Gregory of St Vincent and the rectangular hyperbola

Abstract

The Belgian Jesuit, Gregory of St Vincent (1584 - 1667), along with Cavaleri, Fermat and Descartes was amongst those who prepared the way for the calculus of Newton and Leibniz. He was the author of one long book Opus Geometricum (1647) in which he gave a more precise account of progressions and limits than had been previously available and which Leibniz particularly valued. The term ‘exhaustion’, for the limiting process of the Greeks, is due to Gregory of St Vincent. This book contains a section on the hyperbola in which Gregory studied the area between the curve and an asymptote and this section provided the basis for Anthony de Sarasa's claim in 1649 that the area here was like a logarithm.