View source for Willebrord Snellius

{{Short description|Dutch astronomer and mathematician (1580-1626)}}
{{Lead too short|date=July 2025}}
{{Expand language |langcode=nl |topic=sci |otherarticle=Willebrord Snel van Royen |date=August 2021}}
{{ infobox scientist
| image             = Willebrord Snellius.jpg
| caption           = Willebrord Snel van Royen (1580–1626)
| birth_date        = 13 June 1580
| birth_place       = [[Leiden]], [[Dutch Republic]]
| death_date        = {{death date and age|df=yes|1626|10|30|1580|6|13}}
| death_place       = [[Leiden]], [[Dutch Republic]]
| nationality       = [[Dutch people|Dutch]]
| field             = [[Astronomy]] and [[mathematics]]
| work_institution  = [[University of Leiden]]
| alma_mater        = [[University of Leiden]]
| academic_advisors = [[Ludolph van Ceulen]]<br />[[Rudolph Snellius]]
| notable_students  = [[Jacobus Golius]]
| known_for         = [[Snell's law]], [[Triangulation (surveying)#Willebrord Snell|Snellius's triangulation]], [[Snellius–Pothenot problem]]
}}

'''Willebrord Snellius'''<ref>[https://web.archive.org/web/20110718181424/http://leiden.digitalestamboom.nl/(hylpyvfkxtrpov55tfin4u2g)/detailx.aspx?p=1587788&ID=334195&book=T&role=G&page= Willebrord Snellius] at the Leiden Digital Family Tree.</ref><ref>[[Eerste Nederlandse Systematisch Ingerichte Encyclopaedie]]</ref> (born '''Willebrord Snel van Royen'''<ref>Encarta Winkler Prins, [[Grote Oosthoek]], [[Eerste Nederlandse Systematisch Ingerichte Encyclopaedie]]</ref> (13 June 1580<ref>Sometimes mistakenly noted as 1590 or 1591; Cf. {{cite web|url=http://www.dbnl.org/tekst/molh003nieu07_01/molh003nieu07_01_1918.php|editor1=[[Philipp Christiaan Molhuysen|P.C. Molhuysen]]|editor2=[[Petrus Johannes Blok| P.J. Blok]] | title = Snellius, Willebrord|website=Nieuw Nederlandsch biografisch woordenboek|volume=7|place=Leiden|year= 1927}}.</ref>{{spnd}}30 October 1626), commonly known simply as '''Snellius''' and '''Snell''', was a Dutch [[astronomer]] and [[mathematician]].

Snell is best known for the law of [[refraction]] of light known as [[Snell's law]], his pioneering work in survey known as [[Triangulation (surveying)#Willebrord Snell|Snellius's triangulation]], and the [[Snellius–Pothenot problem]], a means in planar trigonometry of finding an unknown point from known ones. 

Despite being commonly attributed to Snell, the law of refraction was discovered by the Persian scientist [[Ibn Sahl (mathematician)|Ibn Sahl]] around 984 AD.<ref>For a reconstruction of this discovery see [https://www.academia.edu/20607033/Das_Brechungsgesetz_in_der_Fassung_von_Snellius Hentschel 2001]. It is now known that this law was already known to [[Ibn Sahl (mathematician)|Ibn Sahl]] in 984. The same law was also investigated by [[Ptolemy]] and in the Middle Ages by [[Witelo]], but due to lack of adequate [[Mathematical instrument|mathematical instruments]] (i.e. trigonometric functions) their results were saved as tables, not functions.</ref>

== Early life ==
Willebrord Snellius was born in [[Leiden]], [[Netherlands]]. In 1613 he succeeded his father, [[Rudolph Snellius|Rudolph Snel van Royen]] (1546–1613) as professor of [[mathematics]] at the [[University of Leiden]].{{sfn|Chisholm|1911}}

== Surveying ==
{{see also|Triangulation (surveying)#Willebrord Snell}}
[[file:Museum_Boerhaave - Snellius_quadrant.jpg|thumb|left|[[Quadrant (instrument)|Quadrant]] of Snellius, [[Museum Boerhaave]], Leiden]]
[[file:Triangulation Pays-Bas Snellius.jpg|thumb|left|Snellius's Triangulation (1615)]]
[[file:Plaquete huis Willebrord Snellius.jpg|thumb|[[Commemorative plaque]] on Snellius's house in Leiden]]

In 1615, Snellius, became the first known surveyor since [[Eratosthenes]] in 3rd century BC [[Ptolemaic Kingdom|Ptolemaic Egypt]] to use [[triangulation (surveying)|triangulation]] to make a large-scale [[arc measurement]] to determine the [[Earth radius|Earth's circumference]].<ref>Haasbroek, N.D. (1968): Gemma Frisius, Tycho Brahe and Snellius and their triangulation. Publ. Netherl. Geod. Comm., Delft. [https://ncgeo.nl/downloads/14Haasbroek.pdf] {{Webarchive|url=https://web.archive.org/web/20201126211006/https://ncgeo.nl/downloads/14Haasbroek.pdf |date=26 November 2020 }}</ref><ref name="Torge Müller 2012 p. 5">{{cite book | last1=Torge | first1=W. | last2=Müller | first2=J. | title=Geodesy | publisher=De Gruyter | series=De Gruyter Textbook | year=2012 | isbn=978-3-11-025000-8 | url=https://books.google.com/books?id=RcfmBQAAQBAJ&pg=PA6 | access-date=2021-05-02 | page=5}}</ref>

In his work ''The terrae Ambitus vera quantitate'' (1617) under the author's name ("The Dutch Eratosthenes") Snellius describes achieving his result by calculating the distances between a number of high points in the plain west and southwest of the Netherlands using [[triangulation]]. By necessity Snellius's high points were nearly all [[spire|church spire]]s, virtually the only tall buildings at that time in the west of the Netherlands. More or less ordered from north to south and/or in successive order of measuring, Snellius used a network of fourteen measure points to make a total of 53 triangulation measurements.

These cities were: [[Alkmaar]]: [[Grote or Sint-Laurenskerk (Alkmaar)|St. Laurenskerk]]; [[Haarlem]]: [[Sint-Bavokerk]]; [[Leiden]]: a then new part (built in 1599) of the [[city wall]]s;<ref>the tower of the [[Pieterskerk, Leiden|Sint-Pieterskerk]] had collapsed in 1512</ref> [[The Hague]]: [[Grote or Sint-Jacobskerk (The Hague)|Sint-Jacobskerk]]; [[Amsterdam]]: [[Oude Kerk, Amsterdam|Oude Kerk]]; [[Utrecht (city)|Utrecht]]: [[Cathedral of Utrecht]]; [[Zaltbommel]]: {{ill|Grote or Sint-Maartenskerk, Zaltbommel|lt=Sint-Maartenskerk|nl|Grote of Sint-Maartenskerk (Zaltbommel)|de|Grote of Sint-Maartenskerk (Zaltbommel)}}; [[Gouda, South Holland|Gouda]]: [[Sint Janskerk]]; [[Oudewater]]: {{ill|Grote or Sint-Michaelskerk, Oudewater|lt=Sint-Michaelskerk|nl|Grote of Sint-Michaëlskerk (Oudewater)}}; [[Rotterdam]]: [[Grote or Sint-Laurenskerk (Rotterdam)|Sint-Laurenskerk]]; [[Dordrecht]]: [[Grote Kerk, Dordrecht|Grote Kerk]]; [[Willemstad, North Brabant|Willemstad]]: {{ill|Koepelkerk, Willemstad|lt=Koepelkerk|nl|Koepelkerk (Willemstad)|de|Koepelkerk (Willemstad)}}; [[Bergen-op-Zoom]]: [[Gertrudiskerk]]; [[Breda]]: [[Grote Kerk (Breda)|Grote Kerk]].  

Snellius was helped in measuring by two of his students, the Austrian barons Erasmus and Casparus Sterrenberg. In several cities he also received support of friends among the civic leaders (''[[regenten]]'').{{cn|date=July 2025}}

In order to carry out these measurements accurately Snellius had a large [[quadrant (instrument)|quadrant]] built, with which he could accurately measure angles in tenths of degrees. This instrument can still be seen in the [[Museum Boerhaave]] in Leiden. In his calculations Snellius made use of a solution for what is now called the [[Snellius–Pothenot problem]].

He came up with an estimate of 28,500 Rhineland [[rod (unit)|rods]] – in modern units 107.37 [[kilometer|km]]<ref>a Rhenish rod is in this calculation considered as 3.767358 meter</ref> for one degree of [[latitude]]. 360 times 107.37 then gives a [[circumference of the Earth]] of 38,653&nbsp;km. The actual circumference is 40,075 kilometers, making Snellius' estimate 3.5% low.

== Mathematics and physics ==
Snellius was also a distinguished mathematician, producing a new method for calculating [[pi|π]]—the first such improvement since ancient times. He discovered the [[law of refraction]] in 1621.<ref>{{Citation | url = https://www.dwc.knaw.nl/wp-content/berkelbio/49.snellius.pdf | title = Snellius biographies | work = dwc.knaw.nl| access-date = 15 August 2019}}.</ref>

== Other works ==
[[file:Snell - Cyclometricus, 1621 - 183410.jpg|thumb|''Cyclometricus'', 1621]]

In addition to the ''Eratosthenes Batavus'', he published {{lang|la|Cyclometricus, de circuli dimensione}} (1621), and ''Tiphys Batavus'' (1624). He also edited ''Coeli et siderum in eo errantium observationes Hassiacae'' (1618), containing the astronomical observations of Landgrave [[William IV of Hesse]]. A work on [[trigonometry]] (''Doctrina triangulorum'') authored by Snellius was published a year after his death.{{sfn|Chisholm|1911}}

== Death ==
[[file:Snell, Willebrord – Coeli et siderum in eo errantium observationes Hassicae, 1618 – BEIC 4708164.jpg|thumb|''Coeli et siderum in eo errantium observationes Hassicae'', 1618]]

Snellius died in Leiden in October 1626, at the age of 46 from an illness diagnosed as [[colic]].<ref>De Wreede, L. C. (2007). Willebrord Snellius (1580–1626): a humanist reshaping the mathematical sciences. Utrecht University</ref> His grave can be seen in the [[Pieterskerk, Leiden]].

== Legacy ==
[[Snellius Glacier]] in [[Antarctica]] is named after Willebrord Snellius.

The [[lunar crater]] [[Snellius (crater)|Snellius]] is named after Willebrord Snellius.

The Royal Netherlands Navy has named three survey ships after Snellius, including a [[HNLMS Snellius (A802)|currently-serving vessel]].

== Works ==
* {{ cite book | publisher = Joost van Colster, Joris Abrahamsz van der Marsce | language = la | title = Eratosthenes Batavus | location = Lugduni Batavorum | year = 1617 | url = https://gutenberg.beic.it/webclient/DeliveryManager?pid=4708711&search_terms=DTL6 }}
* {{ cite book | publisher = Joost van Colster | language = la | title = Coeli et siderum in eo errantium observationes Hassicae | location = Lugduni Batauorum | year = 1618 | url = https://gutenberg.beic.it/webclient/DeliveryManager?pid=4708164&search_terms=DTL6 }}
* {{ cite book | publisher = Matthijs Elzevier, Bonaventura Elzevier | language = la | title = Cyclometricus | location = Lugduni Batavorum | year = 1621 | url = https://gutenberg.beic.it/webclient/DeliveryManager?pid=183410&search_terms=DTL4 }}
* {{ cite book | publisher = Joannes Maire | language = la | title = Doctrinae triangulorum canonicae libri quatuor | location = Lugduni Batavorum | year = 1627 | url = https://gutenberg.beic.it/webclient/DeliveryManager?pid=184714&search_terms=DTL4 }}

== See also ==
* {{anl|Area of a circle}}

== Notes ==

{{refs}}

== References ==
{{refbegin}}
* [http://dspace.library.uu.nl/handle/1874/22992 Willebrord Snellius (1580-1626): a humanist reshaping the mathematical sciences, thesis of Liesbeth de Wreede, Dissertation Utrecht 2007]
* N. Haasbroek: ''[https://web.archive.org/web/20110722200119/http://www.ncg.knaw.nl/Publicaties/Groen/pdf/14Haasbroek.pdf Gemma Frisius, Tycho Brahe and Snellius and their triangulations]''. Delft 1968.
*{{DSB|first=Dirk Jan|last=Struik|authorlink=Dirk Jan Struik|title=Snel, Willebrord|volume=XII}}
*{{cite encyclopedia|encyclopedia=Nieuw Nederlandsch Biografisch Woordenboek|title=Snellius (Willebrord)|volume=VII}}
*{{MacTutor Biography|id=Snell|title=Willebrord van Royen Snell}}
*{{EB1911|wstitle=Snell, Willebrord|volume=25|page=293}}
* [[Klaus Hentschel]]: ''Das Brechungsgesetz in der Fassung von Snellius. Rekonstruktion seines Entdeckungspfades und eine Übersetzung seines lateinischen Manuskriptes sowie ergänzender Dokumente.'' Archive for History of Exact Sciences 55,4 (2001), doi:10.1007/s004070000026.
{{refend}}

== External links ==
{{commonscat}}

* {{MathGenealogy}}
* {{OL author}} {{in lang|la}}
* {{Internet Archive author|sopt=t}} {{in lang|la}}

{{Authority control}}
{{Use dmy dates|date=March 2016}}
{{DEFAULTSORT:Snellius, Willebrord}}
[[Category:17th-century Dutch mathematicians]]
[[Category:1580 births]]
[[Category:1626 deaths]]

[[Category:Burials at Pieterskerk, Leiden]]
[[Category:17th-century Dutch astronomers]]
[[Category:Geodesists]]
[[Category:Academic staff of Leiden University]]
[[Category:Dutch mathematics educators]]