Vincenzo Riccati was born in 1707 in Castelfranco Veneto, a small town about 30 km north of Padua.

[2] He began his studies at the College of St. Francis Xavier in Bologna, under the guidance of Luigi Marchenti, a pupil of the French mathematician Pierre Varignon.

In 1739 he was assigned to the College of St. Francis Xavier of Bologna, where he taught mathematics for thirty years, succeeding his former teacher Luigi Marchenti.

[5] Riccati's main research continued the work of his father in mathematical analysis, especially in the fields of the differential equations and physics.

In 1746 and 1749 Riccati published two works, in which he discussed the question of the parallelogram of forces in the context of the vis viva controversy.

In 1752, he published the short treatise De usu motus tractorii in constructione aequationum differentialium, in which he proved that all first-order (ordinary) differential equations conceivable at the time could be constructed using tractional motion.

[6] Riccati's main contributions to mathematics and physics were published in two volumes, Opusculorum ad res physicas mathematicas pertinentium (Bologna, 1757-1762), where he introduced the use of hyperbolic functions.

Ten years later Saladini produced an Italian translation of the work under the title Instituzioni Analitiche.

Riccati's Institutiones analyticae is the fullest 18th-century Italian treatise on analytic methods in mathematics.

After the suppression of the Society of Jesus, Riccati retired to his family home in Treviso, where he died on January 17, 1775.

[7] His efforts and implementations of flood control projects saved the regions around Venice and Bologna.

Vincenzo Riccati (1757) introduced hyperbolic functions cosh and sinh, which he denoted as Ch.

with r being set to unity in modern publications, and formulated the addition laws of hyperbolic sine and cosine: He furthermore showed that