- Grégoire de Saint-Vincent
Grégoire de Saint-Vincent (
March 22 1584 Bruges –June 5 1667 Ghent ), aJesuit , was amathematician who discovered that the area under a rectangularhyperbola (i.e. a curve given by "xy = c") is the same over [a,b] as over [c,d] when a/b = c/d. This discovery was fundamental in for the developments of the theory ofLogarithm s and an eventual recognition of thenatural logarithm (whose name and series representation where discovered byNicholas Mercator , but was only later recognized as a log of base e). The stated property allows one to define a function A(x) which is the area under said curve from 1 to x, which has the property that A(xy) = A(x)+A(y). Since this functional property characterizes logarithms, it has become mathematical fashion to call such a function A(x) a logarithm. In particular when we choose the rectangular hyperbola "xy" = 1, one recovers the "natural logarithm".To a large extent, recognition of de Saint-Vincent's achievement in quadrature of the hyperbola is due to his student and co-workerAlphonse Antonio de Sarasa , withMarin Mersenne acting as catalyst. A modern approach to his theorm uses squeeze mapping in linear algebra.Although a circle-squarer he is known for the numerous theorems which he discovered in his search for the impossible;
Jean-Étienne Montucla ingeniously remarks that "no one ever squared the circle with so much ability or (except for his principal object) with so much success." He wrote two books on the subject, one published in 1647 and the other in 1668, which cover some two or three thousand closely printed pages; the fallacy in the quadrature was pointed out byChristiaan Huygens . In the former work he usedBonaventura Cavalieri 's "method of the indivisibles". An earlier work entitled "Theoremata Mathematica", published in 1624, contains a clear account of themethod of exhaustion s, which is applied to severalquadrature s, notably that of thehyperbola .References
* Gregoire de Saint-Vincent (1647) "Opus geometricum quadraturae circuli et sectionum coni", 2 volumes, Antwerp.
*David Eugene Smith (1923) "History of Mathematics", Ginn & Co., v.1, p.425.
* Margaret E. Baron (1969) "The Origins of the Infinitesimal Calculus", Pergamon Press, Oxford et.al., see pp. 135 - 47.External links
* [http://www.faculty.fairfield.edu/jmac/sj/scientists/vincent.htm Gregory Saint Vincent, and his polar coordinates] from "Jesuit history, tradition and spirituality" by Joseph F. MacDonnell.
* [http://www.faculty.fairfield.edu/jmac/sj/jg/jg3.htm Jesuit innovations in various fields of geometry]
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