Evangelista Torricelli

Early life Torricelli was born on 15 October 1608 in Rome, the firstborn child of Gaspare Ruberti and Giacoma Torricelli. His family was from Faenza (in the current 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 (James), 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). Castelli was a student of Galileo Galilei. "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, with whom he became great friends. Career In 1632, shortly after the publication of Galileo's Dialogue Concerning the Two Chief World Systems, 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 under house arrest 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. "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." 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." == Torricelli's work in physics ==

The perusal of Galileo's Two New Sciences (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, 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 (from the Greek word baros, meaning weight) -- the principle of which was described as early as 1631 by René Descartes, 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 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." 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. 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 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, the first barometer, an instrument that would later play a key role in weather forecasting, and the first pressure altimeter, 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, a unit of pressure 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. 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{dy}{dt} = -k \sqrt{y} 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 Christiaan 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: 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: == 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. 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 (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 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 • of the U.S.S.R.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 ==