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**Franciscus van Schooten** (1615, Leiden – 29 May 1660, Leiden) was a Dutch mathematician who is most known for popularizing the analytic geometry of René Descartes.

**Leiden** is a city and municipality in the province of South Holland, Netherlands. The municipality of Leiden had a population of 123,856 in August 2017, but the city forms one densely connected agglomeration with its suburbs Oegstgeest, Leiderdorp, Voorschoten and Zoeterwoude with 206,647 inhabitants. The Netherlands Central Bureau of Statistics (CBS) further includes Katwijk in the agglomeration which makes the total population of the Leiden urban agglomeration 270,879, and in the larger Leiden urban area also Teylingen, Noordwijk, and Noordwijkerhout are included with in total 348,868 inhabitants. Leiden is located on the Oude Rijn, at a distance of some 20 kilometres from The Hague to its south and some 40 km (25 mi) from Amsterdam to its north. The recreational area of the Kaag Lakes (Kagerplassen) lies just to the northeast of Leiden.

A **mathematician** is someone who uses an extensive knowledge of mathematics in his or her work, typically to solve mathematical problems.

In classical mathematics, **analytic geometry**, also known as **coordinate geometry** or **Cartesian geometry**, is the study of geometry using a coordinate system. This contrasts with synthetic geometry.

Van Schooten's father was a professor of mathematics at the University of Leiden, having Christiaan Huygens, Johann van Waveren Hudde, and René de Sluze as students.

**Christiaan Huygens** was a Dutch physicist, mathematician, astronomer and inventor, who is widely regarded as one of the greatest scientists of all time and a major figure in the scientific revolution. In physics, Huygens made groundbreaking contributions in optics and mechanics, while as an astronomer he is chiefly known for his studies of the rings of Saturn and the discovery of its moon Titan. As an inventor, he improved the design of the telescope with the invention of the Huygenian eyepiece. His most famous invention, however, was the invention of the pendulum clock in 1656, which was a breakthrough in timekeeping and became the most accurate timekeeper for almost 300 years. Because he was the first to use mathematical formulae to describe the laws of physics, Huygens has been called the first theoretical physicist and the founder of mathematical physics.

Van Schooten met Descartes in 1632 and read his *Géométrie* (an appendix to his *Discours de la méthode*) while it was still unpublished. Finding it hard to understand, he went to France to study the works of other important mathematicians of his time, such as François Viète and Pierre de Fermat. When Frans van Schooten returned to his home in Leiden in 1646, he inherited his father's position and one of his most important pupils, Huygens.

**François Viète**, Seigneur de la Bigotière, was a French mathematician whose work on new algebra was an important step towards modern algebra, due to its innovative use of letters as parameters in equations. He was a lawyer by trade, and served as a privy councillor to both Henry III and Henry IV of France.

**Pierre de Fermat** was a French lawyer at the *Parlement* of Toulouse, France, and a mathematician who is given credit for early developments that led to infinitesimal calculus, including his technique of adequality. In particular, he is recognized for his discovery of an original method of finding the greatest and the smallest ordinates of curved lines, which is analogous to that of differential calculus, then unknown, and his research into number theory. He made notable contributions to analytic geometry, probability, and optics. He is best known for his Fermat's principle for light propagation and his Fermat's Last Theorem in number theory, which he described in a note at the margin of a copy of Diophantus' *Arithmetica*.

The pendant marriage portraits of him and his wife Margrieta Wijnants were painted by Rembrandt and are kept in the National Gallery of Art:^{ [1] }

**Rembrandt Harmenszoon van Rijn** was a Dutch draughtsman, painter and printmaker. An innovative and prolific master in three media, he is generally considered one of the greatest visual artists in the history of art and the most important in Dutch art history. Unlike most Dutch masters of the 17th century, Rembrandt's works depict a wide range of style and subject matter, from portraits and self-portraits to landscapes, genre scenes, allegorical and historical scenes, biblical and mythological themes as well as animal studies. His contributions to art came in a period of great wealth and cultural achievement that historians call the Dutch Golden Age, when Dutch art, although in many ways antithetical to the Baroque style that dominated Europe, was extremely prolific and innovative, and gave rise to important new genres. Like many artists of the Dutch Golden Age, such as Jan Vermeer of Delft, Rembrandt was also an avid art collector and dealer.

The **National Gallery of Art**, and its attached **Sculpture Garden**, is a national art museum in Washington, D.C., located on the National Mall, between 3rd and 9th Streets, at Constitution Avenue NW. Open to the public and free of charge, the museum was privately established in 1937 for the American people by a joint resolution of the United States Congress. Andrew W. Mellon donated a substantial art collection and funds for construction. The core collection includes major works of art donated by Paul Mellon, Ailsa Mellon Bruce, Lessing J. Rosenwald, Samuel Henry Kress, Rush Harrison Kress, Peter Arrell Browne Widener, Joseph E. Widener, and Chester Dale. The Gallery's collection of paintings, drawings, prints, photographs, sculpture, medals, and decorative arts traces the development of Western Art from the Middle Ages to the present, including the only painting by Leonardo da Vinci in the Americas and the largest mobile created by Alexander Calder.

*Portrait of a Gentleman with a Tall Hat and Gloves**Portrait of a Lady with an Ostrich-Feather Fan*

Van Schooten's 1649 Latin translation of and commentary on Descartes' *Géométrie* was valuable in that it made the work comprensible to the broader mathematical community, and thus was responsible for the spread of analytic geometry to the world.

Over the next decade he enlisted the aid of other mathematicians of the time, de Beaune, Hudde, Heuraet, de Witt and expanded the commentaries to two volumes, published in 1659 and 1661. This edition and its extensive commentaries was far more influential than the 1649 edition. It was this edition that Gottfried Leibniz and Isaac Newton knew.

**Florimond de Beaune** was a French jurist and mathematician, and an early follower of René Descartes. R. Taton calls him "a typical example of the erudite amateurs" active in 17th-century science.

**Johannes****Hudde** was a burgomaster (mayor) of Amsterdam between 1672 – 1703, a mathematician and governor of the Dutch East India Company.

**Hendrik van Heuraet** was a Dutch mathematician also known as **Henrici** van Heuraet. He is noted as one of the founders of the integral, and author of *Epistola de Transmutatione Curvarum Linearum in Rectus* [*On the Transformation of Curves into Straight Lines*] (1659). From 1653 he studied at Leiden University where he interacted with Frans van Schooten, Johannes Hudde, and Christiaan Huygens. In 1658 he and Hudde left for Saumur in France. He returned to Leiden the next year as a physician. After this his trail is lost.

Van Schooten was one of the first to suggest, in exercises published in 1657, that these ideas be extended to three-dimensional space. Van Schooten's efforts also made Leiden the centre of the mathematical community for a short period in the middle of the seventeenth century.

In elementary geometry Van Schooten's theorem is named after him.

**René Descartes** was a French philosopher, mathematician, and scientist. A native of the Kingdom of France, he spent about 20 years (1629–1649) of his life in the Dutch Republic after serving for a while in the Dutch States Army of Maurice of Nassau, Prince of Orange and the Stadtholder of the United Provinces. One of the most notable intellectual figures of the Dutch Golden Age, Descartes is also widely regarded as one of the founders of modern philosophy.

* La Géométrie* was published in 1637 as an appendix to

The year **1637 in science** and technology involved some significant events.

The year **1615 in science** and technology involved some significant events.

The year **1649 in science** and technology involved some significant events.

**René-François Walter de Sluse** was a Walloon mathematician and churchman, who served as the canon of Liège and abbot of Amay.

**Martin (Maarten) van den Hove** was a Dutch astronomer and mathematician. His adopted Latin name is a translation of the Dutch *hof* ("garden"), in Latin *horta*.

**Two-dimensional space** is a geometric setting in which two values are required to determine the position of an element. In mathematics, it is commonly represented by the symbol ℝ^{2}. For a generalization of the concept, see dimension.

In mathematics, **Hudde's rules** are two properties of polynomial roots described by Johann Hudde.

**Joris van Schooten** (1587–1651) was a Dutch Golden Age painter and the uncle of the Leiden mathematician Frans van Schooten.

**Henricus Reneri** or **Renerius** was a Dutch philosopher.

**André Warusfel** was a French mathematician and an alumnus of the École Normale Supérieure.

**Joseph Ehrenfried Hofmann** was a German historian of mathematics, known for his research on Gottfried Wilhelm Leibniz.

**Frans Oort** is a Dutch mathematician, specializing in algebraic geometry.

- ↑ Discovery of portraits of Leiden professor and his wife in NRC, 6 November 2018

- Some Contemporaries of Descartes, Fermat, Pascal and Huygens: Van Schooten, based on W. W. Rouse Ball's
*A Short Account of the History of Mathematics*(4th edition, 1908)

- Mathematische Oeffeningen van Frans van Schooten ‹See Tfd› (in Dutch)
- Biografisch Woordenboek van Nederlandse Wiskundigen: Frans van Schooten ‹See Tfd› (in Dutch)
- Frans van Schooten, and his Ruler Constructions at Convergence
- O'Connor, John J.; Robertson, Edmund F., "Frans van Schooten",
*MacTutor History of Mathematics archive*, University of St Andrews . - An e-textbook developed from Frans van Schooten 1646 by dbook

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Images, videos and audio are available under their respective licenses.