# Willebrord Snellius

Willebrord Snellius
Willebrord Snel van Royen (1580–1626)
Born13 June 1580
Died30 October 1626 (aged 46)
NationalityDutch
Alma materUniversity of Leiden
Known forSnell's law
Snellius' triangulation
Snellius–Pothenot problem
Scientific career
FieldsAstronomy and mathematics
InstitutionsUniversity of Leiden
Rudolph Snellius
Notable studentsJacobus Golius

Willebrord Snellius[1][2] (born Willebrord Snel van Royen)[3] (13 June 1580[4] – 30 October 1626) was a Dutch astronomer and mathematician, AKA Snell. His name is usually associated with the law of refraction of light known as Snell's law.[5]

The lunar crater Snellius is named after Willebrord Snellius. The Royal Netherlands Navy has named three survey ships after Snellius, including a currently-serving vessel.

## Biography

Willebrord Snellius was born in Leiden, Netherlands. In 1613 he succeeded his father, Rudolph Snel van Royen (1546–1613) as professor of mathematics at the University of Leiden.[6]

### Snellius' triangulation

Image: Museum Boerhaave, Leiden

In 1615, Snellius, after the work of Eratosthenes in Ptolemaic Egypt in the 3rd century BC, probably was the first to try to do a large-scale experiment to measure the circumference of the earth using triangulation.[7][8] He was helped in his measurements by two of his students, the Austrian barons Erasmus and Casparus Sterrenberg. In several cities he also received support of friends among the city leaders (regenten). In his work The terrae Ambitus vera quantitate (1617) under the author's name ("The Dutch Eratosthenes") Snellius describes the methods he used. He came up with an estimate of 28,500 Rhineland rods – in modern units 107.37 km[9] for one degree of latitude. 360 times 107.37 then gives a circumference of the Earth of 38,653 km. The actual circumference is 40,075 kilometers, so Snellius underestimated the circumference of the earth by 3.5%.

Snellius came to his result by calculating the distances between a number of high points in the plain west and southwest of the Netherlands using triangulation. In order to carry out these measurements accurately Snellius had a large quadrant built, with which he could accurately measure angles in tenths of degrees. This quadrant can still be seen in the Museum Boerhaave in Leiden. In a network of fourteen cities a total of 53 triangulation measurements were made. In his calculations Snellius made use of a solution for what is now called the Snellius–Pothenot problem.

Snellius' Triangulation (1615)

By necessity Snellius's high points were nearly all church spires. There were hardly any other 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: Alkmaar : St. Laurenskerk; Haarlem : Sint-Bavokerk; Leiden : a then new part (built in 1599) of the City walls;[10] The Hague : Sint-Jacobskerk; Amsterdam : Oude Kerk; Utrecht : Cathedral of Utrecht; Zaltbommel : Sint-Maartenskerk; Gouda : Sint Janskerk; Oudewater : Sint-Michaelskerk; Rotterdam : Sint-Laurenskerk; Dordrecht : Grote Kerk; Willemstad : Koepelkerk; Bergen-op-Zoom : Gertrudiskerk; Breda : Grote Kerk

The actual distance between the two church spires in Alkmaar and Breda, two places nearly on the same meridian,[11] is 116.1 kilometers.[12] The difference in latitude between Alkmaar (52° 37' 57" N) and Breda (51° 35' 20" N) is 1.0436 degree. Assuming Snellius corrected for this he must have calculated a distance of 107.37 * 1.0436 = 112.05 kilometers between the Sint-Laurenskerk in Alkmaar and the Grote Kerk in Breda.

Commemorative plaque on Snellius' house in Leiden

### Mathematics and physics

Snellius was also a distinguished mathematician, producing a new method for calculating π—the first such improvement since ancient times. He rediscovered the law of refraction in 1621.[13]

### Other works

Cyclometricus, 1621

In addition to the Eratosthenes Batavus, he published 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.[6]

### Death

Snellius died in Leiden in October 1626, at the age of 46 from an illness diagnosed as colic.[14] His grave can be seen in the Pieterskerk, Leiden.

Coeli et siderum in eo errantium observationes Hassicae, 1618

## Honours

Snellius Glacier in Antarctica is named after Willebrord Snellius.

## Works

• Eratosthenes Batavus (in Latin). Lugduni Batavorum: Joost van Colster, Joris Abrahamsz van der Marsce. 1617.
• Coeli et siderum in eo errantium observationes Hassicae (in Latin). Lugduni Batauorum: Joost van Colster. 1618.
• Cyclometricus (in Latin). Lugduni Batavorum: Matthijs Elzevier, Bonaventura Elzevier. 1621.
• Doctrinae triangulorum canonicae libri quatuor (in Latin). Lugduni Batavorum: Joannes Maire. 1627.

## Notes

1. ^ Willebrord Snellius at the Leiden Digital Family Tree.
2. ^ Eerste Nederlandse Systematisch Ingerichte Encyclopaedie
3. ^ Encarta Winkler Prins, Grote Oosthoek, Eerste Nederlandse Systematisch Ingerichte Encyclopaedie
4. ^ Sometimes mistakenly noted as 1590 or 1591; Cf. P.C. Molhuysen; P.J. Blok, eds. (1927). "Snellius, Willebrord". Nieuw Nederlandsch biografisch woordenboek. Leiden..
5. ^ For a reconstruction of this discovery see Hentschel 2001. It is now known that this law was already known to 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 instruments (i.e. trigonometric functions) their results were saved as tables, not functions.
6. ^ a b
7. ^ Haasbroek, N.D. (1968): Gemma Frisius, Tycho Brahe and Snellius and their triangulation. Publ. Netherl. Geod. Comm., Delft. [1]
8. ^ Torge, W.; Müller, J. (2012). Geodesy. De Gruyter Textbook. De Gruyter. p. 5. ISBN 978-3-11-025000-8. Retrieved 2 May 2021.
9. ^ a Rhenish rod is in this calculation considered as 3.767358 meter
10. ^ the tower of the Sint-Pieterskerk had collapsed in 1512
11. ^ There is a difference of two 0.02 degrees
12. ^ Calculated on the basis of the coordinates given in the Dutch language wikipedia of the Sint-Laurenskerk in Alkmaar and the Grote Kerk in Breda.
13. ^ "Snellius biographies" (PDF), dwc.knaw.nl, retrieved 15 August 2019.
14. ^ De Wreede, L. C. (2007). Willebrord Snellius (1580–1626): a humanist reshaping the mathematical sciences. Utrecht University