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Evangelista Torricelli ( , also , ; 15 October 160825 October 1647) was an
Italian Italian(s) may refer to: * Anything of, from, or related to the people of Italy over the centuries ** Italians, an ethnic group or simply a citizen of the Italian Republic or Italian Kingdom ** Italian language, a Romance language *** Regional Ita ...
physicist and mathematician, and a student of Galileo. He is best known for his invention of the
barometer A barometer is a scientific instrument that is used to measure air pressure in a certain environment. Pressure tendency can forecast short term changes in the weather. Many measurements of air pressure are used within surface weather analysis ...
, but is also known for his advances in
optics 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, ultrav ...
and work on the
method of indivisibles In geometry, Cavalieri's principle, a modern implementation of the method of indivisibles, named after Bonaventura Cavalieri, is as follows: * 2-dimensional case: Suppose two regions in a plane are included between two parallel lines in that p ...
. The
Torr The torr (symbol: Torr) is a unit of pressure based on an absolute scale, defined as exactly of a standard atmosphere (). Thus one torr is exactly (≈ ). Historically, one torr was intended to be the same as one " millimeter of merc ...
is also named after him.


Biography


Early life

Torricelli was born on 15 October 1608 in
Rome , established_title = Founded , established_date = 753 BC , founder = King Romulus (legendary) , image_map = Map of comune of Rome (metropolitan city of Capital Rome, region Lazio, Italy).svg , map_caption ...
, the firstborn child of Gaspare Torricelli and Caterina Angetti. His family was from Faenza in the
Province of Ravenna The province of Ravenna ( it, provincia di Ravenna; ) is a Provinces of Italy, 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 , giving it ...
, 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 (James), a Camaldolese
monk A monk (, from el, μοναχός, ''monachos'', "single, solitary" via Latin ) is a person who practices religious asceticism by monastic living, either alone or with any number of other monks. A monk may be a person who decides to dedica ...
, 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 , established_title = Founded , established_date = 753 BC , founder = King Romulus (legendary) , image_map = Map of comune of Rome (metropolitan city of Capital Rome, region Lazio, Italy).svg , map_caption ...
to study science under the
Benedictine , image = Medalla San Benito.PNG , caption = Design on the obverse side of the Saint Benedict Medal , abbreviation = OSB , formation = , motto = (English: 'Pray and Work') , foun ...
monk
Benedetto Castelli Benedetto Castelli (1578 – 9 April 1643), born Antonio Castelli, was an Italian mathematician. Benedetto was his name in religion on entering the Benedictine Order in 1595. Life Born in Brescia, Castelli studied at the University of Padua and ...
, professor of mathematics at the Collegio della Sapienza (now known as the
Sapienza University of Rome The Sapienza University of Rome ( it, Sapienza – Università di Roma), also called simply Sapienza or the University of Rome, and formally the Università degli Studi di Roma "La Sapienza", is a public research university located in Rome, Ita ...
). Castelli was a student of
Galileo Galilei Galileo di Vincenzo Bonaiuti de' Galilei (15 February 1564 – 8 January 1642) was an Italian astronomer, physicist and engineer, sometimes described as a polymath. Commonly referred to as Galileo, his name was pronounced (, ). He wa ...
. "Benedetto Castelli made experiments on running water (1628), and he was entrusted by Pope Urban VIII with hydraulic undertakings." 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 in a private arrangement. 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 Bonaventura Francesco Cavalieri ( la, Bonaventura Cavalerius; 1598 – 30 November 1647) was an Italian mathematician and a Jesuate. He is known for his work on the problems of optics and motion, work on indivisibles, the precursors of in ...
, with whom he became great friends. It was in Rome that Torricelli also became friends with two other students of Castelli,
Raffaello Magiotti Raffaello Magiotti (1597–1656) was an Italian astronomer, mathematician and physicist. Born at Montevarchi, he studied at Florence, and, having taken his vows, moved to Rome, following Cardinal Sacchetti. In 1636, he began to work at the Vatic ...
and Antonio Nardi. Galileo referred to Torricelli, Magiotti, and Nardi affectionately as his "triumvirate" in Rome.


Career

In 1632, shortly after the publication of Galileo's ''
Dialogue Concerning the Two Chief World Systems The ''Dialogue Concerning the Two Chief World Systems'' (''Dialogo sopra i due massimi sistemi del mondo'') is a 1632 Italian-language book by Galileo Galilei comparing the Copernican system with the traditional Ptolemaic system. It was tran ...
'', 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 Claudius Ptolemy (; grc-gre, Πτολεμαῖος, ; la, Claudius Ptolemaeus; AD) was a mathematician, astronomer, astrologer, geographer, and music theorist, who wrote about a dozen scientific treatises, three of which were of importance ...
and seen almost everything of
Tycho Brahe Tycho Brahe ( ; born Tyge Ottesen Brahe; generally called Tycho (14 December 154624 October 1601) was a Danish astronomer, known for his comprehensive astronomical observations, generally considered to be the most accurate of his time. He was ...
, Kepler and Longomontanus, finally, forced by the many congruences, came to adhere to
Copernicus Nicolaus Copernicus (; pl, Mikołaj Kopernik; gml, Niklas Koppernigk, german: Nikolaus Kopernikus; 19 February 1473 – 24 May 1543) was a Renaissance polymath, active as a mathematician, astronomer, and Catholic canon, who formulated ...
, 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, Torricelli did not accept until just three months before Galileo's death. The reason for this was that Torricelli's mother, Caterina Angetti died. "(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." After Galileo's death on 8 January 1642, Grand Duke
Ferdinando II de' Medici Ferdinando II de' Medici (14 July 1610 – 23 May 1670) was grand duke of Tuscany from 1621 to 1670. He was the eldest son of Cosimo II de' Medici and Maria Maddalena of Austria. He was remembered by his contemporaries as a man of culture a ...
asked Torricelli to succeed Galileo as the grand-ducal mathematician and chair of mathematics at the
University of Pisa The University of Pisa ( it, Università di Pisa, UniPi), officially founded in 1343, is one of the oldest universities in Europe. History The Origins The University of Pisa was officially founded in 1343, although various scholars place ...
. Right before the appointment, Torricelli was considering returning to Rome because of there being nothing left for him in Florence, where he had invented the
barometer A barometer is a scientific instrument that is used to measure air pressure in a certain environment. Pressure tendency can forecast short term changes in the weather. Many measurements of air pressure are used within surface weather analysis ...
. In this new role he solved some of the great mathematical problems of the day, such as finding a
cycloid In geometry, a cycloid is the curve traced by a point on a circle as it rolls along a straight line without slipping. A cycloid is a specific form of trochoid and is an example of a roulette, a curve generated by a curve rolling on another cu ...
'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. 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. "He was interested in
Optics 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, ultrav ...
, and invented a method whereby microscopic lenses might be made of glass which could be easily melted in a lamp." 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 Florence ( ; it, Firenze ) is a city in Central Italy and the capital city of the Tuscany Regions of Italy, region. It is the most populated city in Tuscany, with 383,083 inhabitants in 2016, and over 1,520,000 in its metropolitan area.Bilan ...
. On 11 June 1644, he famously wrote in a letter to
Michelangelo Ricci Michelangelo Ricci (1619–1682) was an Italian mathematician and a Cardinal of the Roman Catholic Church. Biography Michelangelo Ricci was born on 30 January 1619 in Rome, then capital of the Papal States, to a family of low social standing th ...
: 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 it appears that Torricelli reached his solution independently, the matter was still in dispute up to his death.


Death

Torricelli died of fever, most likely
typhoid Typhoid fever, also known as typhoid, is a disease caused by ''Salmonella'' serotype Typhi bacteria. Symptoms vary from mild to severe, and usually begin six to 30 days after exposure. Often there is a gradual onset of a high fever over several d ...
, in Florence on 25 October 1647, 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." 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."


Honours

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. The asteroid 7437 Torricelli and a crater on the Moon were named in his honour. In 1830, botanist
Augustin Pyramus de Candolle Augustin Pyramus (or Pyrame) de Candolle (, , ; 4 February 17789 September 1841) was a Swiss botanist. René Louiche Desfontaines launched de Candolle's botanical career by recommending him at a herbarium. Within a couple of years de Candoll ...
published '' Torricellia'', which is a genus of
flowering plant Flowering plants are plants that bear flowers and fruits, and form the clade Angiospermae (), commonly called angiosperms. The term "angiosperm" is derived from the Greek words ('container, vessel') and ('seed'), and refers to those plants th ...
s from Asia belonging to the family
Torricelliaceae The Torricelliaceae are a family of trees native to Madagascar and southwest Asia. It contains three genera, ''Aralidium'', ''Melanophylla'' and ''Torricellia''. Under the APG II system, each of these genera was placed in its own family, but with ...
. They were named in Evangelista Torricelli's honour.


Torricelli's work in physics

The perusal of Galileo's ''
Two New Sciences The ''Discourses and Mathematical Demonstrations Relating to Two New Sciences'' ( it, Discorsi e dimostrazioni matematiche intorno a due nuove scienze ) published in 1638 was Galileo Galilei's final book and a scientific testament covering muc ...
'' (1638) inspired Torricelli 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 Florence ( ; it, Firenze ) is a city in Central Italy and the capital city of the Tuscany Regions of Italy, region. It is the most populated city in Tuscany, with 383,083 inhabitants in 2016, and over 1,520,000 in its metropolitan area.Bilan ...
, where he met Galileo, and acted as his amanuensis during the three remaining months of his life.


Suction pumps and the invention of the barometer

Torricelli's work led to first speculations about atmospheric pressure, and to the corollary invention of the
mercury barometer A barometer is a scientific instrument that is used to measure air pressure in a certain environment. Pressure tendency can forecast short term changes in the weather. Many measurements of air pressure are used within surface weather analysis ...
(from the Greek word baros, meaning weight) -- the principle of which was described as early as 1631 by
René Descartes René Descartes ( or ; ; Latinized: Renatus Cartesius; 31 March 1596 – 11 February 1650) was a French philosopher, scientist, and mathematician, widely considered a seminal figure in the emergence of modern philosophy and science. Ma ...
, although there is no evidence that Descartes ever built such an instrument. The barometer arose from the need to solve a theoretical and practical problem: a
suction pump A vacuum pump is a device that draws gas molecules from a sealed volume in order to leave behind a partial vacuum. The job of a vacuum pump is to generate a relative vacuum within a capacity. The first vacuum pump was invented in 1650 by Otto v ...
could only raise water up to a height of 10 metres (34 ft) (as recounted in Galileo's ''Two New Sciences''). In the early 1600s, Torricelli's teacher, Galileo, argued that suction pumps were able to draw water from a well because of the "force of vacuum." This argument, however, failed to explain the fact that suction pumps could only raise water to a height of 10 metres. After Galileo's death, Torricelli proposed, rather, that we live in a "sea of air" that exerts a pressure analogous in many ways to the pressure of water on submerged objects. According to this hypothesis, at sea level, the air in the atmosphere has weight that roughly equals the weight of a 10-meter column of water. When a suction pump creates a vacuum inside a tube, the atmosphere no longer pushes on the water column below the piston but still pushes down on the surface of the water outside, thus causing the water to rise until its weight counterbalances the weight of the atmosphere. This hypothesis might have led him to a striking prediction: That a suction pump might only raise mercury, which is 13 times heavier than water, to 1/13 the height of the water column (76 centimeters) in a similar pump. (It is possible however that Torricelli carried out the mercury experiment first, and then formulated his sea of air hypothesis). In 1643, Torricelli filled a meter-long tube (with one end sealed off) with mercury—thirteen times denser than water—and set the open end of the tube into a basin of the liquid metal and raised the sealed end so the tube stood vertically. The mercury level in the tube fell until it was about above the surface of the mercury basin, producing a Torricellian vacuum above. This was also the first recorded incident of creating permanent vacuum. A second unambiguous prediction of Torricelli's sea of air hypothesis was made by Blaise Pascal, who argued, and proved, that the mercury column of the barometer should drop at higher elevations. Indeed, it dropped slightly on top of a 50-meter bell tower, and much more so at the peak of a 1460-meter mountain. As we know now, the column's height fluctuates with
atmospheric pressure Atmospheric pressure, also known as barometric pressure (after the barometer), is the pressure within the atmosphere of Earth. The standard atmosphere (symbol: atm) is a unit of pressure defined as , which is equivalent to 1013.25 millibars, ...
at the same location, a fact which plays a key role in weather forecasting. Baseline changes in the column's height at different elevations, in turn, underlie the principle of the altimeter. Thus, this work laid the foundations for the modern concept of
atmospheric pressure Atmospheric pressure, also known as barometric pressure (after the barometer), is the pressure within the atmosphere of Earth. The standard atmosphere (symbol: atm) is a unit of pressure defined as , which is equivalent to 1013.25 millibars, ...
, the first
barometer A barometer is a scientific instrument that is used to measure air pressure in a certain environment. Pressure tendency can forecast short term changes in the weather. Many measurements of air pressure are used within surface weather analysis ...
, an instrument that would later play a key role in weather forecasting, and the first pressure
altimeter An altimeter or an altitude meter is an instrument used to measure the altitude of an object above a fixed level. The measurement of altitude is called altimetry, which is related to the term bathymetry, the measurement of depth under water. The m ...
, which measures altitude and is often used in hiking, climbing, skiing, and aviation. The solution to the suction pump puzzle and the discovery of the principle of the barometer and altimeter have perpetuated Torricelli's fame with terms such as "Torricellian tube" and "Torricellian vacuum". The
torr The torr (symbol: Torr) is a unit of pressure based on an absolute scale, defined as exactly of a standard atmosphere (). Thus one torr is exactly (≈ ). Historically, one torr was intended to be the same as one " millimeter of merc ...
, a unit of
pressure Pressure (symbol: ''p'' or ''P'') is the force applied perpendicular to the surface of an object per unit area over which that force is distributed. Gauge pressure (also spelled ''gage'' pressure)The preferred spelling varies by country and e ...
used in vacuum measurements, is named after him.


Torricelli's law

Torricelli also discovered a 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 In fluid dynamics, Bernoulli's principle states that an increase in the speed of a fluid occurs simultaneously with a decrease in static pressure or a decrease in the fluid's potential energy. The principle is named after the Swiss mathematici ...
. He 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 : \frac = -k \sqrt for some constant ''k'' > 0.


Torricelli's principle

The concept of center of gravity was discovered by Archimedes. Torricelli, following in his footsteps, discovered an important new principle, Torricelli’s principle, which says: if any number of bodies be so connected that, by their motion, their centre of gravity can neither ascend nor descend, then those bodies are in equilibrium. This is essentially a version of the principle of virtual work. This principle was later used by Christian Huygens to study pendulum motion.


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 An envelope is a common packaging item, usually made of thin, flat material. It is designed to contain a flat object, such as a letter or card. Traditional envelopes are made from sheets of paper cut to one of three shapes: a rhombus, a sh ...
: 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'' ( parabola of safety)."


Cause of wind

Torricelli gave the first scientific description of the cause of
wind Wind is the natural movement of air or other gases relative to a planet's surface. Winds occur on a range of scales, from thunderstorm flows lasting tens of minutes, to local breezes generated by heating of land surfaces and lasting a few ho ...
:


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 Gabriel's horn (also called Torricelli's trumpet) is a particular geometry, geometric figure that has infinite surface area but finite volume. The name refers to the Christian tradition where the archangel Gabriel blows the horn to announce Last ...
) whose surface area is
infinite Infinite may refer to: Mathematics * Infinite set, a set that is not a finite set *Infinity, an abstract concept describing something without any limit Music *Infinite (group), a South Korean boy band *''Infinite'' (EP), debut EP of American m ...
, 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. 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, \ldots and showed the corresponding
telescoping series In mathematics, a telescoping series is a series whose general term t_n can be written as t_n=a_n-a_, i.e. the difference of two consecutive terms of a sequence (a_n). As a consequence the partial sums only consists of two terms of (a_n) after c ...
(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. Torricelli developed further the
method of indivisibles In geometry, Cavalieri's principle, a modern implementation of the method of indivisibles, named after Bonaventura Cavalieri, is as follows: * 2-dimensional case: Suppose two regions in a plane are included between two parallel lines in that p ...
of Cavalieri. Many 17th century mathematicians learned of the method through Torricelli whose writing was more accessible than Cavalieri's.


Italian submarines

Several Italian Navy submarines were named after Evangelista Torricelli: * A ''Micca '' class submarine, built in 1918, stricken in 1930 * An ''Archimede'' class submarine (1934), transferred to Spain in 1937 and renamed ''General Mola'', stricken in 1959 * A ''Benedetto Brin'' class submarine (1937), sank in the Red Sea due to the British Navy in 1940 * ''Evangelista Torricelli'', the former USS ''Lizardfish'', transferred to Italy in 1960 and decommissioned in 1976


Selected works

His original manuscripts are preserved at Florence, Italy. The following have appeared in print: * ''Trattato del moto'' (before 1641) * ''Opera geometrica'' (1644) *
''Lezioni accademiche'' (Firenze, 1715)
* ''Esperienza dell'argento vivo'' (Berlin, 1897)


See also

*
Geometric median In geometry, the geometric median of a discrete set of sample points in a Euclidean space is the point minimizing the sum of distances to the sample points. This generalizes the median, which has the property of minimizing the sum of distances ...
*
Logarithmic spiral A logarithmic spiral, equiangular spiral, or growth spiral is a self-similar spiral curve that often appears in nature. The first to describe a logarithmic spiral was Albrecht Dürer (1525) who called it an "eternal line" ("ewige Linie"). More ...
* Torricellian chamber * Vena contracta *
Gasparo Berti Gasparo Berti ( 1600–1643) was an Italian mathematician, astronomer and physicist. He was probably born in Mantua and spent most of his life in Rome. He is most famous today for his experiment in which he unknowingly created the first working b ...
*
Stefano degli Angeli Stefano degli Angeli (Venice, September 23, 1623 – Padova, October 11, 1697) was an Italian mathematician, philosopher, and Jesuate. He was member of the Catholic Order of the Jesuats (Jesuati). In 1668 the order was suppressed by Pope Clemen ...


Notes


References

* * * * * * * * *


External links

* Evangelista Torricelli, Encyclopædia Britannic
Evangelista Torricelli , Italian physicist and mathematician
* Evangelista Torricelli, Treccani Enciclopedi
Torricèlli, Evangelista nell'Enciclopedia Treccani
*


The Galileo Correspondence Project at Stanford University

Scientist of the Day – Evangelista Torricelli
at
Linda Hall Library The Linda Hall Library is a privately endowed American library of science, engineering and technology located in Kansas City, Missouri, sitting "majestically on a urban arboretum." It is the "largest independently funded public library of scien ...
* * * * * {{DEFAULTSORT:Torricelli, Evangelista 1608 births 1647 deaths Italian Roman Catholics 17th-century Italian mathematicians Burials at San Lorenzo, Florence Deaths from typhoid fever 17th-century Italian inventors 17th-century Italian physicists People from Faenza Italian scientific instrument makers University of Pisa faculty