Torricelli also stood in for Castelli at Rome and lectured at the university during the academic year 1640-1641. Part of the correspondence dating to Torricelli’s early life has been preserved, most notably a letter of September 11, 1632, to Galileo in which he described having read the latter’s Dialogo sopra i due massimi sistemi del mondo (1632; Dialogue Concerning the Two Chief Systems of the World, 1661) with delight. In his letter, Torricelli acknowledged being a follower of Galileo “in profession and sect.” Yet, after Galileo’s trial in 1633, Torricelli decided to shift his attention from astronomy to mathematics, an area that seemed less controversial than the Copernican theory defended by Galileo.

Life’s Work

In April, 1641, Torricelli’s treatise on the path of projectiles (De motu gravium naturaliter descendentium et proiectorum) was presented to Galileo by Castelli. Galileo, then a man of seventy-eight, was so impressed with Torricelli’s work that he invited him to his house at Arcetri, near Florence. Wishing to care for his ailing mother, Torricelli accepted the invitation but was forced to delay his departure. He finally arrived at Galileo’s villa on October 10, but, after Galileo’s death only three months later (January 8, 1642), he was asked to succeed the great scientist as Grand Duke Ferdinando II de’ Medici’s mathematician and philosopher. Torricelli remained in Florence for the rest of his life, living in the ducal palace and lecturing as professor of mathematics at the local university. He was elected to the Accademia della Crusca in Florence in 1642.

Under the auspices of the grand duke, Torricelli’s Opera geometrica (works on geometry) was published in three parts in October, 1644. As with many scientific works published at the time, it was written in Latin because this language still expressed ideas and reported events with a precision that the vernacular lacked. Torricelli’s volume included his monograph on the parabolic motion of projectiles of 1631, a commentary on Archimedes, and a series of treatises on the parabola, the cycloid, and other dimensional figures. The texts received much acclaim throughout Europe and were praised for the clarity and precision with which the author discussed rather difficult concepts. Moreover, in his work, Torricelli rendered Bonaventura Cavalieri’s theory of indivisibles accessible and expanded the latter’s method of indivisibles to cover curved indivisibles. With these tools, he was able to show that rotating the unlimited area of a rectangular hyperbola between the y-axis and a fixed point on the curve resulted in a finite volume when rotated around the y-axis.

In his Opera geometrica, Torricelli also paid attention to hydraulics, showing that, aside from his theoretical work, he had practical skills too. As an example, Torricelli advised the grand duke on marsh drainage on the Chiana Valley in Tuscany. In fact, attempting to solve a practical problem with which Ferdinand’s pumpmakers had been posed, he realized that, if water could be pumped upward, this was because it was exerted by the surrounding air. Instead of water, he decided to use mercury, and he created a tube filled with quicksilver and inverted over the same liquid. This led to the development of a device that he described to his friend Michelangelo Ricci in a letter of June 11, 1644. Known first as “Torricelli’s tube,” it was named “barometer” by the Frenchman Edme Mariotte in his Discours de la nature de l’air (discourse on the nature of air) of 1676. Torricelli’s practical skills were also applied to ballistics and optics. He studied projectile motion, built several large lenses, and devised telescopes and simple microscopes, making substantial financial gains from his skill in lens grinding in the last period of his life. In 1644, the grand duke gave him a golden chain bearing the words virtutis praemia (rewards for your talent) in return for some of the scientific instruments Torricelli had designed.

In October, 1647, Torricelli contracted typhoid fever and died a few days later at the age of thirty-nine. He was buried in the church of San Lorenzo in Florence. In his will, he entrusted his unpublished manuscripts and letters to his friends Cavalieri and Ricci, who were to prepare the material for publication. However, Cavalieri died weeks after Torricelli, and Ricci failed to accomplish the task, resulting in the bulk of Torricelli’s texts being published as late as 1919. Some of the lectures given at the Accademia della Crusca had, however, already been published by Tommaso Bonaventura in 1715.

Impact

Torricelli’s contribution to physical and mathematical sciences is outstanding. Attempting to prove wrong the old saying that “nature abhors a vacuum,” to which Galileo himself had also adhered, Torricelli was the first person to create a sustained vacuum (the so-called Torricellian vacuum). He demonstrated that atmospheric pressure determines the height to which a fluid will rise in a tube inverted over the same liquid. With his experiment, he was able to discover the principle of a barometer. As proof of Torricelli’s lasting impact, his method of getting a very high vacuum is still often employed.

In the field of mathematics, Torricelli devised a problem due to the French mathematician Pierre de Fermat when he determined the point in the plane of a triangle so that the sum of its distances from the vertices is as small as possible. Torricelli’s correspondence to Roberval on the area and the center of gravity of the cycloid reveals his honesty and modesty. Torricelli’s achievements were extolled by many of his contemporaries, in particular by René Descartes and Constantijn Huygens. Blaise Pascal described Torricelli’s work on geometry as “surpassing the discoveries made by all ancient mathematicians.” The asteroid 7437 Torricelli and the torr, a unit of pressure, were named in Torricelli’s honor.

Bibliography

Clanet, Christophe. “Clepsydrae, from Galilei to Torricelli,” Physics of Fluids 12 (2000): 2743-2751. Deals with the free fall of a solid particle, carefully studied by Galileo, and the free fall of a fluid particle along a stream line, introduced by Torricelli.

Martini, Horst, Konrad Jörg Swanepoel, and Günter Weiss. “The Fermat-Torricelli Problem in Normed Planes and Spaces.” Journal of Optimization Theory and Applications 115, no. 2 (2002): 283-314. The authors study the Fermat-Torricelli locus in a geometric way.

Middleton, William Eugene Knowles. The History of the Barometer. Baltimore: The Johns Hopkins University Press, 1964. The volume devotes several chapters to Torricelli’s main invention. It is also an extremely thorough examination of precedents attempting to devise the barometer. Bibliography and illustrations.

Pascal, Blaise. The Physical Treatises of Pascal. Translated by I. H. B. Spiers and A. G. H. Spiers, with introduction and notes by Frederick Barry. New York: Columbia University Press, 1937. Of interest since it includes English translations of excerpts from Torricelli’s works.

Smith, Frederick, and John Jervis. Evangelista Torricelli (Written on the Occasion of the Tercentenary Commemoration of the Italian Philosopher). New York: Oxford University Press, 1908. A short paper that successfully puts Torricelli’s mathematical work on hydraulics and physics into context.

Teed, Frank Litherland. Torricelli “Contra mundum.” London: H. K. Lewis, 1931. Attempts to elaborate the teaching of Torricelli. Examines some of the scientific controversies in which Torricelli was engaged toward the end of his life, particularly with Roberval.