## Leonhard Euler

## Evangelista Torricelli

Elif Demir

was a Camaldolese monk. Torricelli entered a Jesuit College in 1624 and studied mathematics and philosophy there until 1626. At the Jesuit College, Torricelli showed that he had outstanding talents and his uncle, Brother Jacopo, arranged for him to study with Benedetto Castelli. As well as being taught mathematics, mechanics, hydraulics, and astronomy by Castelli, Torricelli became his secretary and held this post from 1626 to 1632. Much later he took over Castelli's teaching when he was absent from Rome. Torricelli was an ambitious young man, and he greatly admired Galileo, so he took the opportunity to inform Galileo of his own mathematical work. Torricelli began by telling Galileo that he was a professional mathematician and that he had studied the classical texts of Apollonius, Archimedes, and Theodosius. He had also read almost everything that the contemporary mathematicians Brahe, Kepler, and Longomontanus had written and, he told Galileo, he was convinced by the theory of Copernicus that the Earth revolved around the sun.

By 1641, Torricelli had completed much of the work which he was to publish in three parts as Opera geometrica in 1644. This basically carried on developing Galileo's study of the parabolic motion of projectiles which had appeared in Discourses and mathematical demonstrations concerning the two new sciences published in 1638.

In looking at Torricelli's achievements we should first put his mathematical work into context. In De motu gravium Ⓣ which was published as part of Torricelli's 1644 Opera geometrica Ⓣ, Torricelli also proved that the flow of liquid through an opening is proportional to the square root of the height of the liquid, a result now known as Torricelli's theorem. It was another remarkable contribution that has led to some suggesting that this result makes him the founder of hydrodynamics. Also, in De motu gravium, Torricelli studied projectile motion. He developed Galileo's ideas on the parabolic trajectory of projectiles launched horizontally, giving a theory for projectiles launched at any angle. He also gave numerical tables which would help gunners find the correct elevation of their guns to give the required range.

Torricelli not only had great skills in theoretical work, but he also had great skill as a maker of instruments. He was a skilled lens grinder, making excellent telescopes and small, short focus, simple microscopes, and he seems to have learned these techniques during the time he lived with Galileo.

Collections of paradoxes that arose through inappropriate use of the new calculus were found in his manuscripts and show the depth of his understanding.

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. 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.

Torricelli's remarkable contributions mean that had he lived, he would certainly have made other outstanding mathematical discoveries. In fact, he may indeed have made contributions that will never be known, for the full range of his ideas were never properly recorded.

References:

Amir Alexander (2014). Infinitesimal: How a Dangerous Mathematical Theory Shaped the Modern World. Scientific American / Farrar, Straus and Giroux. ISBN 978-0374176815.

Biography in Encyclopaedia Britannica. http://www.britannica.com/biography/Evangelista-Torricelli

M Gliozzi, Biography in Dictionary of Scientific Biography (New York 1970-1990).

"Evangelista Torricelli." Famous Scientists. famousscientists.org. 31 Aug. 2019. Web. 7/5/2021 “www.famousscientists.org/evangelista-torricelli/”.

Being raised in a fairly poor family, Evangelista Torricelli, a famous physician and mathematician, had remarkable talents and lacked the resources to provide an education for him by his family early on in his life and was sent to his uncle, who