Willebrord Snellius

Willebrord Snellius^[1][2] (born Willebrord Snel van Royen^[3] (13 June 1580^[4] – 30 October 1626), commonly known as Snell, was a Dutch astronomer and mathematician.

Willebrord Snellius
Willebrord Snel van Royen (1580–1626)
Born	13 June 1580 Leiden, Dutch Republic
Died	30 October 1626(1626-10-30) (aged 46) Leiden, Dutch Republic
Nationality	Dutch
Alma mater	University of Leiden
Known for	Snell's law, Snellius's triangulation, Snellius–Pothenot problem
Scientific career
Fields	Astronomy and mathematics
Institutions	University of Leiden
Academic advisors	Ludolph van Ceulen Rudolph Snellius
Notable students	Jacobus Golius

His name is usually associated with the law of refraction of light known as Snell's law.^[5]

Early life

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]

Surveying

See also: Triangulation (surveying) § Willebrord Snell

Quadrant of Snellius, Museum Boerhaave, Leiden

Snellius's Triangulation (1615)

Commemorative plaque on Snellius's house in Leiden

In 1615, Snellius, after the work of Eratosthenes in Ptolemaic Egypt in the 3rd century BC, probably was the first to use triangulation to do a large-scale arc measurement for determining the circumference of the earth.^[7][8]

In his work The terrae Ambitus vera quantitate (1617) under the author's name ("The Dutch Eratosthenes") Snellius describes the methods he used. 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. 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;^[9] The Hague: Sint-Jacobskerk; Amsterdam: Oude Kerk; Utrecht: Cathedral of Utrecht; Zaltbommel: Sint-Maartenskerk [nl; de]; Gouda: Sint Janskerk; Oudewater: Sint-Michaelskerk [nl]; Rotterdam: Sint-Laurenskerk; Dordrecht: Grote Kerk; Willemstad: Koepelkerk [nl; de]; Bergen-op-Zoom: Gertrudiskerk; Breda: Grote Kerk. In a network of fourteen cities a total of 53 triangulation measurements were made. 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).^{[citation needed]}

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 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 rods – in modern units 107.37 km^[10] 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%.

Mathematics and physics

Snellius was also a distinguished mathematician, producing a new method for calculating π—the first such improvement since ancient times. He discovered the law of refraction in 1621.^[11]

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

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.^[12] His grave can be seen in the Pieterskerk, Leiden.

Legacy

Snellius Glacier in Antarctica is named after Willebrord Snellius.

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.

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.

See also

• Area of a circle – Concept in geometry