Evangelista Torricelli was an Italian scientist and mathematician who studied under Benedetto Castelli. He is most famous for inventing the barometer. He also made important contributions to the study of light and worked on a mathematical method called the method of indivisibles. A unit of pressure called the torr is named in his honor. Torricelli was born on October 15, 1608, and died on October 25, 1647.

Biography

Torricelli was born on October 15, 1608, in Rome. He was the first child of Gaspare Ruberti and Giacoma Torricelli. His family was from Faenza, which is now part of the Province of Ravenna in Italy. At that time, Faenza was part of the Papal States. His father worked with textiles, and the family was very poor. His parents noticed his talents and sent him to Faenza to be educated by his uncle, Giacomo, a Camaldolese monk. Giacomo first made sure Torricelli received a strong basic education. In 1624, Torricelli entered a Jesuit College, possibly in Faenza, to study mathematics and philosophy until 1626. By this time, his father, Gaspare, had died. His uncle then sent Torricelli to Rome to study science with Benedetto Castelli, a Benedictine monk and professor of mathematics at the Collegio della Sapienza, now known as Sapienza University of Rome. Castelli had studied under Galileo Galilei. Castelli conducted experiments on running water in 1628 and worked on water-related projects for Pope Urban VIII. There is no proof Torricelli was officially enrolled at the university, but it is likely he studied under Castelli. In exchange for his education, Torricelli worked as Castelli’s secretary from 1626 to 1632. This allowed him to participate in experiments funded by Pope Urban VIII. While in Rome, Torricelli also studied with Bonaventura Cavalieri, a mathematician, and became friends with Raffaello Magiotti and Antonio Nardi, who were also students of Castelli. Galileo called Torricelli, Magiotti, and Nardi his “triumvirate” in Rome.

In 1632, after Galileo published Dialogue Concerning the Two Chief World Systems, Torricelli wrote to Galileo, saying he had studied geometry, Ptolemy, Tycho Brahe, Kepler, and Longomontanus, and had come to support Copernicus’s ideas. This was the only known time Torricelli openly stated he believed in the Copernican view. The Vatican condemned Galileo in 1633. Between 1632 and 1641, little is known about Torricelli’s activities. In 1641, Castelli sent a paper on projectile motion to Galileo, who was under house arrest in Arcetri. Galileo invited Torricelli to visit, but Torricelli did not accept until three months before Galileo’s death. This delay was because Torricelli’s mother, Caterina Angetti, had died. After meeting Galileo, Torricelli completed a dialogue under Galileo’s guidance, which was published in 1674 by Viviani, another of Galileo’s students. After Galileo’s death on January 8, 1642, Grand Duke Ferdinando II de’ Medici asked Torricelli to replace Galileo as the grand-ducal mathematician and chair of mathematics at the University of Pisa. Before accepting, Torricelli considered returning to Rome, as he had no ties left in Florence, where he had invented the barometer. In this role, Torricelli solved important mathematical problems, such as calculating the area and center of gravity of a cycloid. He wrote a book called Opera Geometrica, published in 1644, describing his findings.

Before publishing Opera Geometrica, little was known about Torricelli’s work in geometry. After its publication, he gained recognition in the field. He was interested in optics and developed a method to create microscopic lenses from easily melted glass. He designed telescopes and microscopes, and some large lenses with his name engraved remain in Florence. On June 11, 1644, Torricelli wrote a letter to Michelangelo Ricci. His work on the cycloid led to a dispute with Gilles de Roberval, who accused him of copying Roberval’s earlier solution. While Torricelli likely solved the problem independently, the disagreement continued until his death.

Torricelli died of fever, likely typhoid, in Florence on October 25, 1647, 10 days before his 40th birthday. He was buried at the Basilica of San Lorenzo. He left all his belongings to his adopted son, Alessandro. Some of his early work, including pamphlets on spherical solids and contact, was collected by Viviani after Torricelli’s death. These works were influenced by the study of classical texts. Sixty-eight years after his death, his achievements were still admired, as shown by an anagram on the front of Lezioni accademiche d'Evangelista Torricelli published in 1715: “En virescit Galileus alter,” meaning “Here blossoms another Galileo.”

In Faenza, a statue of Torricelli was created in 1868 to honor his contributions to science. The asteroid 7437 Torricelli and a lunar crater are named after him. The Torricelli Mountains on New Guinea also carry his name. In 1830, botanist Augustin Pyramus de Candolle named a plant genus, Torricellia, after Torricelli. This genus belongs to the family Torricelliaceae and is found in Asia.

Torricelli's work in physics

The study of Galileo's Two New Sciences (1638) inspired Torricelli to develop ideas about mechanical principles described in the book. He wrote a treatise called De motu, which was published in Opera geometrica in 1644. In 1641, Castelli shared Torricelli's work with Galileo and suggested that Torricelli live with him. This led Torricelli to travel to Florence, where he met Galileo and helped him write during the last three months of Galileo's life.

Torricelli's research led to early ideas about atmospheric pressure and the invention of the mercury barometer. The word baros means "weight" in Greek. René Descartes described the barometer's principle as early as 1631, though there is no proof he built one.

The barometer was created to solve a problem: suction pumps could only lift water to a height of 10 meters (34 feet), as Galileo noted in Two New Sciences. Galileo believed suction pumps worked because of a "force of vacuum," but this did not explain why water could not rise higher.

After Galileo's death, Torricelli proposed that Earth is surrounded by a "sea of air" that exerts pressure, similar to how water pushes on submerged objects. He suggested that the air's weight at sea level equals the weight of a 10-meter column of water. When a suction pump creates a vacuum, the atmosphere pushes down on the water outside the pump, causing it to rise until its weight balances the air pressure. This idea led Torricelli to predict that mercury, which is 13 times heavier than water, could only be lifted to 76 centimeters (30 inches) by a suction pump.

In 1643, Torricelli filled a sealed tube with mercury and placed the open end in a basin of mercury. When the tube was raised vertically, the mercury level dropped to about 76 centimeters above the basin, creating a vacuum above the mercury. This was the first recorded permanent vacuum.

Blaise Pascal later tested Torricelli's idea by showing that the mercury column in a barometer drops at higher elevations. Experiments on a 50-meter bell tower and a 1460-meter mountain confirmed this.

Today, the height of the mercury column in a barometer changes with atmospheric pressure, which helps in weather forecasting. Differences in height at various elevations also led to the invention of the altimeter. Torricelli's work laid the foundation for understanding atmospheric pressure, the first barometer, and the first altimeter.

Torricelli's discovery of the barometer and altimeter earned him lasting recognition, such as the terms "Torricellian tube" and "Torricellian vacuum." The unit of pressure called the "torr" is named after him.

Torricelli also discovered a law about fluid speed, which is a specific example of Bernoulli's principle. He found that water flows out of a hole in a container at a rate related to the square root of the water's depth. If a container is a cylinder with a small leak at the bottom, the water's depth at time t is proportional to the square root of the depth y.

Archimedes discovered the concept of center of gravity. Torricelli expanded on this by creating Torricelli's principle, which states that if objects are connected in a way that their center of gravity cannot rise or fall, they are in balance. This principle was later used by Christiaan Huygens to study pendulum motion.

Torricelli studied how projectiles move through the air. His most important contribution was identifying the "envelope" of projectile paths: when objects are launched at the same speed in all directions, their paths form parabolas that touch a common shape called the "parabola of safety."

Torricelli provided the first scientific explanation for wind.

Torricelli's work in mathematics

Torricelli is also known for discovering a shape called Torricelli's trumpet, which is sometimes called Gabriel's Horn. This shape has an infinite surface area but a finite volume. This idea was considered surprising by many people, including Torricelli himself, and led to a strong debate about the concept of infinity, which also involved the philosopher Hobbes.

Torricelli was also an early researcher in the study of infinite series. In his work "De dimensione parabolae" from 1644, he examined a sequence of numbers that decrease in value, such as a₀, a₁, a₂, and so on. He showed that a specific type of series, written as (a₀ − a₁) + (a₁ − a₂) + ⋯, always adds up to a₀ − L, where L is the final value of the sequence. This helped prove the formula for the sum of a geometric series.

Torricelli improved upon a method called the "method of indivisibles," which was developed by Cavalieri. Many 17th-century mathematicians learned about this method through Torricelli's writings, which were easier to understand than Cavalieri's.

Italian submarines

Several Italian Navy submarines were named after Evangelista Torricelli:

• A Micca class submarine, built in 1918, taken out of service in 1930
• A 1959 commemorative stamp from the U.S.S.R. featuring Evangelista Torricelli and a title page from an 1823 copy of Lezioni accademiche
• An Archimede class submarine (1934), transferred to Spain in 1937 and renamed General Mola, taken out of service in 1959
• A Benedetto Brin class submarine (1937), sank in the Red Sea after being attacked by the British Navy in 1940
• Evangelista Torricelli, the former USS Lizardfish, transferred to Italy in 1960 and decommissioned in 1976

Selected works

His original writings are kept in Florence, Italy. The following works were published:

• Trattato del moto (before 1641)
• Opera geometrica (1644)
• Lezioni accademiche (Firenze, 1715)
• Esperienza dell'argento vivo (Berlin, 1897)