Grégoire de Saint-Vincent
Encyclopedia
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Bruges
Bruges is the capital and largest city of the province of West Flanders in the Flemish Region of Belgium. It is located in the northwest of the country....
– 5 June 1667 Ghent
Ghent
Ghent is a city and a municipality located in the Flemish region of Belgium. It is the capital and biggest city of the East Flanders province. The city started as a settlement at the confluence of the Rivers Scheldt and Lys and in the Middle Ages became one of the largest and richest cities of...
), a Jesuit, was a mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
who discovered that the area under a rectangular hyperbola
Hyperbola
In mathematics a hyperbola is a curve, specifically a smooth curve that lies in a plane, which can be defined either by its geometric properties or by the kinds of equations for which it is the solution set. A hyperbola has two pieces, called connected components or branches, which are mirror...
(i.e. a curve given by xy = k) 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 of Logarithm
Logarithm
The logarithm of a number is the exponent by which another fixed value, the base, has to be raised to produce that number. For example, the logarithm of 1000 to base 10 is 3, because 1000 is 10 to the power 3: More generally, if x = by, then y is the logarithm of x to base b, and is written...
s and an eventual recognition of the natural logarithm
Natural logarithm
The natural logarithm is the logarithm to the base e, where e is an irrational and transcendental constant approximately equal to 2.718281828...
(whose name and series representation were discovered by Nicholas Mercator
Nicholas Mercator
Nicholas Mercator , also known by his Germanic name Kauffmann, was a 17th-century mathematician....
, but was only later recognized as a log of base e
E (mathematical constant)
The mathematical constant ' is the unique real number such that the value of the derivative of the function at the point is equal to 1. The function so defined is called the exponential function, and its inverse is the natural logarithm, or logarithm to base...
). 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
Quadrature (mathematics)
Quadrature — historical mathematical term which means calculating of the area. Quadrature problems have served as one of the main sources of mathematical analysis.- History :...
of the hyperbola is due to his student and co-worker Alphonse Antonio de Sarasa
Alphonse Antonio de Sarasa
Alphonse Antonio de Sarasa was a Jesuit mathematician who contributed to the understanding of logarithms, particularly as areas under a hyperbola....
, with Marin Mersenne
Marin Mersenne
Marin Mersenne, Marin Mersennus or le Père Mersenne was a French theologian, philosopher, mathematician and music theorist, often referred to as the "father of acoustics"...
acting as catalyst. A modern approach to his theorem uses squeeze mapping in linear algebra.
Although a circle-squarer
Squaring the circle
Squaring the circle is a problem proposed by ancient geometers. It is the challenge of constructing a square with the same area as a given circle by using only a finite number of steps with compass and straightedge...
he is known for the numerous theorems which he discovered in his search for the impossible; Jean-Étienne Montucla
Jean-Étienne Montucla
Jean-Étienne Montucla was a French mathematician.-Biography:Montucla was born at Lyon.In 1754 he published an anonymous treatise entitled Histoire des récherches sur la quadrature du cercle, and in 1758 the first part of his great work, Histoire des mathématiques, the first history of mathematics...
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 by Christiaan Huygens. In the former work he used Bonaventura Cavalieri
Bonaventura Cavalieri
Bonaventura Francesco Cavalieri was an Italian mathematician. He is known for his work on the problems of optics and motion, work on the precursors of infinitesimal calculus, and the introduction of logarithms to Italy...
's method of the indivisibles. An earlier work entitled Theoremata Mathematica, published in 1624, contains a clear account of the method of exhaustion
Method of exhaustion
The method of exhaustion is a method of finding the area of a shape by inscribing inside it a sequence of polygons whose areas converge to the area of the containing shape. If the sequence is correctly constructed, the difference in area between the n-th polygon and the containing shape will...
s, which is applied to several quadratures
Quadrature (mathematics)
Quadrature — historical mathematical term which means calculating of the area. Quadrature problems have served as one of the main sources of mathematical analysis.- History :...
, notably that of the hyperbola
Hyperbola
In mathematics a hyperbola is a curve, specifically a smooth curve that lies in a plane, which can be defined either by its geometric properties or by the kinds of equations for which it is the solution set. A hyperbola has two pieces, called connected components or branches, which are mirror...
.
External links
- Gregory Saint Vincent, and his polar coordinates from Jesuit history, tradition and spirituality by Joseph F. MacDonnell.
- Jesuit innovations in various fields of geometry