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===Christiaan Huygens=== {{main|Christiaan Huygens}} [[File:Christiaan_Huygens-painting.jpeg|thumb|upright|Christiaan Huygens (1629–1695)]] The Dutch physicist, mathematician, astronomer and inventor Christiaan Huygens (1629–1695) was the leading scientist in Europe between Galileo and Newton. Huygens came from a family of nobility that had an important position in the Dutch society of the 17th century; a time in which the [[Dutch Republic]] flourished economically and culturally. This period – roughly between 1588 and 1702 – of the [[history of the Netherlands]] is also referred to as the [[Dutch Golden Age]], an era during the Scientific Revolution when Dutch science was among the most acclaimed in Europe. At this time, intellectuals and scientists like René Descartes, [[Baruch Spinoza]], [[Pierre Bayle]], [[Antonie van Leeuwenhoek]], [[John Locke]] and [[Hugo Grotius]] resided in the Netherlands. It was in this intellectual environment that Christiaan Huygens grew up. Christiaan's father, [[Constantijn Huygens]], was, apart from an important poet, the secretary and diplomat for the Princes of Orange. He knew many scientists of his time because of his contacts and intellectual interests, including René Descartes and [[Marin Mersenne]], and it was because of these contacts that Christiaan Huygens became aware of their work, especially Descartes, whose mechanistic philosophy was going to have a huge influence on Huygens' own work. Descartes was later impressed by the skills Huygens showed in geometry, as was Mersenne, who christened him "the new Archimedes" (which led Constantijn to refer to his son as "my little Archimedes"). A child prodigy, Huygens began his correspondence with Marin Mersenne when he was 17 years old. Huygens became interested in [[games of chance]] when he encountered the work of [[Fermat]], [[Blaise Pascal]] and [[Girard Desargues]]. It was Pascal who encouraged him to write ''Van Rekeningh in Spelen van Gluck'', which [[Frans van Schooten]] translated and published as ''De Ratiociniis in Ludo Aleae'' in 1657. The book is the earliest known scientific treatment of the subject, and at the time the most coherent presentation of a mathematical approach to games of chance. Two years later Huygens derived geometrically the now standard formulae in classical mechanics for the [[centripetal force|centripetal-]] and [[centrifugal force]] in his work ''De vi Centrifuga'' (1659). Around the same time Huygens' research in [[horology]] resulted in the invention of the [[pendulum clock]]; a breakthrough in timekeeping and the most accurate timekeeper for almost 300 years. The theoretical research of the way the pendulum works eventually led to the publication of one of his most important achievements: the [[Horologium Oscillatorium]]. This work was published in 1673 and became one of the three most important 17th century works on mechanics (the other two being Galileo's ''[[Discourses and Mathematical Demonstrations Relating to Two New Sciences]]'' (1638) and Newton's ''[[Philosophiæ Naturalis Principia Mathematica]]'' (1687)<ref name="bell">{{cite journal | url=https://www.britannica.com/EBchecked/topic/277775/Christiaan-Huygens?anchor=ref136385 | title=The Horologium Oscillatorium of Christian Huygens | date = 30 Aug 1941 | access-date=14 November 2013 | author=Bell, A. E. | journal=Nature | volume=148 | issue=3748 | pages=245–248 | doi= 10.1038/148245a0| bibcode=1941Natur.148..245B | s2cid=4112797 }}</ref>). The ''Horologium Oscillatorium'' is the first modern treatise in which a physical problem (the [[Acceleration|accelerated motion]] of a falling body) is [[Mathematical model|idealized by a set of parameters]] then analyzed mathematically and constitutes one of the seminal works of [[applied mathematics]].<ref name=":0">{{Cite book|last=Yoder|first=Joella G.|author-link=Joella Yoder |url=https://www.cambridge.org/core/books/unrolling-time/1427509C7A14C464B08209322E42ABB6|title=Unrolling Time: Christiaan Huygens and the Mathematization of Nature|date=1988|publisher=Cambridge University Press|isbn=978-0-521-34140-0|location=Cambridge}}</ref><ref name=":5">Bruce, I. (2007). ''[http://www.17centurymaths.com/contents/huygenscontents.html Christian Huygens: Horologium Oscillatorium]''. Translated and annotated by Ian Bruce.</ref> It is for this reason, Huygens has been called the first [[Theoretical physics|theoretical physicist]] and one of the founders of modern [[mathematical physics]].<ref name=":6">Dijksterhuis, F. J. (2008) Stevin, Huygens and the Dutch republic. ''Nieuw archief voor wiskunde'', ''5'', pp. 100–107.[https://research.utwente.nl/files/6673130/Dijksterhuis_naw5-2008-09-2-100.pdf]</ref><ref>Andriesse, C. D. (2005) ''Huygens: The Man Behind the Principle''. Cambridge University Press. Cambridge: 6.</ref> Huygens' ''Horologium Oscillatorium'' influenced the work of Isaac Newton, who admired the work. For instance, the laws Huygens described in the ''Horologium Oscillatorium'' are structurally the same as Newton's first two [[Newton's laws of motion|laws of motion]].<ref>{{cite book |author=Iliffe |first1=Rob |url=https://books.google.com/books?id=se27CwAAQBAJ&dq=Although+Huygens+does+not+state+his+second+law+in+the+full+generality+found+in+the+Principia%2C+the+model+is+structurally+the+same%3A+first%2C+an+inertial+motion&pg=PA75 |title=The Cambridge Companion to Newton |last2=Smith |first2=George E. |date=2016 |publisher=Cambridge University Press |isbn=9781107015463 |page=75}}</ref> Five years after the publication of his ''Horologium Oscillatorium'', Huygens described his [[wave theory of light]]. Though proposed in 1678, it was not published until 1690 in his [[Traité de la Lumière]]. His mathematical theory of light was initially rejected in favour of Newton's corpuscular theory of light, until [[Augustin-Jean Fresnel]] adopted Huygens' principle to give a complete explanation of the rectilinear propagation and diffraction effects of light in 1821. Today this principle is known as the [[Huygens–Fresnel principle]]. As an astronomer, Huygens began grinding lenses with his brother Constantijn Jr. to build telescopes for astronomical research. He was the first to identify the rings of [[Saturn]] as "a thin, flat ring, nowhere touching, and inclined to the ecliptic," and discovered the first of Saturn's moons, [[Titan (moon)|Titan]], using a [[refracting telescope]]. Huygens was also the first who brought mathematical rigor to the description of physical phenomena. Because of this, and the fact that he developed institutional frameworks for scientific research on the continent, he has been referred to as "the leading actor in 'the making of science in Europe{{'"}}<ref>{{Cite book|last=Aldersey-Williams|first=H.|url=https://books.google.com/books?id=7n7VDwAAQBAJ&q=In+the+case+of+two+bodies+which+meet%2C+the+quantity+obtained+by+taking+the+sum+of+their+masses+multiplied+by+the+squares+of+their+velocities+will+be+found+to+beequal+before+and+after+the+collision.%E2%80%99&pg=PP86|title=Dutch Light: Christiaan Huygens and the Making of Science in Europe|date=2020|publisher=Pan Macmillan|isbn=978-1-5098-9332-4|language=en|access-date=28 August 2021|page=24}}</ref>
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