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Vincenzo Riccati was the second son of Jacopo Riccati and his early education was at home and from the Jesuits. He entered the Jesuit order in 1726 going to the Jesuit College in Piacenza in 1728 to teach literature. In 1729 he moved to Padua, then to Parma in 1734, studied theology in Rome for a while, then returned to Bologna in 1739 where he taught mathematics in the College of San Francesco Saverio for 30 years.
Vincenzo continued his father's work on integration and differential equations. He was skilled in hydraulic engineering and carried out flood control projects which saved the Venetian and Bolognian region from flooding.
Vincenzo studied hyperbolic functions and used them to obtain solutions of cubics. He found the standard addition formulae for hyperbolic functions, their derivatives and their relation to the exponential function. Lambert is often cited as the first to introduce the hyperbolic fuctions but he did not do so until 1770 while Vincenzo Riccati's work (some joint with Saladini) was published between 1757 and 1767.
Vincenzo Riccati and Saladini worked on the 'rose curves' introduced by Grandi. They also worked on Alhazen (al-Haytham)'s problem:-
Given points A and B find the point C on a circular mirror so that a ray of light from A is reflected at C to B.
Al-Haytham had a less than satisfactory solution, Huygens found a good solution which Vincenzo Riccati and Saladini simplified and improved.
Article by: J J O'Connor and E F Robertson
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