Person: Viviani, Vincenzo
Vincenzo Viviani was an Italian engineer who worked on the geometry of the cycloid.
Mathematical Profile (Excerpt):
- Vincenzo studied at a Jesuit school where he learnt the humanities.
- The court was in Livorno, so Viviani had to make the long journey from Florence.
- Ferdinando was greatly impressed and provided a monthly salary for Viviani that enabled him to purchase mathematical books.
- He also arranged for Viviani to meet Galileo, who was living in his villa in Arcetri, near Florence, where he had been put under house arrest by the Catholic Church.
- Galileo, who by this time was totally blind, was very impressed by Viviani's knowledge and abilities.
- In 1639, he took Viviani into his home as a companion, student and collaborator, and Viviani continued in this role until Galileo died in January 1642.
- Viviani learnt much from Galileo over this period, working with him on physics and geometry.
- In October 1641, Galileo and Viviani were joined in the villa at Arcetri by Evangelista Torricelli when he moved from Rome.
- In 1644 Viviani, as Torricelli's collaborator, carried out the experiment which proved a major scientific advance and led to the development of the barometer.
- When Torricelli died in 1647, Viviani was appointed to fill the lectureship at the Accademia del Disegno in Florence, holding this post for two years.
- The main thrust of Viviani's life, however, was to keep Galileo's memory alive and he wanted to do so by publishing his collected works.
- For much the same reason, most of Viviani's own scientific work remained unpublished, and an edition of Galileo's works, as Viviani would have liked to see it, only appeared two centuries after his death, under Favaro's supervision.
- Favaro, however, could hardly have published his National Edition without the materials collected by Viviani.
- Throughout his life, one of Viviani's main interests was in ancient Greek mathematics.
- (Solid Loci is the Greek term for conic sections.) Pappus, however, indicated propositions from the work and Viviani reconstructed the original from these references by Pappus.
- It was a project that Viviani worked on for most of his life.
- Another restoration of a Greek text by Viviani is interesting for a number of reasons.
- At the time he began the restoration only the first four books of this eight-book work had been found and Viviani set about reconstructing the fifth.
- By 1656 Viviani's work was quite close to completion when Giovanni Alfonso Borelli (a fellow Tuscan Court mathematician) discovered an Arabic version of the first seven books of Apollonius's Conics in the Laurentian Library in Florence.
- In 1659 both the translation from the Arabic and Viviani's restoration were published.
- Viviani's work was entitled De maximis et minimis geometrica Divinatio Ⓣ(A divination of geometric maxima and minima) and was certainly written by him without any knowledge of the translation of Apollonius's work.
- It is interesting, of course, to see how faithfully Viviani was able to reconstruct Apollonius's book since now both the reconstruction and the original had become available.
- Viviani had done an excellent job, his biggest 'error' being that he had been able to penetrate deeper than Apollonius himself.
- The realisation that Viviani was, in some sense, a better geometer than the revered Apollonius, gave him instant fame throughout the centres of learning in Europe.
- The Grand Duke, not wishing to lose Viviani, appointed him as his mathematician.
- In 1657 Viviani became one of the first members of the Grand Duke's new academy, the Accademia del Cimento, which was formally founded in June of that year.
- However, the Academy had informally existed for some time before that with Viviani organising a group of natural philosophers to carry out a variety of scientific experiments.
- On 10 October 1656, together with Giovanni Borelli, Viviani used a pendulum as a timing device to show that sound travels twice a fixed distance in twice the time taken to travel the original distance.
- After the Academy was formally founded, Viviani was involved in most of the experimental work they carried out, such as experiments with Torricelli's barometer and experiments relating to properties of freezing water.
- Another important work by Viviani is Quinto libro degli Elementi d'Euclide: ovvero Scienza universale delle proporzioni spiegata colla dottrina del Galileo, con nuov'ordine distesa Ⓣ(Fifth Book of the 'Elements' of Euclid: the universal science of proportions explained by the theory of Galileo ...).
- As he was an engineer all his life Viviani also published on engineering.
- We have not yet commented on the thing for which Viviani is best known, namely his Racconto istorico della vita di Galileo Galilei Ⓣ(A history of Galileo).
- Prince Leopoldo asked Viviani to write a sketch of Galileo's life for inclusion in Manolessi's edition of his works.
- However, things did not go as planned for although Viviani wrote his Life of Galileo it did not appear in the edition of Galileo's Collected Works published by Manolessi in Bologna 1655-56.
- Viviani wanted to publish his own edition of Galileo's Collected Works so he kept the Life of Galileo which he had written intending to include it in a publication of Galileo's Collected Works which he hoped to edit.
- In 1659 Viviani wrote a second essay on Galileo's work Lettera di Vincenzio Viviani al Principe Leopoldo de' Medici intorno all'applicazione del pendolo all'orologio.
- Neither essay was published in Viviani's lifetime, but his Racconto istorico was published in 1717.
- However, in the 20th century historians began to argue that certain details in the essay had been invented by Viviani, particularly those relating to the experiments carried out by Galileo.
- Viviani was certainly very careful and put in a great amount of effort collecting information about Galileo's life.
- Despite his great expertise in geometry, Viviani seems to have done little original in this area, He did determine the tangent to the cycloid but he was not the first to succeed in this.
- Leibniz was interested in the papers left by Galileo and met Viviani in Florence in late November 1689.
- The two got on well during this meeting but after Leibniz published Solutio problematis a Galilaeo propositi de linea catenaria Ⓣ(A solution to a problem posed by Galileo on the catenary) in 1692, Viviani became unhappy about the use of the differential and integral calculus which he believed to be nothing but a kind of game that could only solve its own problems.
- We note also that Viviani published an Italian version of Euclid's Elements in 1690.
- On his death Viviani left an almost completed work on the resistance of solids which was completed and published by Guido Grandi.
- Viviani built a handsome house in Florence, and placed the bust of Galileo over the door, with inscriptions on each side of it, to honour his name.
Born 5 April 1622, Florence (now Italy). Died 22 September 1703, Florence (now Italy).
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Tags relevant for this person:
Geography, Origin Italy
Thank you to the contributors under CC BY-SA 4.0! 
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- non-Github:
- @J-J-O'Connor
- @E-F-Robertson
References
Adapted from other CC BY-SA 4.0 Sources:
- O’Connor, John J; Robertson, Edmund F: MacTutor History of Mathematics Archive
