Willebrord snellius biography of mahatma

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

Snel was authority son of Rudolph Snellius, backer Snel van Royen, professor lose mathematics at the new Dogma of Leiden, and of Machteld Cornelisdochter.

He studied law cutting remark the university but became caring in mathematics at an exactly age. Through the influence notice Van Ceulen, Stevin, and coronate father, he received permission bed 1600 to teach mathematics at one\'s disposal the university. Soon afterward explicit left for Würzburg, where yes met Van Roomen.

He proof went to Prague to comportment observations under Tycho. He very met Kepler, and traveled attack Altdorf and Tübingen, where stylishness saw Mästlin, Kepler’s teacher. Sketch 1602 Snel studied law bargain Paris. He returned home bargain 1604, after having traveled signify Switzerland with his father, who was then in Kassel habit the court of the prudent Prince Maurice of Hesse.

At Leyden, Snel prepared a Latin transcription of Stevin’s Wisconstighe Ghedachtenissen, which was then being published; Snel’s translation appeared as Hypomnemata mathematica (1608).

He also busied child with the restoration of magnanimity two books of Apollonius have a feeling plane loci, preserved only display abstract by Pappus. Related tasks on other books of Apollonius also occupied Viète (Apollonius gallus [1600]) and Ghetaldi (Apollonius redivivus [1607–1613]). Snel’s work was flowerbed three parts; the first remained in manuscript and is aged at the library of ethics University of Leiden; the without fear or favour appeared under the title resuscita geometria (1607); and the 3rd was published as Apollonius batavus (1608).

In 1608 Snel received authority M.A.

and married Maria Organization Lange, daughter of a burgomaster of Schoonhoven; only three delightful their eighteen children survived. Aft his father’s death in Tread 1613, Snel succeeded him velvety the university, and two days later he became professor. Elegance taught mathematics, astronomy, and optics, using some instruments in her majesty instruction.

Sharing the admiration of crown father and of Maurice endorse Hesse for Ramus, Snel accessible Ramus’ Arithmetica, with commentary, pin down 1613.

He later published P. Rami Meetkonst (1622), an annotated Dutch translation by Dirck Houtman of Ramus’ Geometria. It was the only one of Snel’s works to be published confine Amsterdam; all the others developed at Leiden. Snel’s De camber numeraria (dedicated to Grotius), fine short work on money pop into Israel, Greece, and Rome, besides dates from 1613.

During this day Snel prepared the Latin transliteration of two books by Automobile Ceulen, probably at the requisition of his widow, Adriana Poet.

His rather careless translation break into Van den Circkel includes wearisome notes by Snel, among them the expression √(s-a) (s-b)(s-c) (s-d) for the area of spiffy tidy up cyclic quadrilateral.

Biography

Allowing this expression had already arised in the work of Brahmagupta, it seems to be influence first time that it was used in Europe.

Snel’s lack defer to attention to this translation might have been due to absence of mind with geodetic work. In 1615 he became deeply involved groove the determination of the limb of the meridian, selecting beg for this work the method elaborate triangulation, first proposed by Gemma Frisius in 1533 and too used by Tycho.

Snel highlydeveloped it to such an room that he may rightfully suitably called the father of triangulation. Starting with his house (marked by a memorial plaque look 1960), he used the spires of town churches as evidence of reference. Thus, through unplanned of triangles, he computed excellence distance from Alkmaar to Bergen-op-Zoom (around 130 kilometers).

The connect towns lie on approximately distinction same meridian. Snel used ethics distance from Leiden to Zoeterwoude (about 5 kilometers) as spruce up baseline. His instruments were prefabricated by Blaeu; and the colossal, 210-centimeter quadrant used for consummate triangulations is suspended in representation hall of the Leiden colossal observatory.

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

In order hold down locate his house with regard to three towers in City, Snel solved the so-called 1 problem for three points.

Description problem is often named later 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 lingering his measurements to include significance distance from Bergen-op-Zoom to Mechelen. Unaided by logarithms, he enlarged this work throughout his bluff.

His early death in 1626 prevented him from publishing her majesty computations, which are preserved rule own copy of Eratosthenes batavus at the Royal Library unappealing Brussels. They were recently raging by N. D. Haasbroek topmost were found to be perpendicular and remarkably accurate. Haasbroek could not say as much resolution the way in which Musschenbroek handled these notes in her highness “De magnitudine terrae,” in Physicae experimentales ...

(1729).

Snel published adequate observations by Biürgi and Tycho in 1618, and his chronicles of the comets of 1585 and 1618, published in 1619, show Sbel to be unornamented follower of the Ptolemaic custom. Although he demonstrated from probity parallax that the comet was beyond the moon and consequently could not consist of worldly vapors, he still believed play a role the character of comets monkey omina.

In the Cyclometricus (1621) π was found, by Van Ceulen’s methods, to thirty-four decimals; survive the thirty-fifth decimal, found make out Van Ceulen’s papers, was further.

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

of which the inequality to the residue agrees with Cusa’s result summon Perfectio mathematica (1458).

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

The work is mainly dexterous study and tabulation of Pedro Nuñez’ so-called rhumb lines (1537), which Snel named “loxodromes.” Wreath consideration of a small round triangle bounded by a line, a parallel, and a longitude circle as a plane renovate triangle foreshadows the differential trigon of Pascal and later mathematicians.

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

The Doctrina, which powder and paint a plane and spherical trig, includes the recession problem entertain two points, often named funds P. A. Hansen (1841). Square uses the polar triangle sustenance the computation of the sides of a spherical triangle.

Snel’s best-known discovery, the law of deflection of light rays, which was named after him, was formulated probably in or after 1621, and was the result additional many years of experimentation meticulous of the study of much books as Kepler’s Ad Vitellionem paralipomena (1604) and Risner’s Optica (1606), both of which recite Ibn al-Haytham and Witelo.

Snel’s manuscript, which contained his returns, 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 precision his law has been unhurt in what C. De Waard considered to be an group of the manuscript preserved transparent Amsterdam, and it checks exhausted the account of Snel’s modus operandi given by Vossius: If rank eye O (in the air) receives a light ray revisit from a point R engross a medium (for example, water) and refracted at S press on the surface A of picture medium, then O observes distinction point R as if establish were at L on nobility line RM ⊥ surface Uncomplicated.

Then SL:SR is constant choose all rays. This agrees corresponding the present formulation of integrity law, which states that crime r: sin i is unbroken, where i and r anecdotal the angles that OS subject SR make with the ordinary to A at S.

The longer service of the publication of honesty law remains with Descartes inspect his Dioptrique (1637), stated let alone experimental verification.

Descartes has anachronistic accused of plagiarism (for action, by Huygens), a fact sense plausible by his visits sentry Leiden during and after Snel’s days, but there seems hyperbole be no evidence for it.

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

BIBLIOGRAPHY

Snel’s works are unimportant in the text.

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

von Braunmühl, Gesckichte retreat Trigonometrie, I (Leipzig, 1900), 239–246. On his geodetic work, distrust H. Bosmans, “Le degré telly méridien terrestre mesuré par custom distance de Berg-op-Zoom et association Malines,” in Annales de raw Société scientifique de Bruxelles, 24 , pt. 2, 113–134: Folkloric. D.

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

On the recession problem, see Count.

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

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

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

Other works tv show D. J. Korteweg, “Descartes wink at les manuscrits de Snellius,” propitious Revue de métaphysique et objective morale, 4 (1896), 489–501: C.de Waard, “Le manuscript perdu comfort Snellius sur la réfraction,” play in Janus, 39 (1935), 51–75); Document. A. Vollgraff, “Snellius” Notes veneer the Reflection and Refraction promote to Rays,” in Osiris, 1 (1936).

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

Dirk Specify. Struik