**Evangelista Torricelli** was an Italian scientist who was the first man to create a sustained vacuum and to discover the principle of a barometer. He also achieved some important results in the development of the calculus.

- Brother Jacopo saw that Evangelista was given a sound education until he was old enough to enter a Jesuit school.
- Torricelli entered a Jesuit College in 1624 and studied mathematics and philosophy there until 1626.
- The most likely events seem to be that after Gaspare Torricelli died, Caterina and her two younger sons moved to Rome to be with Evangelista who was either already living there or about to move to that city.
- There is no evidence that Torricelli was actually enrolled at the university, and it is almost certain that he was simply being taught by Castelli as a private arrangement.
- As well as being taught mathematics, mechanics, hydraulics, and astronomy by Castelli, Torricelli became his secretary and held this post from 1626 to 1632.
- There does still exist a letter which Torricelli wrote to Galileo on 11 September 1632 and it gives us some very useful information about Torricelli's scientific progress.
- Galileo had written to Castelli but, since Castelli was away from Rome at the time, his secretary Torricelli wrote to Galileo to explain this fact.
- 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.
- Moreover, he had carefully studied Dialogue Concerning the Two Chief Systems of the World - Ptolemaic and Copernican which Galileo had published about six months before Torricelli wrote his letter.
- It was clear from his letter that Torricelli was fascinated by astronomy and was a strong supporter of Galileo.
- After Galileo's trial in 1633, Torricelli realised that he would be on dangerous ground were he to continue with his interests in the Copernican theory so he deliberately shifted his attention onto mathematical areas which seemed less controversial.
- We do not know where Torricelli lived during this period but, as Ciampoli served as governor of a number of cities in Umbria and the Marches, it is likely that he lived for periods in Montalto, Norcia, San Severino and Fabriano.
- By 1641 Torricelli had completed much of the work which he was to publish in three parts as Opera geometrica Ⓣ(Works of geometry) in 1644.
- Torricelli was certainly in Rome in early 1641 when he asked Castelli for his opinion on De motu gravium.
- In April 1641 Castelli travelled from Rome to Venice and, on the way, stopped in Arcetri to give Galileo a copy of Torricelli's manuscript and suggest that he employed him as an assistant.
- Torricelli remained in Rome while Castelli was on his travels and gave his lectures in his place.
- Although Galileo was keen to have Torricelli's assistance there was a delay before this could happen.
- On 10 October 1641 Torricelli arrived at Galileo's house in Arcetri.
- In looking at Torricelli's achievements we should first put his mathematical work into context.
- Torricelli studied the methods being proposed by Cavalieri and at first was suspicious of them.
- Torricelli also computed the area and centre of gravity of the cycloid.
- Notice that we have stated this result in the modern notation of coordinate geometry which was totally unavailable to Torricelli.
- We mentioned Torricelli's results on the cycloid and these resulted in a dispute between him and Roberval.
- a letter dated October 1643, by which Torricelli gets in touch with Roberval and reports to him about his views and results on the centre of gravity of the parabola, the semigeneral parabolas, the surface of the cycloid and its history, the solid of revolution generated by a conic and the hyperbolic acute solid.
- We should also note another fine contribution made by Torricelli was in solving a problem due to Fermat when he determined the point in the plane of a triangle so that the sum of its distances from the vertices is a minimum (known as the isogonic centre of the triangle).
- Torricelli was the first person to create a sustained vacuum and to discover the principle of a barometer.
- Torricelli wrote a letter to his friend Michelangelo Ricci, who like him had been a student of Castelli, on 11 June 1644.
- At this stage Torricelli was in Florence, writing to his friend Ricci who was in Rome.
- Aristotle had simply claimed that a vacuum was a logical contradiction, but difficulties with this had led Renaissance scientists to modify this to the claim that 'nature abhors a vacuum' which is in line with those who Torricelli suggests believe a vacuum exists despite 'the repugnance of nature'.
- In De motu gravium Ⓣ(Motion of weights) which was published as part of Torricelli's 1644 Opera geometrica Ⓣ(Works of geometry), 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.
- Also in De motu gravium Torricelli studied projectile motion.
- The two corresponded on the topic with Torricelli saying that his theory was in fact based on ignoring certain effects which would make the experimental data slightly different.
- Torricelli not only had great skills in theoretical work but he also had great skill as a maker of instruments.
- one of Torricelli's telescope lenses ...
- Much of Torricelli's mathematical and scientific work has not survived, mainly because he published only the one work we referred to above.
- We referred above to the argument between Torricelli and Roberval concerning the cycloid, and in 1646 Torricelli began gathering together the correspondence which had passed between the two on the topic.
- It is clear that Torricelli was an honest man who felt that he needed to publish the material to present the truth to the world.
- However, before he completed the task of preparing the correspondence for publication Torricelli contracted typhoid in October 1647 died a few days later at the young age of 39 while in his prime as a research mathematician and scientist.
- Some of Torricelli's manuscripts were lost and it was not until 1919 that the remaining material was published as Torricelli had wished.
- His collected works were published with Gino Loria and Guiseppe Vassura as editors, three volumes being published in 1919 and the fourth volume in 1944 nearly 300 years after Torricelli's death.
- Sadly material left by him, bearing his own signature, was destroyed in the Torricelli Museum in Faenza in 1944.
- Torricelli's remarkable contributions mean that had he lived he would certainly have made other outstanding mathematical discoveries.

Born 15 October 1608, Faenza, Romagna (now Italy). Died 25 October 1647, Florence, Tuscany (now Italy).

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Analysis, Astronomy, Origin Italy

**O’Connor, John J; Robertson, Edmund F**: MacTutor History of Mathematics Archive