Evangelista Torricelli

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Evangelista Torricelli
Evangelista Torricelli by Lorenzo Lippi (circa 1647, Galleria Silvano Lodi & Due).jpg
Evangelista Torricelli by Lorenzo Lippi (circa 1647)
Born15 October 1608
Died25 October 1647 (aged 39)
Nationality Italian
Citizenship Papal States
Alma mater Sapienza University of Rome
Known for Barometer
Torricelli's law
Scientific career
Fields Physicist,
Academic advisors Benedetto Castelli
Notable students Vincenzo Viviani
Influences Galileo Galilei
Influenced Robert Boyle [1]

Evangelista Torricelli (Italian:  [evandʒeˈlista torriˈtʃɛlli] , Loudspeaker.svg listen  ; 15 October 1608 25 October 1647) was an Italian physicist and mathematician, best known for his invention of the barometer, but is also known for his advances in optics and work on the method of indivisibles.

A barometer is a scientific instrument used to measure air pressure. Pressure tendency can forecast short term changes in the weather. Many measurements of air pressure are used within surface weather analysis to help find surface troughs, high pressure systems and frontal boundaries.

Optics The branch of physics that studies light

Optics is the branch of physics that studies the behaviour and properties of light, including its interactions with matter and the construction of instruments that use or detect it. Optics usually describes the behaviour of visible, ultraviolet, and infrared light. Because light is an electromagnetic wave, other forms of electromagnetic radiation such as X-rays, microwaves, and radio waves exhibit similar properties.



Early life

Evangelista Torricelli was born on 15 October 1608 in Rome; he invented the barometer in Florence, Italy. The firstborn child of Gaspare Torricelli and Caterina Angetti. [2] His family was from Faenza in the Province of Ravenna, then part of the Papal States. His father was a textile worker and the family was very poor. Seeing his talents, his parents sent him to be educated in Faenza, under the care of his uncle, Giacomo (Jacob), 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). [3] [4] Castelli was a student of Galileo Galilei. [5] "Benedetto Castelli made experiments on running water (1628), and he was entrusted by Pope Urban VIII with hydraulic undertakings." [6] There is no actual evidence that Torricelli was enrolled at the university. It is almost certain that Torricelli was taught by Castelli. In exchange he worked for him as his secretary from 1626 to 1632 as a private arrangement. [7] Because of this, Torricelli was exposed to experiments funded by Pope Urban VIII. While living in Rome, Torricelli became also the student of the mathematician Bonaventura Cavalieri, with whom he became great friends. [5] It was in Rome that Torricelli also became friends with two other students of Castelli, Raffaello Magiotti and Antonio Nardi. Galileo referred to Torricelli, Magiotti, and Nardi affectionately as his "triumvirate" in Rome. [8]

Rome Capital city and comune in Italy

Rome is the capital city and a special comune of Italy. Rome also serves as the capital of the Lazio region. With 2,872,800 residents in 1,285 km2 (496.1 sq mi), it is also the country's most populated comune. It is the fourth-most populous city in the European Union by population within city limits. It is the centre of the Metropolitan City of Rome, which has a population of 4,355,725 residents, thus making it the most populous metropolitan city in Italy. Rome is located in the central-western portion of the Italian Peninsula, within Lazio (Latium), along the shores of the Tiber. The Vatican City is an independent country inside the city boundaries of Rome, the only existing example of a country within a city: for this reason Rome has been often defined as capital of two states.

Faenza Comune in Emilia-Romagna, Italy

Faenza is an Italian city and comune, in the province of Ravenna, Emilia-Romagna, situated 50 kilometres southeast of Bologna.

Province of Ravenna Province of Italy

The province of Ravenna is a province in the Emilia-Romagna region of Italy. Its capital is the city of Ravenna. As of 2015, it has a population of 391,997 inhabitants over an area of 1,859.44 square kilometres (717.93 sq mi), giving it a population density of 210.81 inhabitants per square kilometre. Its provincial president is Claudio Casadio.


Torricelli's statue in the Museo di Storia Naturale di Firenze Evangelista Torricelli - Museo di Storia Naturale di Firenze.JPG
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.)

Ptolemy Greco-Egyptian writer and astronomer of Alexandria

Claudius Ptolemy was a Greco-Roman mathematician, astronomer, geographer and astrologer. He lived in the city of Alexandria in the Roman province of Egypt, wrote in Koine Greek, and held Roman citizenship. The 14th-century astronomer Theodore Meliteniotes gave his birthplace as the prominent Greek city Ptolemais Hermiou in the Thebaid. This attestation is quite late, however, and, according to Gerald Toomer, the translator of his Almagest into English, there is no reason to suppose he ever lived anywhere other than Alexandria. He died there around AD 168.

Tycho Brahe Danish astronomer and alchemist

Tycho Brahe was a Danish nobleman, astronomer, and writer known for his accurate and comprehensive astronomical and planetary observations. He was born in the then Danish peninsula of Scania. Well known in his lifetime as an astronomer, astrologer and alchemist, he has been described as "the first competent mind in modern astronomy to feel ardently the passion for exact empirical facts." His observations were some five times more accurate than the best available observations at the time.

Johannes Kepler German mathematician, astronomer and astrologer

Johannes Kepler was a German astronomer, mathematician, and astrologer. He is a key figure in the 17th-century scientific revolution, best known for his laws of planetary motion, and his books Astronomia nova, Harmonices Mundi, and Epitome Astronomiae Copernicanae. These works also provided one of the foundations for Newton's theory of universal gravitation.

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. The reason for this was that Torricelli's mother, Caterina Angetti died. [5] "(T)his short intercourse with the great mathematician enabled Torricelli to finish the fifth dialogue under the personal direction of its author; it was published by Viviani, another pupil of Galileo, in 1674." [6] 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 chair of mathematics at the University of Pisa. Right before the appointment, Torricelli was considering returning to Rome because of there being nothing left for him in Florence. [5] 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. As a result of this study, he wrote the book the Opera Geometrica in which he described his observations. The book was published in 1644. [5]

A monograph is a specialist work of writing on a single subject or an aspect of a subject, often by a single author, and usually on a scholarly subject.

Arcetri human settlement in Italy

Arcetri is a location in Florence, Italy, positioned among the hills south of the city centre.

University of Pisa Italian public research university located in Pisa

The University of Pisa is an Italian public research university located in Pisa, Italy. It was founded in 1343 by an edict of Pope Clement VI. It is the 19th oldest extant university in the world and the 10th oldest in Italy. The university is ranked within the top 10 nationally and the top 400 in the world according to the ARWU and the QS. It houses the Orto botanico di Pisa, Europe's oldest academic botanical garden, which was founded in 1544.

Little was known about Torricelli in regard to his works in geometry when he accepted the honorable position, but after he published Opera Geometrica two years later, he became highly esteemed in that discipline. [9] "He was interested in Optics, and invented a method whereby microscopic lenses might be made of glass which could be easily melted in a lamp." [6] As a result, he designed and built a number of telescopes and simple microscopes; several large lenses, engraved with his name, are still preserved in Florence. On 11 June 1644, he famously wrote in a letter to Michelangelo Ricci:

Florence Comune in Tuscany, Italy

Florence is the capital city of the Italian region of Tuscany. It is the most populous city in Tuscany, with 383,084 inhabitants in 2013, and over 1,520,000 in its metropolitan area.

Michelangelo Ricci Mathematician and Roman Catholic Cardinal

Michelangelo Ricci (1619–1682) was an Italian mathematician and a Cardinal of the Roman Catholic Church.

Noi viviamo sommersi nel fondo d'un pelago d'aria. (We live submerged at the bottom of an ocean of air.) [10]

However his work on the cycloid involved him in a controversy with Gilles de Roberval, who accused him of plagiarizing his earlier solution of the problem of its quadrature. Although there seems no room for doubt that Torricelli's was arrived at independently, the matter was still in dispute up to his death. [11]


Evangelista Torricelli portrayed on
the frontpage of Lezioni d'Evangelista Torricelli Libr0367.jpg
Evangelista Torricelli portrayed on
the frontpage of Lezioni d'Evangelista Torricelli
NSRW Torricelli's experiment NSRW Torricelli's experiment.jpg
NSRW Torricelli's experiment
Torricelli lunar crater map Torricelli lunar crater map.jpg
Torricelli lunar crater map

Torricelli died of fever, most likely typhoid, [2] [12] in Florence on 25 October 1647, [13] 10 days after his 39th birthday, and was buried at the Basilica of San Lorenzo. He left all his belongings to his adopted son Alessandro. "Belonging to that first period are his pamphlets on Solidi spherali, Contatti and the major part of the propositions and sundry problems which were gathered together by Viviani after Torricelli's death. This early work owes much to the study of the classics." [5] Sixty-eight years after Torricelli had died, his genius still filled his contemporaries with admiration, as evidenced by the anagram below the frontispice 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 in gratitude for all that Torricelli had done in advancing science during his short lifetime. [6] The asteroid 7437 Torricelli and a crater on the Moon were named in his honor.

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 traveling to Florence, where he met Galileo, and acted as his amanuensis during the three remaining months of his life. [11]


Torricelli's chief invention was the mercury barometer. "This instrument is named from two Greek words, signifying two measures of weight, since by it a column of air is weighed against a column of mercury." [14] The barometer arose from the need to solve a practical problem. Pump makers of the Grand Duchy 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, thirteen 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. "12 years before Torricelli's observations, Descartes, the French philosopher, had made the same observation, although he does not appear to have turned it to any account." [14]

Torricelli's law

Torricelli also discovered a law, now known as 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. "Evangelista Torricelli found that water leaks out a small hole in the bottom of a container at a rate proportional to the square root of the depth of the water. So if the container is an upright cylinder with a small leak at the bottom and y is the depth of the water at time t, then

for some constant k > 0." [15]

The study of projectiles

Torricelli studied projectiles and how they traveled through the air. "Perhaps his most notable achievement in the field of projectiles was to establish for the first time the idea of an envelope: projectiles sent out at [...] the same speed in all directions trace out parabolas which are all tangent to a common paraboloid. This envelope became known as the parabola di sicurezza (safety parabola)." [5] [4]

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. [3]

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 and showed the corresponding telescoping series necessarily converges to , 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.

Torricelli developed further the method of indivisibles of Cavalieri. Many 17th century mathematicians learned of the method through Torricelli whose writing was more accessible than Cavalieri's. [16]

Italian submarines

Torricelli (S-512);0837310 Torricelli (S-512);0837310.jpg
Torricelli (S-512);0837310
1959 Evangelista Torricelli commemorative stamp of the U.S.S.R. 1959 CPA 2279.jpg
1959 Evangelista Torricelli commemorative stamp of the U.S.S.R.

Several Italian Navy submarines were named after Evangelista Torricelli:

Selected works

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

See also


  1. Marie Boas, Robert Boyle and Seventeenth-century Chemistry, CUP Archive, 1958, p. 43.
  2. 1 2 Frank N. Magill (13 September 2013). The 17th and 18th Centuries: Dictionary of World Biography. Taylor & Francis. pp. 3060–. ISBN   978-1-135-92421-8.
  3. 1 2 O'Connor, John J.; Robertson, Edmund F., "Evangelista Torricelli", MacTutor History of Mathematics archive , University of St Andrews .
  4. 1 2 Chisholm 1911.
  5. 1 2 3 4 5 6 7 Robinson, Philip (March 1994). "Evangelista Torricelli". The Mathematical Gazette. 78 (481): 37. doi:10.2307/3619429. JSTOR   3619429.
  6. 1 2 3 4 Jervis-Smith, Frederick John (1908). Evangelista Torricelli. Oxford University Press. p. 9. ISBN   9781286262184.
  7. "Evangelista Torricelli". Turnbull world wide web server. J J O'Conno and E F Robertson. Retrieved 2016-08-05.
  8. Favaro, Antonio, ed. (1890–1909). Opere di Galileo Galilei. Edizione Nazionale. Vol. XVIII (in Italian). Florence: Barbera. p. 359.
  9. Mancosu, Paolo; Ezio, Vailati (March 1991). "Torricelli's Infinitely Long Solid and Its Philosophical Reception in the Seventeenth Century". Isis. 82 (1): 50–70. doi:10.1086/355637. JSTOR   233514.
  10. Walker, Gabrielle (2010). An Ocean of Air: A Natural History of the Atmosphere. London: Bloomsbury. ISBN   9781408807132.
  11. 1 2 Wikisource-logo.svg One or more of the preceding sentences incorporates text from a publication now in the public domain : Chisholm, Hugh, ed. (1911). "Torricelli, Evangelista"  . Encyclopædia Britannica . 27 (11th ed.). Cambridge University Press. pp. 61–62.
  12. Annelies Wilder-Smith; Marc Shaw; Eli Schwartz (7 June 2007). Travel Medicine: Tales Behind the Science. Routledge. p. 71. ISBN   978-1-136-35216-4.
  13. Timbs, John (1868). Wonderful Inventions: From the Mariner's Compass to the Electric Telegraph Cable. London: George Routledge and Sons. p. 41. ISBN   978-1172827800. Torricelli died in 1647, ...
  14. 1 2 Timbs, John (1868). Wonderful Inventions: From the Mariner's Compass to the Electric Telegraph Cable. London: George Routledge and Sons. p. 41. ISBN   978-1172827800 . Retrieved 2 June 2014.
  15. Driver, R. (May 1998). "Torricelli's Law: An Ideal Example of an Elementary ODE". The American Mathematical Monthly. 105 (5): 454. doi:10.2307/3109809. JSTOR   3109809.
  16. Amir Alexander (2014). Infinitesimal: How a Dangerous Mathematical Theory Shaped the Modern World. Scientific American / Farrar, Straus and Giroux. ISBN   978-0374176815.

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