# Michelangelo Ricci

### Quick Info

Born
30 January 1619
Rome (now Italy)
Died
12 May 1682
Rome (now Italy)

Summary
Michelangelo Ricci was an Italian churchman who made some early applications of induction.

### Biography

Michelangelo Ricci was born into a large family of modest means. His father, Prosper Ricci, came from Como while his mother, Veronica Cavalieri, came from Bergamo. Prosper and Veronica made great sacrifices to give their children a good education. Michelangelo quickly profited by these educational opportunities, quickly mastering Latin and Greek. He was also highly praised for his style of his Italian writing. However, among the subjects he was taught, mathematics and physics were the ones that he loved most. Throughout his life, Ricci suffered from epileptic fits, a condition which began when he was a child. His achievements, from childhood and throughout his life, are all the more remarkable when one considers that he had this severe handicap with which to contend.

Ricci became a friend of Evangelista Torricelli who came to Rome in 1627; in fact both were taught by the Benedictine monk Benedetti Castelli (1578-1643) (his name was Antonio Castelli but he took on the name Benedetti when he entered the Benedictine Order). Castelli was appointed professor of mathematics in Pisa when Galileo left in 1592 but moved to become professor of mathematics at La Sapienza, the University of Rome. He was a friend of Galileo and published innovative work on hydraulics in 1630. When Castelli was away from Rome, Torricelli took over his teaching and, in this way, he also taught Ricci. In addition to mathematics, Ricci studied theology and law in Rome, principally because he needed a career which would provide him with a steady income. At this time he also became friends with René de Sluze who studied law at La Sapienza between 1642 and 1643. Although awarded a doctorate in law in 1643, de Sluze remained in Rome for several years enjoying the scholarly environment. It is clear that de Sluze, Torricelli and Ricci had a considerable influence on each other in the mathematics which they studied.

Ricci made his career in the Roman Catholic Church. His income came from the Church, certainly from 1650 he received such funds, but perhaps surprisingly he was never ordained. Some have suggested that the fact that he suffered from epileptic fits could have prevented him being ordained. Ricci served successive popes (Alexander VII, Clement IX and Innocent XI) in several different roles before being made a cardinal by Pope Innocent XI on 1 September 1681. In particular he served as Secretary of the Sacred Congregation of Indulgences and Sacred Relics. Several requests that he brought before this body, in particular requests from the Irish bishops in 1670 and 1671, are recorded. He also served as a Consultor of the Supreme Sacred Congregation of the Roman and Universal Inquisition. This had been set up by Pope Paul III in 1542:-
... to maintain and defend the integrity of the faith and to examine and proscribe errors and false doctrines.
As a scientist who was at the forefront of the scientific research of his day and as an enthusiast for the new ideas being put forward by Galileo and others, he was able to play an important role in moderating the Church's approach to "modern science". In particular, he frequently intervened to avoid censorship by the Church of the activities of those engaged in up-to-the-minute research. Of course, the argument between Galileo and the Church happened long before Ricci was in a position to help (he was only 14 years old when Galileo was tried). However, he did work at making Galileo's ideas acceptable to the Church and tried to ensure that other scientist did not suffer similar consequences. For example, in 1658 he wrote to Domenico Rossetti:-
Learn at Galileo's expense. He ran into so much trouble just because he picked fights.
Ricci corresponded with Vincenzo Viviani about the articles Viviani was writing on Galileo's life and his work, trying to encourage him to get across Galileo's ideas without causing the Church to become upset. For example, here are three quotes from the letters that Ricci wrote to Viviani after reading sections on Galileo:-
I would moderate those terms of persecution and such when speaking of Father Grassi and other Jesuits and imitators.
It is necessary to limit those praises of the book about the two systems to the many natural problems solved in it, so that it cannot be said that Copernican opinions are being defended and approved.
I consider Your Lordship's advice prudent, to use few words when discussing the details of the misfortune that befell Galileo over the 'Dialogues', and to expatiate further on other astronomical and geometrical matters, his meaningful experiences and wise reflections.
Ricci's main mathematical work was Exercitatio geometrica, De maximis et minimis (1666) which was later reprinted as an appendix to Nicolaus Mercator's Logarithmo-technia (1668). It only consisted of 19 pages and it is remarkable that his high reputation rests solely on such a short publication. In this work Ricci finds the maximum of $x^{m}(a - x)^{n}$ and the tangents to $y^{m} = kx^{n}$. The methods are early examples of induction. Ricci dedicated this work to the philosopher and polymath Stefano Gradi (1613-1683), whose interests included mathematics and science - Gradi eventually became Head of the Vatican library. A manuscript of Ricci's, devoted to algebra but never published, is in the library of the Mathematical Institute of Genoa. It shows that Ricci was familiar with current research in algebra around 1640 which was developing as a result of the work of François Viète.

In his own time Ricci's fame as a mathematician (which was remarkably high - some believed him to be the best mathematician in Italy of his generation) rested more on the many letters he wrote on mathematical topics, rather than on his published work. He corresponded with many mathematicians across Europe including Torricelli, Clavius, Viviani and de Sluze. Results of his own contributions contained in these letters include work on spirals (1644) and on families of curves which generalised cycloids (1674). He states explicitly in a letter of 1668 that finding tangents and finding areas are inverse operations. His correspondence is, however, even more important for the results which others sent him. In 1641 Torricelli discovered that by rotating a rectangular hyperbola he could get a solid of revolution that was infinite in length but finite in volume. He communicated this result, and other similar results, in 1643 to Jean-Francois Niceron in Paris although he gave no proofs. Ricci was sent the statement of these results and replied in a letter to Torricelli in June 1643 [5]:-
Father Niceron writes me that all the excellent men of that kingdom desire to see your works and that the sheet of propositions I sent them is passing through everyone's hands with great praise of your beautiful discoveries.
On 11 June 1644, Torricelli wrote to Ricci his famous letter about his invention of a barometer, showing that he had proved the existence of a vacuum. The letter begins:-
To Michelangelo Ricci in Rome
Most Illustrious Sir and Most Learned Patron
Several weeks ago I sent to Sig Antonio Nardi several of my demonstrations of the areas of cycloids, and asked him that after he had examined them he would send them on at once to yourself or to Sig Magiotti. I have already called attention to the fact that there are in progress certain philosophical experiments, I do not know just what, relating to vacuum, designed not simply to make a vacuum but to make an instrument which will show the changes in the atmosphere, as it is now heavier and more gross and now lighter and more subtle.
Ricci replied on 18 June, showing his concern at the reaction of certain people within the Church to Torricelli's discoveries:-
I estimate that you will unfortunately be too nauseated by the temerarious opinion of these Theologians, and by their constant habit of mixing up things of God with natural questions, where they should instead be treated with greater respect and reverence.
Torricelli wrote again to Ricci giving further details of his experiments on 28 June. Marin Mersenne, who was greatly interested in the barometer in the last years of his life, visited Italy in October 1644 and at this time he was able to hold discussions about the barometer with Torricelli as well as with Ricci. We note that when Bonaventura Cavalieri died in November 1647, he left a request that Torricelli and Ricci collaborate in editing his unpublished manuscripts and letters. In fact, unknown to Cavalieri, Torricelli had died a few days earlier so his request for editing his works fell entirely to Ricci. However, Ricci felt that he had too many duties to be able to undertake the task so it was not until 1919 that the remaining material left by Cavalieri was eventually published (some material had been lost by that time).

As well as having an important role in the development of mathematics and physics through his correspondence, Ricci also took an active role as Roman correspondent in the Accademia del Cimento which was founded in Florence in 1657 by Giovanni Alfonso Borelli and Vincenzo Viviani. Beginning in 1666, the Academy published Saggi di naturali esperienze fatte nell'Academia del Cimento sotto la protezione del Serenissimo Principe Leopoldo di Toscan e descrittedal segretario di essa Accademia and Ricci acted as an editor for this important journal. In 1668, Ricci, in collaboration with Giovanni Giusto Ciampini (1633-1698) and Francesco Nazari (1634-1714), founded the wide-ranging journal Giornale de letterati. This journal provided information on topical issues as well as reviews and translations of important articles in other journals. For example, the journal tackled issues such as the nature of matter - followers of Galileo and of Descartes argued over this topic, and it also raised theological issues with the Church. Ricci was a major figure in the production of the journal until 1675 when he handed over control to his younger colleagues.

Other regular correspondents of Ricci included Leopoldo de' Medici, brother of the Grand Duke of Tuscany, who was a patron of the arts with interests in science, technology, rare books and paintings. Their correspondence was much concerned with the Accademia del Cimento and its Saggi. Christina Alexandra (1626-1689), Queen of Sweden, abdicated in 1654, converted to Catholicism, and in the following year went to Rome. She had broad literary and scientific interests, and the group of scholars she eventually gathered round her in Rome included Ricci. We noted above that he was made a cardinal by Pope Innocent XI on 1 September 1681, and this appears to have been partly though Christina's influence. However, this is not quite as simple as it might at first appear since, when the Pope informed him that he would be made a cardinal, Ricci politely and humbly replied to the Pope in a long letter refusing to accept the position:-
... with great energy, and strength of reasons, and the same level of erudition, makes me determined to reject the dignity conferred.
However, the Pope's wishes were paramount and Ricci was forced the accept the honour. After his death, only a few months later, Ricci's funeral was held in the church of Santa Maria in Vallicella in Rome on 14 May 1682. His body was then taken to the church of San Francesco a Ripa in Rome where he was buried in the family tomb (it can still be seen in the first chapel on the right as one enters the church). The monument to Ricci erected over the tomb was designed by Domenico Guidi.

### References (show)

1. A Agostini, Massimi e minimi nella corrispondenza di E Torricelli con M Ricci, Atti del IV Congresso dell'Unione maematica italiana 2 (Rome, 1953), 629-632.
2. D Besso, Sopra un opusculo di Michelangelo Ricci, Periodico di matematica per l'insegnamento secondario 8 (1892), 1-16.
3. J E Hofmann, Über die 'Exercitatio geometrica' des M A Ricci, Centaurus 9 (1964), 139-193.
4. P Mancosu and E Vailati, Torricelli's Infinitely Long Solid and Its Philosophical Reception in the Seventeenth Century, Isis 82 (1) (1991), 50-70.
5. L Tenca, Relazioni fra Vincenzio Viviani e Michel Angelo Ricci, Ist. Lombardo Sci. Lett. Rend. Cl. Sci. Mat. Nat. (3) 18(87) (1954), 212-228.
6. L Tenca, Michel Angelo Ricci, Memorie Accademia Patavina, Class. Sci. Mat. Nat. 68 (1955-6).