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Vicenzo 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.
Vicenzo studied hyperbolic functions and used them to obtain solutions of cubics. He found the standard addition formulas 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 Vicenzo Riccati's work (some joint with Saladini) was published between 1757 and 1767.
Vicenzo Riccati and Saladini worked on the 'rose curves' introduced by Grandi. They also worked on al'Haitam'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'Haitam had a less than satisfactory solution, Huygens found a good solution which Vicenzo Riccati and Saladini simplified and improved.
References elsewhere in this archive:
He worked on Rhodenea curves
References:
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