Frisi entered the Barnabite Arcimbolde school in Milan in or before 1741. The Barnabites were a religious Order, devoted to the study of the Pauline Letters. They had founded the Arcimbolde school in Milan, which is also known as the College of Sant'Alessandro, in 1663. The headquarters of the Order was in Milan, in the church of St Barnabas (hence the name of the Order). Pietro Verri (1728-1797) was the same age as Frisi and they studied together at the Arcimbolde school. Verri, the author of a biography of Frisi , became a well known philosopher, historian and writer. He remembered that in 1741-42 Frisi, who was at that time his companion in the Arcimbolde, stood out for his reliability and attendance at the Ambrosiana Library. Frisi joined the Barnabite Order and on 11 July 1743 he was admitted to the novitiate of the church of Santa Maria of Carrobiolo in Monza. Verri certainly felt that Frisi did not exhibit deep religious feelings and was following this religious path more because it offered him a quality education from learned men and also gave him the opportunity to study without having to worry about his material needs. He took his vows on 15 October 1744 and returned to the College of Sant'Alessandro for courses on literature and philosophy. He studied the classics with father Onofrio Branda and poetry in Italian and Latin. Paolo Onofrio Branda (1710-1776) was a scholar who wrote Della lingua toscana Ⓣ (1759). Now natural philosophy according to Aristotle had been taught at the Arcimbolde up to 1744 but, in that year, Francesco Maria De Regi (1720-1794) began teaching ideas of Newton's natural philosophy. De Regi was a mathematician specialising in engineering and hydraulics; he published Theoremata Ⓣ in 1757. After studying the philosophy courses at the Arcimbolde, Frisi went on to study mathematics on his own.
In 1747 Frisi went to Pavia where he studied theology in the Ordine School. However, in Pavia he attended courses by the mathematician and physicist Ramiro Rampinelli (1697-1759). Rampinelli, who had taught Maria Gaetana Agnesi while at the San Vittore al Corso monastery in Milan, had been appointed to the chair of mathematics and physics at the University of Pavia in 1747. A friend of Giovanni Poleni and Jacopo Riccati, Rampinelli was an expert in hydraulics and supervised the construction of the Pavia-Milan canal and other similar projects. Rampinelli supervised Frisi's mathematical studies and had him read his unpublished work 'Institutiones mechanicae ac staticae'. While in Pavia Frisi also read the 'Treatise of fluxions' of Colin Maclaurin, the 'Instituzioni analitiche' of Agnesi, and some writings of Leonard Euler. In addition, he read the commentary on Newton's Principia by the two Minim fathers, Thomae Le Sueur and Francois Jacquier (1711-1788). This work, entitled 'Isaaci Newtoni philosophiae naturalis principia mathematica, perpetuis commentariis illustrata' was published in four parts in three volumes between 1739 and 1742. Reading this work encouraged him to begin a correspondence with Jacquier. By the time he left Pavia at the end of 1749, Frisi had completed his theological studies and, in addition to the mathematical texts mentioned above, had also studied works of the French school up to Alexis Claude Clairaut and Jean Le Rond d'Alembert.
Leaving Pavia, Frisi was sent to teach philosophy in the College of San Giovanni alle Vigne in Lodi. He remained there for two years and during this time, in February 1751, he was ordained a priest. In 1751 he published two works, Disquisitio mathematica in causam physicam figurae et magnitudinis telluris nostrae Ⓣ and Del modo di regolare fiumi e torrenti Ⓣ. The first of these works presented problems since the censors of the Order denied him permission to print the work because it was based on a heliocentric model. Frisi's brother Antonio, who we mentioned above, worked for Count Donato Il Silva and Antonio showed the Disquisitio Ⓣ to Count Il Silva who offered to finance its publication. Frisi, having started printing without the permission of the Barnabite Order, was told to stop, but nevertheless publication went ahead. This work was remarkable since it discussed the figure of the earth and whether there was a equatorial bulge, not just from geodetic measurements but from a discussion of the movement of the Earth and the effect that had on its shape. He came up with 229:230 as the ration of the polar to equatorial radius.
Now in 1751 he requested that he be transferred to the seminary in Bologna since he knew many of the scientists there and felt that would further his scientific studies. However, this did not happen and instead he was sent to the College of Casale Monferrato to succeed to the chair of philosophy which had been vacated by Giacinto Sigismondo Gerdil (1718-1802) in 1749 when he was appointed as professor of philosophy at the University of Turin. Appointed by the Savoy government, Frisi taught philosophy at Casale from November 1751. Once at Casale he became friends with I Radicati, Count of Cocconato, who was a free thinker, and the two continued to correspond for over twenty years. While at the College of Casale, Frisi wrote his first work on pure mathematics, De methodo fluxionum geometricarum et eius usu in investigandis praecipuis curvarum affectionibus Ⓣ which was published in Milan in 1753. The Barnabite Order was unhappy with Frisi's dedication to science and his neglect of religion and, in 1752, they asked the Savoy government to remove him from his chair at Casale. The Barnabite Order wanted him to go to their house of penance but, in November 1752, Frisi managed to postpone the decision citing health reasons. He had poor eyesight, and was also suffering from partial deafness. He was then sent as a preacher to Novara but managed to spent only a short time there. By the spring of 1753 he was teaching philosophy at the College of Sant'Alessandro in Milan. In the same year he was elected as a corresponding member of the Paris Académie des Sciences.
Back in Milan he re-established contact with Pietro Verri but there were few there to share his scientific interests and he worked on his own. He published a work on electricity, Nova electricitatis theoria quam ... J B Landriani publice propugnabat Ⓣ in 1755 and, in the same year, Saggio morale di filosofia Ⓣ. In the following year he published De motu diurno terrae dissertatio Ⓣ. He left Milan in 1756 to take up a post as professor of philosophy at the University of Pisa. Appointed by Leopold, the Grand Duke of Tuscany, he began his duties in February. In Pisa he lived in the Barnabite lodgings at San Frediano and made contacts with a number of scientists including Giovanni Gualberto de Soria (1707-1767), Giovanni Battista Caraccioli (1695-1765) who wrote Geometria algebraica universa quantitatum finitarum, et infinite minimarum Ⓣ (1759), Ottaviano Cametti (1711-1789) who had published Elementa geometriae Ⓣ in 1755, and Tommaso Perelli (1704-1783) who was the director of the Pisa Observatory. Perelli, in particular, had a large influence on Frisi who often made the relatively short journey to Florence where Galileo's influence was strong. His scientific work continued to be recognised internationally and he was elected to the St Petersburg Academy of Sciences in 1757, the Royal Society of London in 1757 and the Berlin Academy of Science in 1758. Frisi was able to publish works on celestial mechanics after 1757 since Pope Benedict XIV had promoted scientific learning and instructed those drawing up the Index of Forbidden Books to act with restraint. Frisi published Memorie sopra la fisica e l'istoria naturale Ⓣ (1757), De aberratione lucis opusculum Ⓣ (1757), and De atmosphaera caelestium corporum dissertatio physico-mathematica Ⓣ (1759). He had made a submission to the 1758 Grand Prix of the Paris Academy of Sciences which argued that the planets had atmospheres. Although he continued to follow the rules of his religious Order, he was now living a life of increased freedom. He was able to enjoy the company of friends and had now sufficient freedom to include some pleasures.
Between June and autumn 1760, Frisi made a journey to Rome and Naples. When in Rome he had an audience with Pope Clement XIII who asked his opinion of a Rhine River project. This was not something that Frisi had looked at before but he quickly immersed himself in the vast literature on the subject and drew up a plan.
After holding the post in Pisa for eight years, Frisi returned to Milan becoming professor of mathematics at the Scuola Palatina in April 1764. He was a leading authority on mathematics and science in his day, and considered of such importance that when he left Pisa for Milan the Tuscan government decreed that his name should remain on the list of professors at the University of Pisa. In 1764 the city senate of Bologna appointed him an honorary university mathematics professor. He continued to make visits abroad and in 1766 visited first France in May and then England in August. In Paris he met, among others, Jean d'Alembert, Denis Diderot, Georges-Louis Leclerc de Buffon, Marie-Jean Caritat de Condorcet, Jean-Étienne Montucla, and Louis-Antoine de Bougainville. In London he met, among others, Benjamin Franklin, Edward Waring, Nevil Maskelyne, and the philosopher David Hume. In Paris he showed his work De gravitate universal corporum Ⓣ to members of the Academy and Jean d'Alembert and Étienne Bézout wrote positive reports on the work which they presented to the Academy in September. Frisi discussed the three body problem with French mathematicians, visited science museums and observatories of Paris and Greenwich, and attended meetings of the Royal Society of London and the Paris Academy of Sciences. Frisi returned to Milan in April 1767.
Two years later he visited Vienna, arriving in July 1768. His main purpose was to present to Joseph II, the Holy Roman Emperor, a copy of De gravitate universal corporum Ⓣ which Frisi had dedicated to him. Joseph II had become Holy Roman Emperor in 1765 and, when Frisi visited, he was jointly ruling with his mother Maria Theresa. Joseph, who was a highly intelligent man, was keen to discuss with Frisi the latest developments in science, particularly in electricity, and since he had lost two wives to smallpox, he was naturally keen to discuss developments in inoculation. Joseph II also wanted to discuss church-state relations with Frisi for he already had in mind ways to limit the influence of the Church.
We have already indicated many contributions that Frisi made to mathematics, physics and astronomy. In physics he worked on light and electricity but, although his work was very up to date for its time, his explanations were based on vibrations in the ether and did little to advance the topic. He was, however, the first to introduce the lightning conductor into Italy. His work on astronomy was based on Newton's theory of gravitation and is therefore of considerably more importance than his work in physics. He studied the motion of the earth and he was awarded a prize by the Berlin Academy of Science for his outstanding memoir De moto diurno terrae Ⓣ (1756). As we have already mentioned, he also studied the physical causes for the shape and the size of the earth using the theory of gravity. Other astronomical phenomena which he studied included the difficult problem of the motion of the moon.
He studied kinematics and hydraulics and he was responsible for drawing up plans for a canal between Milan and Pavia. In fact the work on this canal was not undertaken in Frisi's lifetime, but in 1819, thirty-five years after Frisi's death, the canal was built to his plan. His major work on hydraulics is Del modo di regolare i fiumi, e i torrenti, principalmente del Bolognese, e della Romagna Ⓣ written in 1762. This book was translated into French and published in 1774 and four English editions were also published. In the paper De problematis quibusdam isoperimetricis Ⓣ of 1761 Frisi discussed isoperimetric problems. These were popular problems at this time with both Jacob Bernoulli and Johann Bernoulli having made important contributions and Euler, in 1744, having given a rule to determine a minimising arc between two points on a curve having continuous second derivatives. Frisi looked at problems involving both maximising and minimising.
Frisi also wrote on the contributions of Galileo: Elogio del Galileo Ⓣ (1775), Cavalieri: Elogio di Bonaventura Cavalieri Ⓣ (1778) Newton: Elogio del cavaliere Isacco Newton Ⓣ (1778), and d'Alembert: Elogio del signor d'Alembert Ⓣ (1786), and brought their ideas to a wide audience. Such writings were widely read for Frisi was considered, in Italy, to be :-
... a scientific authority and [he] was also well known abroad, so much so that his major works (which he wrote in Latin) were translated into French and English.These major works include Algebra e geometrica analitica Ⓣ (1782), Meccanica Ⓣ (1783), and Cosmografia Ⓣ (1785) which contain much of Frisi's earlier work, but written up in a polished form.
Frisi was also editor of the newspaper Il caffè. The paper was influenced by the ideas of the Illuminati (Enlightened Ones) which promoted free thought and democratic political theories. Through this paper Frisi had a major influence on the :-
... cultural, social, and political life of Milan ...Letters written by Frisi and to Frisi are discussed in  and . Letters between Teodoro Bonati (1724-1820) and Frisi discussing questions of mechanics and hydraulic mechanics are given in . A letter by Frisi written in 1753 on mechanics and geometry is given and discussed in .
In 1773 Pope Clement XIV suppressed the Society of Jesus, more commonly known as the Jesuits. After this, the Scuola Palatina, where Frisi was professor of mathematics, was moved to the Palazzo Brera, which had been a Jesuit College until the suppression. This was far from where Frisi lived in the lodgings of the Barnabite Order, so he requested that he be allowed live with his family. This was impossible if he was to remain in the Barnabite Order, so his request was really for secularisation. This was not something to be taken lightly by the Church but, eventually, in 1776 Pope Pius VI granted him secular status as long as he remained a public professor. He lived with his mother, three brothers and a sister but, without the support of his Order, his life had economic problems. In August 1778 Frisi made a third trip abroad, going to Switzerland. In the following summer his health began to deteriorate and he suffered nervous disorders. Although he recovered, these health problems caused him to reduce his work load. However, in 1782 he published a collection of his greatest scientific work, which he revised and expanded, but he also added previously unpublished work. In May 1784 Gustav III, king of Sweden, visited Frisi in Milan; this was considered a great honour. In the summer of 1784 he suffered from many abscesses and his doctors advised him to rest at home. By the autumn his condition had become more severe and his doctors advised surgery but infection followed. He died shortly after taking the last rites. Despite having left the Barnabite Order some years before, the Barnabites still wanted him buried in Sant'Alessandro.
Frisi was honoured by election to many academies; we have indicted when he was elected to several of these academies above. Let us here record that he has been honoured, and is remembered by many today, by having several institutions and streets named after him. The schools and institutes name after him include: the Istituto di Istruzione Secondaria Superiore "Paolo Frisi" in Milan; the Scuola "Paolo Frisi in Milan"; the Liceo Scientifico Statale "Paolo Frisi" in Monza; and the Scuola Secondaria di I Grado "Paolo Frisi" in Melegnano. Streets named after Frisi include: the Via Paolo Frisi, Milan; the Via Paolo Frisi, Melegnano; the Via Paolo Frisi, Lissone; the Via Paolo Frisi, Pavia; the Via Paolo Frisi, Rome; and the Via Paolo Frisi, Bologna.
Article by: J J O'Connor and E F Robertson