# Evangelista Torricelli

Evangelista Torricelli

Evangelista Torricelli portrayed on
the frontpage of Lezioni d'Evangelista Torricelli
Born 15 October 1608
Faenza, Province of Ravenna,
Papal States
Died 25 October 1647 (aged 39)
Florence, Grand Duchy of Tuscany
Citizenship Papal States
Fields Physicist,
mathematician
Notable students Vincenzo Viviani
Known for Barometer
Torricelli's Law
Influences Galileo Galilei

Evangelista Torricelli (Italian: [evandʒeˈlista torriˈtʃɛlli] ) (1608–1647) was an Italian physicist and mathematician, best known for his invention of the barometer.

## Biography

### Early life

Torricelli was born on 15 October in 1608 in Faenza in the Province of Ravenna, then part of the Papal States, the firstborn child of Gaspare Torricelli and Caterina Angetti. His father was a textile worker and the family was very poor. Seeing his talents, his parents sent him to be educated under the care of his uncle, Jacobo, a Camaldolese monk, who first ensured that his nephew was given a sound basic education. He then entered young Torricelli into a Jesuit College in 1624, possibly the one in Faenza itself, to study mathematics and philosophy until 1626, by which time his father, Gaspare, had died. The uncle then sent Torricelli to Rome to study science under the Benedictine monk Benedetto Castelli, professor of mathematics at the Collegio della Sapienza (now known as the Sapienza University of Rome).[1]

### Career

Torricelli's statue in the Museo di Storia Naturale di Firenze

In 1632, shortly after the publication of Galileo's Dialogues of the New Science, Torricelli wrote to Galileo of reading it "with the delight [...] of one who, having already practiced all of geometry most diligently [...] and having studied Ptolemy and seen almost everything of Tycho Brahe, Kepler and Longomontanus, finally, forced by the many congruences, came to adhere to Copernicus, and was a Galileian in profession and sect". (The Vatican condemned Galileo in June 1633, and this was the only known occasion on which Torricelli openly declared himself to hold the Copernican view.)

Aside from several letters, little is known of Torricelli's activities in the years between 1632 and 1641, when Castelli sent Torricelli's monograph of the path of projectiles to Galileo, then a prisoner in his villa at Arcetri. Although Galileo promptly invited Torricelli to visit, he did not accept until just three months before Galileo's death. During his stay, however, he wrote out the Fifth Day of Galileo's Discourses. After Galileo's death on 8 January 1642, Grand Duke Ferdinando II de' Medici asked him to succeed Galileo as the grand-ducal mathematician and professor of mathematics at the University of Pisa. In this role he solved some of the great mathematical problems of the day, such as finding a cycloid's area and center of gravity. He also designed and built a number of telescopes and simple microscopes; several large lenses, engraved with his name, are still preserved in Florence. On 11th June, 1644, he famously wrote in a letter to Michelangelo Ricci:

Noi viviamo sommersi nel fondo d'un pelago d'aria. (We live submerged at the bottom of an ocean of air.)[2]

### Death

Torricelli died in Florence on 25 October 1647, a few days after having contracted typhoid fever, and was buried at the Basilica of San Lorenzo. The asteroid 7437 Torricelli was named in his honor. He left all his belongings to his adopted son Alexander.

## Torricelli's work in physics

The perusal of Galileo's Two New Sciences (1638) inspired him with many developments of the mechanical principles there set forth, which he embodied in a treatise De motu (printed amongst his Opera geometrica, 1644). Its communication by Castelli to Galileo in 1641, with a proposal that Torricelli should reside with him, led to Torricelli repairing to Florence, where he met Galileo, and acted as his amanuensis during the three remaining months of his life.

### Barometer

Torricelli's chief invention was the mercury barometer, which arose from solving a practical problem. Pump makers of the Grand Duke of Tuscany attempted to raise water to a height of 12 meters or more, but found that 10 meters was the limit with a suction pump (as recounted in Galileo's Dialogue). Torricelli employed mercury, fourteen times more dense than water. In 1643 he created a tube approximately one meter long, sealed at the top, filled it with mercury, and set it vertically into a basin of mercury. The column of mercury fell to about 76 cm, leaving a Torricellian vacuum above. As we now know, the column's height fluctuated with changing atmospheric pressure; this was the first barometer. The discovery of the principle of the barometer has perpetuated his fame ("Torricellian tube", "Torricellian vacuum"). The torr, a unit of pressure used in vacuum measurements, is named after him.

### Torricelli's Law

1959 Evangelista Torricelli commemorative stamp of the U.S.S.R.

Torricelli also discovered Torricelli's Law, regarding the speed of a fluid flowing out of an opening, which was later shown to be a particular case of Bernoulli's principle.

### Cause of wind

Torricelli gave the first scientific description of the cause of wind:

... winds are produced by differences of air temperature, and hence density, between two regions of the earth.[1]

## Torricelli's work in mathematics

Torricelli is also famous for the discovery of the Torricelli's trumpet (also - perhaps more often - known as Gabriel's Horn) whose surface area is infinite, but whose volume is finite. This was seen as an "incredible" paradox by many at the time, including Torricelli himself, and prompted a fierce controversy about the nature of infinity, also involving the philosopher Hobbes. It is supposed by some to have led to the idea of a "completed infinity". Torricelli tried several alternative proofs, attempting to prove that its surface area was also finite - all of which failed.[citation needed]

Torricelli was also a pioneer in the area of infinite series. In his De dimensione parabolae of 1644, Torricelli considered a decreasing sequence of positive terms $a_0, a_1, a_2 \cdots$ and showed the corresponding telescoping series $(a_0-a_1) + (a_1-a_2) + \cdots$ necessarily converges to $a_0-L$, where L is the limit of the sequence, and in this way gives a proof of the formula for the sum of a geometric series.

## Italian submarines

Several Italian Navy submarines were named after Evangelista Torricelli:

## Selected works

His manuscripts are preserved at Florence, Italy. The following have appeared in print:

• Trattato del moto (before 1641)
• Opera geometrica (1644)
• Esperienza dell'argento vivo (Berlin, 1897).