Hendrik van Heuraet (1634 - 1660?), also known as Henrici van Heuraet, was a Dutch

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematica ...

. He is noted as one of the founders of the

integral In mathematics, an integral is the continuous analog of a Summation, sum, which is used to calculate area, areas, volume, volumes, and their generalizations. Integration, the process of computing an integral, is one of the two fundamental oper ...

, and author of ''Epistola de Transmutatione Curvarum Linearum in Rectus'' 'On the Transformation of Curves into Straight Lines''(1659).

Life

He was born in 1634 and became financially independent after he inherited his father's estate - who was a cloth merchant - when he was 21 years old. From 1653 he initially studied medicine at

Leiden University Leiden University (abbreviated as ''LEI''; ) is a Public university, public research university in Leiden, Netherlands. Established in 1575 by William the Silent, William, Prince of Orange as a Protestantism, Protestant institution, it holds the d ...

, where he became acquainted with

Frans van Schooten Frans van Schooten Jr. also rendered as Franciscus van Schooten (15 May 1615 – 29 May 1660) was a Dutch mathematician who is most known for popularizing the analytic geometry of René Descartes. He translated La Géométrie in Latin and wrote c ...

and later

Johannes Hudde Johannes (van Waveren) Hudde (23 April 1628 – 15 April 1704) was a mathematician, burgomaster (mayor) of Amsterdam between 1672 – 1703, and governor of the Dutch East India Company. Hudde initially studied law at the University of Le ...

and

Christiaan Huygens Christiaan Huygens, Halen, Lord of Zeelhem, ( , ; ; also spelled Huyghens; ; 14 April 1629 – 8 July 1695) was a Dutch mathematician, physicist, engineer, astronomer, and inventor who is regarded as a key figure in the Scientific Revolution ...

. He continued studying medicine, but decided to study mathematics privately with Van Schooten. In 1658 he and Hudde left for

Saumur Saumur () is a Communes of France, commune in the Maine-et-Loire Departments of France, department in western France. The town is located between the Loire and Thouet rivers, and is surrounded by the vineyards of Saumur itself, Chinon, Bourgu ...

in France. From Saumur he wrote a letter to van Schooten entitled ''Epistola de transmutatione curvarum linearum in rectas'' (On the Transformation of Curves into Straight Lines). He returned to Leiden the next year as a

physician A physician, medical practitioner (British English), medical doctor, or simply doctor is a health professional who practices medicine, which is concerned with promoting, maintaining or restoring health through the Medical education, study, Med ...

. After this his trail is lost.

Work

Van Heuraet's work was published in Van Schooten's edited Latin translation of Descartes' ''

La Géométrie ''La Géométrie'' () was published in 1637 as an appendix to ''Discours de la méthode'' ('' Discourse on the Method''), written by René Descartes. In the ''Discourse'', Descartes presents his method for obtaining clarity on any subject. ''La ...

'' of 1659. This work also contained appendices by

Johan de Witt Johan de Witt (24 September 1625 – 20 August 1672) was a Dutch statesman and mathematician who was a major political figure during the First Stadtholderless Period, when flourishing global trade in a period of rapid European colonial exp ...

and

. It contained two papers written by Van Heuraet. In one of the papers, Van Heureaet gives the construction of

inflection point In differential calculus and differential geometry, an inflection point, point of inflection, flex, or inflection (rarely inflexion) is a point on a smooth plane curve at which the curvature changes sign. In particular, in the case of the graph ...

s on the conchoid; the importance of the discovery of properties of curves of this type eventually led to methods which gave rise to the differential and integral

calculus Calculus is the mathematics, mathematical study of continuous change, in the same way that geometry is the study of shape, and algebra is the study of generalizations of arithmetic operations. Originally called infinitesimal calculus or "the ...

. In particular, in the paper, he computed an

and applied his methods to the parabola. Furthermore, Van Heuraet proved in his papers that he could find the

arc length Arc length is the distance between two points along a section of a curve. Development of a formulation of arc length suitable for applications to mathematics and the sciences is a problem in vector calculus and in differential geometry. In the ...

of the

semicubical parabola In mathematics, a cuspidal cubic or semicubical parabola is an algebraic plane curve that has an implicit equation of the form : y^2 - a^2 x^3 = 0 (with ) in some Cartesian coordinate system. Solving for leads to the ''explicit form'' : y = \ ...

, which eventually led to a priority dispute with

Bibliography

References

External links

*
Geometria, à Renato Des Cartes Anno 1637
' (1683) with ''Epistola de Transmutatione Curvarum Linearum in Rectus'', p. 517, @GoogleBooks.

at Turnbull WWW server

(Dutch) {{DEFAULTSORT:Heuraet, Hendrik van 1633 births 1660s deaths 17th-century Dutch mathematicians People from Haarlem Leiden University alumni