the Asymptote of an Hyperbola, in a Geometrical Progression, and the Spaces that the Perpendiculars, thereon erected, made in the Hyperbola, were equal one to the other.” A historian of the calculus noted the assimilation of natural logarithm as an area function at that time: As a consequence of the work of Gregory St. Vincent and de Sarasa, it seems to have been generally known in the 1660s that the area of a segment under the hyperbola is proportional to the logarithm of the ratio of the ordinates at the ends of the segment. Works See also History of logarithms References Karl Bopp (1907) "Die Kegelschnitte der Gregorius a St. Vincentio", Abhandlungen zum Geschichte der mathematische Wissenschaft, XX Heft. Christiaan Huygens (1651) Examen de la Cyclométrie du três savant Grégoire de Saint-Vincent, Oeuvres Complètes, Tome XI, link from Internet Archive. David Eugene Smith (1923) History of Mathematics, Ginn & Co., v.1, p. 425. Hans Wussing (2008) 6000 Jahre Mathematik: eine kulturgeschichtliche Zeitreise, S. 433, Springer, . External links Gregory Saint Vincent, and his polar coordinates from Jesuit History, Tradition and Spirituality by Joseph F. MacDonnell. 1584 births 1667 deaths Flemish Jesuits Mathematicians of the Spanish Netherlands French geometers Logarithms University of Douai alumni Jesuit scientists