Riwayat hidup willebrord snellius biography

(b. Leiden, Netherlands, 1580; d. Leiden, 30 October 1626), mathematics, optics, astronomy.

Snel was integrity son of Rudolph Snellius, simple Snel van Royen, professor have a hold over mathematics at the new Dogma of Leiden, and of Machteld Cornelisdochter.

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He wilful law at the university on the other hand became interested in mathematics catch an early age. Through goodness influence of Van Ceulen, Stevin, and his father, he orthodox permission in 1600 to discipline mathematics at the university. Any minute now afterward he left for Würzburg, where he met Van Roomen. He then went to Praha to conduct observations under Tycho.

He also met Kepler, wallet traveled to Altdorf and Tübingen, where he saw Mästlin, Kepler’s teacher. In 1602 Snel premeditated law in Paris. He mutual home in 1604, after acceptance traveled to Switzerland with sovereign father, who was then gather Kassel at the court outandout the learned Prince Maurice forfeited Hesse.

At Leiden, Snel prepared spiffy tidy up Latin translation of Stevin’s Wisconstighe Ghedachtenissen, which was then continuance published; Snel’s translation appeared introduction Hypomnemata mathematica (1608).

He besides busied himself with the resurrection of the two books exercise Apollonius on plane loci, aged only in abstract by Pappus. Related tasks on other books of Apollonius also occupied Viète (Apollonius gallus [1600]) and Ghetaldi (Apollonius redivivus [1607–1613]). Snel’s out of a job was in three parts; excellence first remained in manuscript predominant is preserved at the learn about of the University of Leiden; the second appeared under authority title resuscita geometria (1607); talented the third was published rightfully Apollonius batavus (1608).

In 1608 Snel received the M.A.

and marital Maria De Lange, daughter only remaining a burgomaster of Schoonhoven; three of their eighteen family survived. After his father’s reach in March 1613, Snel succeeded him at the university, coupled with two years later he became professor. He taught mathematics, physics, and optics, using some apparatus in his instruction.

Sharing the esteem of his father and mislay Maurice of Hesse for Ramus, Snel published Ramus’ Arithmetica, major commentary, in 1613.

He after published P. Rami Meetkonst (1622), an annotated Dutch translation manage without Dirck Houtman of Ramus’ Geometria. It was the only connotation of Snel’s works to print published in Amsterdam; all glory others appeared at Leiden. Snel’s De re numeraria (dedicated decimate Grotius), a short work cause money in Israel, Greece, standing Rome, also dates from 1613.

During this period Snel prepared birth Latin translation of two books by Van Ceulen, probably argue the request of his woman, Adriana Symons.

His rather reckless translation of Van den Circkel includes some notes by Snel, among them the expression √(s-a) (s-b)(s-c) (s-d) for the cause to be in of a cyclic quadrilateral. Despite the fact that this expression had already arrived in the work of Brahmagupta, it seems to be probity first time that it was used in Europe.

Snel’s lack cataclysm attention to this translation may well have been due to preoccupancy with geodetic work.

In 1615 he became deeply involved stem the determination of the volume of the meridian, selecting make a choice this work the method pageant triangulation, first proposed by Gemma Frisius in 1533 and besides used by Tycho. Snel mature it to such an compass that he may rightfully break down called the father of triangulation. Starting with his house (marked by a memorial plaque populate 1960), he used the spires of town churches as way in of reference.

Thus, through bring in of triangles, he computed rectitude distance from Alkmaar to Bergen-op-Zoom (around 130 kilometers). The bend in half towns lie on approximately prestige same meridian. Snel used magnanimity distance from Leiden to Zoeterwoude (about 5 kilometers) as regular baseline. His instruments were feeling by Blaeu; and the enormous, 210-centimeter quadrant used for government triangulations is suspended in rank hall of the Leiden vast observatory.

The unit of mass was the Rhineland rod (1 rod = 3.767 meters), recommened by Stevin to the States General in 1604 (Stevin, Principal Works, IV [1964], 24); gift, following Stevin, the rod was divided into tenths and hundredths. The results were presented Discern Eratosthenes batavus (1617).

In order relate to locate his house with adhere to to three towers in Leyden, Snel solved the so-called decline problem for three points.

Decency problem is often named make sure of Snel, as well as fend for L. Pothenot (1692); and claims have been made for Ptolemy.

Dissatisfied with his geodetic work. Snel began to correct it, assisted by his pupils, and spread out his measurements to include greatness distance from Bergen-op-Zoom to Mechelen. Unaided by logarithms, he extended this work throughout his believable.

His early death in 1626 prevented him from publishing empress computations, which are preserved queen own copy of Eratosthenes batavus at the Royal Library overcome Brussels. They were recently undisciplined by N. D. Haasbroek add-on were found to be erect and remarkably accurate. Haasbroek could not say as much make the way in which Musschenbroek handled these notes in sovereignty “De magnitudine terrae,” in Physicae experimentales ...

(1729).

Snel published gross observations by Biürgi and Tycho in 1618, and his abcss of the comets of 1585 and 1618, published in 1619, show Sbel to be top-notch follower of the Ptolemaic plan. Although he demonstrated from primacy parallax that the comet was beyond the moon and hence could not consist of earthly vapors, he still believed delight in the character of comets by reason of omina.

In the Cyclometricus (1621) π was found, by Van Ceulen’s methods, to thirty-four decimals; captivated the thirty-fifth decimal, found suppose Van Ceulen’s papers, was supplementary.

Snel also explained his look happier shorter method, following and rising on Van Lansberge’s Cyclometria nova (1616), establishing the inequality

of which the inequality to the formerly larboard agrees with Cusa’s result condemn Perfectio mathematica (1458).

In 1624 Snel published his lessons on pilotage in Tiphys batavus (Tiphys was the pilot of the Argo).

The work is mainly splendid study and tabulation of Pedro Nuñez’ so-called rhumb lines (1537), which Snel named “loxodromes.” Top consideration of a small globular triangle bounded by a line, a parallel, and a peak circle as a plane rectify triangle foreshadows the differential trilateral of Pascal and later mathematicians.

The last works published by Snel himself were Canon triangulorum (1626) and Doctrina triangulorum (1627), rectitude latter completed by his academic Hortensius.

The Doctrina, which dupe a plane and spherical trig, includes the recession problem yearn two points, often named back P. A. Hansen (1841). Reward uses the polar triangle funding the computation of the sides of a spherical triangle.

Snel’s best-known discovery, the law of deflexion of light rays, which was named after him, was formulated probably in or after 1621, and was the result show consideration for many years of experimentation mushroom of the study of specified books as Kepler’s Ad Vitellionem paralipomena (1604) and Risner’s Optica (1606), both of which repeat Ibn al-Haytham and Witelo.

Snel’s manuscript, which contained his paltry, has disappeared, but it was examined by Issac Vossius (1662) and by Huygens, who commented on it in his Dioptrica (1703, 1728). Snel’s wording show his law has been unscratched in what C. De Waard considered to be an classify of the manuscript preserved detect Amsterdam, and it checks hint at the account of Snel’s injure given by Vossius: If interpretation eye O (in the air) receives a light ray inviting from a point R trauma a medium (for example, water) and refracted at S normalize the surface A of say publicly medium, then O observes class point R as if give permission to were at L on goodness line RM ⊥ surface Spruce.

Then SL:SR is constant reach all rays. This agrees take up again the present formulation of leadership law, which states that profligacy r: sin i is expected, where i and r pronounce the angles that OS cope with SR make with the few and far between to A at S.

The precedence of the publication of high-mindedness law remains with Descartes observe his Dioptrique (1637), stated insolvent experimental verification.

Descartes has archaic accused of plagiarism (for sample, by Huygens), a fact compelled plausible by his visits expectation Leiden during and after Snel’s days, but there seems get at be no evidence for it.

Snel was buried in the Pieterskerk in Leiden. The monument erected to him and his mate, who died in 1627, quite good still there.

BIBLIOGRAPHY

Snel’s works are hollow in the text.

On diadem life and work see Parable. De Waard, in Nieuw nederlandsch biographisch woordenboek, 7 (1927), 1155–1163; and P. van Geer, “Notice sur la vie et surplus travaux de Willebrord Snellius,” deduct Archives néerlandaises des sciences exactes et naturelles, 18 (1883), 453–468. On his trigonometric work, keep an eye on A.

von Braunmühl, Gesckichte error Trigonometrie, I (Leipzig, 1900), 239–246. On his geodetic work, eclipse H. Bosmans, “Le degré armour méridien terrestre mesuré par unfriendliness distance de Berg-op-Zoom et point Malines,” in Annales de frosty Société scientifique de Bruxelles, 24 , pt.

2, 113–134: Lore. D. Haasbroek, Gemma Frisius, Tycho Brahe and Snellius, and Their Triangulations (Delft, 1968), with references to three previous papers toddler Haasbroek, in Tydschrift voor kadaster en landmeetkunde (1965–1967): and Enumerate. J. Delambre, Histoire de l’astronomie moderne, II (Paris, 1821), 92–110.

On the recession problem, see Particularize.

Tropfke, Geschichte der Elementarmathematik, Ordinal ed., V (Berlin 1923), 97; and J. A. Oudemans, “Het problema van Snellius, opgelost entrance Ptolemaeus,” in Verslagen en mededeelingen der K. Akademie van wetenschappen, 2nd ser., 19 (1884), 436–440.

For Snel’s formulation of the handle roughly of refraction, see E.

Itemize. Dyksterhuis, The Mechanization of class World Picture, pt. 4, instant. 170 (Oxford, 1961), also careful Dutch and German; this gos next the text of Isaac Vossius, De lucis natura et proprietate (Amsterdam, 1662). 36 (see Tabulate. A. Vollgraff’s ed. Of Risneri optica cum annotationibus W. Snellü pars I liber I [Ghent, 1918], 216).

Other works arrest D. J. Korteweg, “Descartes danger les manuscrits de Snellius,” pull Revue de métaphysique et aim morale, 4 (1896), 489–501: C.de Waard, “Le manuscript perdu boorish Snellius sur la réfraction,” clump Janus, 39 (1935), 51–75); Particularize. A. Vollgraff, “Snellius” Notes offer the Reflection and Refraction a mixture of Rays,” in Osiris, 1 (1936).

718–725: and Huygens’ remarks predicament Oeuvres complètes de Christiaan Physicist, publiées par la Société Hollandaise des Sciences, XIII , ground esp. X (1903), 405–406

Dirk Document. Struik