The Italian mathematician and physicist Evangelista Torricelli (1608-1647) invented the mercury barometer and made important contributions to calculus and the theories of hydraulics and dynamics.

# Evangelista Torricelli

Evangelista Torricelli was born in Faenza on Oct. 15, 1608. Left fatherless early in life, he was educated by his uncle, who was in monastic orders. In 1627 his uncle sent him to Rome to study mathematics and natural philosophy under Benedetto Castelli, professor of mathematics at the Collegio di Sapienza, who had been one of Galileo's pupils.

Torricelli spent the next 10 years in study. He corresponded with Galileo and studied his writings. He was especially impressed by the *Dialogues concerning Two New Sciences* (1638) and at once generalized Galileo's analysis of projectile motion. His conclusions on this and other subjects were set down in his book *De motu gravium* (1640; published 1644). Galileo invited Torricelli to Florence in 1641, and he became the amanuensis and companion of the great scientist until Galileo died 3 months later. Soon after, Torricelli succeeded him as grand-ducal mathematician and professor of mathematics at the Florentine Academy.

## Scientific Work

Torricelli experimented with telescopes and simple microscopes, grinding his own lenses, and by carefully controlling their curvature, he produced telescopes superior to most of those of his contemporaries. His most important practical invention was the mercury barometer, first described in a letter to Michelangelo Ricci dated June 11, 1644. Torricelli had repeated Galileo's experiments with the thermoscope and was led to his discovery when he substituted mercury for water in the tube. He found also that water could be used as the liquid in the barometer if the containing vessel was sufficiently long ("18 cubits, " that is, approximately 33 feet), and he realized that the column of liquid was held up by the pressure of the atmosphere.

In the course of his experiments, Torricelli observed that the quantities of water discharged from a hole in the bottom of a tank in equal increments of time were propor-tional, from the last increment to the first, to successive odd numbers. This observation is said to have reminded him of Galileo's law of the velocity of a falling body, and it suggested to him that he should treat the jet of water as a series of freely falling particles, each with a speed determined by the original height of the water surface in the tank— Torricelli's law of efflux.

## Mathematical Work

Torricelli saw the advantages of the method of indivisibles, which is used in mathematics to find lengths, areas, and volumes. He thought that the ancients might have used the method in the discovery of difficult theorems, the proofs of which were put in geometrical forms "to hide the secret of their method or to avoid giving jealous detractors an opportunity to object." In a book on the areas of parabolas, he gave 21 propositions on areas, 10 by the methods of the ancients and 11 by the geometry of indivisibles.

Torricelli used the methods of so many other mathematicians that he was frequently involved in disputes over priority. Especially bitter was his controversy with G. P. Roberval, which flared up after Torricelli had published in 1644 a tract on the properties of the cycloid. Roberval accused him of plagiarizing his earlier solution of the problem of its quadrature. The controversy was still alive when Torricelli died in Florence on Oct. 25, 1647.

## Further Reading on Evangelista Torricelli

Most of the biographical writings on Torricelli are in Italian. On the history of the barometer see William E. Knowles Middleton, *The History of the Barometer* (1964). For background see Abraham Wolf, *A History of Science, Technology and Philosophy in the 16th and 17th Centuries* (1935; rev. ed. 1950).