Jacopo Riccati

Jacopo Francesco Riccati (28 May 1676 – 15 April 1754) was a Venetian mathematician and jurist from Venice, known for his widely influential work on solving differential equations. He is best known for having studied the equation that bears his name.

Jacopo Riccati
Jacopo Francesco Riccati (1676–1754)
Born	(1676-05-28)28 May 1676 Venice, Venetian Republic
Died	15 April 1754(1754-04-15) (aged 77) Treviso, Venetian Republic
Nationality	Italian
Alma mater	University of Padua (LL.D., 1696)
Known for	Riccati equation
Scientific career
Fields	Mathematician
Notable students	Vincenzo Riccati
Notes
Father of Vincenzo Riccati and Giordano Riccati.

Biography

Early life and education

Jacopo Riccati was born on May 28, 1676 to a noble family. His mother belonged to the Colonna family, one of the most influential princely families in Renaissance Rome.^[1] His father, a nobleman, died when he was still a boy.^[2] He was educated first at the Jesuit school for the nobility in Brescia, and in 1693 he entered the University of Padua to study law. He received a doctorate in law (LL.D.) in 1696. Encouraged by Stefano degli Angeli to pursue mathematics, he studied mathematical analysis.^[2] By 1710 he was familiar with the ideas of differential and integral calculus. His main work was in the field of differential equations, and he introduced new methods to solve them, such as the methods of separating variables and lowering the order of the equation. He corresponded with several European mathematicians, including Leonhard Euler and Daniel and Nicholas Bernoulli. Riccati personally supervised the education of Ramiro Rampinelli, the teacher of Maria Gaetana Agnesi and Paolo Frisi.^[3]

Career

Riccati received various academic offers but declined them in order to devote his full attention to the study of mathematical analysis on his own. In 1696 he married the countess Elisabetta Onigo, and established his residence in Treviso, refusing the invitation by Peter the Great to become the president of the St. Petersburg Academy of Sciences.^[4] He was also asked to Vienna as an imperial councillor (Consigliere Aulico) and offered a professorship as the University of Padua.^[5] He declined all these offers, preferring to stay in Italy and devote himself to his studies privately.^[5]

Riccati played a pivotal role in the diffusion of Newton's ideas in Italy.^[6] Most of his scientific work concerns mathematical analysis, especially differential equations. He is best known for introducing the differential equation that bears his name: $${\displaystyle y'(x)=q_{0}(x)+q_{1}(x)\,y(x)+q_{2}(x)\,y^{2}(x)}$$ where ${\displaystyle q_{0}(x)\neq 0}$ and ${\displaystyle q_{2}(x)\neq 0}$. If ${\displaystyle q_{0}(x)=0}$

This non-linear ordinary differential equation was to become of paramount importance in the centuries to come.^[2] Some of his work on polynomials was included by Maria Gaetana Agnesi, at Riccati's request, in the book on integral calculus of her Analytical Institutions.^[7] Riccati was very interested in hydraulics as well, and was often consulted by the Senate of Venice on the construction of canals and dikes along rivers. In addition, he studied economics, history, theology, ethics, metaphysics, and poetry. His works were collected and published in four volumes after his death (Lucca 1761-1765).

Personal life

His father, Conte Montino Riccati, came from a noble family who owned land near Venice. His mother was from the powerful Colonna family. His father died in 1686, when Riccati was only ten, leaving the youth a handsome estate.

Riccati and his wife had nine children, three of whom followed in their father's footsteps. Vincenzo Riccati, a Jesuit, pioneered the development of hyperbolic functions. Giordano Riccati was the first to measure the ratio of Young's moduli of metals—preceding the better known Thomas Young by 25 years.^[8]

Honors

Jacopo Riccati was named honorary Academician of the Academy of Sciences of the Institute of Bologna in 1723. The 6,5-kilometer sized main-belt asteroid 14074 Riccati, discovered at the San Vittore Observatory in 1996, was named in honor of him and his two sons, Vincenzo and Giordano.^[9]

Opere, 1761

Works

• [Opere] (in Italian). Vol. 1. Lucca: Iacopo Giusti. 1761.
• [Opere] (in Italian). Vol. 2. Lucca: Iacopo Giusti. 1762.
• [Opere] (in Italian). Vol. 3. Lucca: Iacopo Giusti. 1764.
• [Opere] (in Italian). Vol. 4. Lucca: Giuseppe Rocchi. 1765.
• M. L. Soppelsa, ed. (1985). Jacopo Riccati - Antonio Vallisneri, Carteggio (1719-1729). Florence: Leo S. Olschki. ISBN 978-8822233097.