We now focus on the third and final member of what I refer to as the Galileo–Castelli school of mathematics; Giovanni Alfonso Borelli (1608–1679).
Borelli’s seventy years of existence in seventeenth-century Italy resembles the storyline of a mid-Victorian novel. Born Giovanni Francesco Antonio on 28 January 1608 in Spanish-controlled Naples, he was the eldest son of Miguel Alonso, a Spanish infantryman, and his Italian partner Laura Porello (also spelled porrello, porrella, borrella, borriello, borrelli). He would later take on his mother’s surname and replace his two middle names with the Italian variant of his father’s last name. He had four brothers and a sister. Despite his relatively modest and impoverished origins, he somehow obtained an education, and his considerable aptitude for mathematics was acknowledged. This led to his placement in Rome after 1628, where he studied mathematics under Benedetto Castelli (1578–1643) at the Sapienza University. This suggests he had a patron, though the identity is unknown; a potential candidate could be Tommaso Campanella (1568–1639). Borelli’s time in Rome coincided with that of Evangelista Torricelli (1608–1647).
Upon Castelli’s recommendation, he was appointed to a public lectureship in mathematics at the University of Messina in Sicily. In 1640, when a mathematics chair in Pisa became open, Castelli wrote two letters to Galileo advocating for Borelli. However, Galileo chose his own protégé, Vicenzo Renieri (1605–1647). Borelli remained in Messina until 1656. In 1642, the university senate funded a trip to the prominent universities of Italy to seek out and recruit excellent instructors, particularly in law and medicine.
Borelli’s travels likely began in Naples and then moved to Rome, but no records confirm this. We do know he traveled to Florence but arrived too late to meet Galileo, who had passed away in January that year. Nevertheless, he encountered Vincenzo Viviani (1622–1703), Galileo’s amanuensis for the last three years of his life, who was now collaborating with Torricelli, who had succeeded Galileo as court mathematician to Grand Duke Ferdinando II.
He also met Ferdinando’s younger brother, Prince Leopoldo de’ Medici. These encounters would significantly influence Borelli’s future.
From Florence, he proceeded to Bologna, where he met Bonaventura Cavalieri (1598–1647), another student of Castelli and a leading mathematician in Italy, leaving a favorable impression.
After departing Bologna, he continued to Padua and ultimately reached Venice, from where he returned to Messina by ship. Though still unpublished, he had gained recognition among the right circles in Italy.
Borelli went back to Messina, where he would reside until 1655. Here, he produced his first academic works. In 1644, he engaged in a pamphlet dispute with Pietro Emmanuele, a mathematician from Palermo, but these publications did not hold significant importance. His next endeavor was his initial medical publication. In response to an epidemic of fevers that affected Sicily, especially Messina, he published Delle cagioni delle febbri maligne di Sicilia negli anni 1647 e 1648, … (On the causes of the malignant fevers of Sicily in the years 1647 and 1648…) based on his empirical research. He dismissed both meteorological and astrological explanations, proposing instead that the cause was an invasion from external sources. An appendix presented his chemical perspective on digestion, in which he described digestion as the action of a succo acido corrosivo transforming food into a liquid state.
Following Cavalieri’s death, he was nominated for the mathematics chair in Bologna, but the position was awarded to Giovanni Domenico Cassini (1652–1712), who would become one of Europe’s leading astronomers.
In 1654, an edition of the Conics of Apollonius by Francesco Maurolico (1494–1575), featuring his attempted reconstruction of Books V and VI, was published in his Emendatio et restitutio conicorum Apollonii Pergaei in Messina.
At that time, only the first four books of the original eight were known. It is unclear whether Borelli was involved in this project; however, he did create a summary of Books I to IV, which would later influence his work in Pisa. The Medici had obtained an Arabic version of the text, and in the spring of 1656, he wrote to Leopoldo de’ Medici suggesting that with the assistance of someone familiar with Arabic, he could reconstruct.