Editing Simon Stevin (section)

== Discoveries and inventions ==
[[File:Simon Stevins zeilwagen voor Prins Maurits 1649.jpg|thumb|Wind chariot or [[land yacht]] (Zeilwagen) designed by Simon Stevin for [[Maurice of Nassau, Prince of Orange|Prince Maurice of Orange]] (engraving by Jacques de Gheyn).]]

Stevin is responsible for many discoveries and inventions. Stevin wrote numerous bestselling books, and he was a pioneer of the development and the practical application of (engineering related) science such as [[mathematics]], [[physics]] and applied science like [[hydraulic engineering]] and [[surveying]]. He was thought to have invented the [[decimal fraction]]s until the middle of the 20th century, when researchers discovered that decimal fractions had been previously introduced by the medieval Islamic scholar [[al-Uqlidisi]] in a book written in 952. Moreover, a systematic development of decimal fractions was given well before Stevin in the book ''Miftah al-Hisab'' written in 1427 by [[Al-Kashi]].

His contemporaries were most struck by his invention of a so-called [[Land sailing|land yacht]], a carriage with sails, of which a model was preserved in [[Scheveningen]] until 1802. The carriage itself had been lost long before. Around the year 1600 Stevin, with [[Maurice of Nassau, Prince of Orange|Prince Maurice of Orange]] and twenty-six others, used the carriage on the beach between [[Scheveningen]] and [[Petten]]. The carriage was propelled solely by the force of wind and acquired a speed which exceeded that of horses.<ref name=EB1911/> 

=== Management of waterways ===
Stevin's work in the ''waterstaet'' involved improvements to the [[sluice]]s and [[spillway]]s to control [[flood]]ing, exercises in [[hydraulic engineering]]. [[Windmill]]s were already in use to pump the water out but in ''Van de Molens'' (''On mills''), he suggested improvements including ideas that the wheels should move slowly with a better system for meshing of the [[gear teeth]]. These improved threefold the efficiency of the windmills used in pumping water out of the [[polder]]s.<ref>The Story of Science: Power, Proof & Passion – EP4: Can We Have Unlimited Power?</ref> He received a [[patent]] on his innovation in 1586.<ref name=isis/>

=== Philosophy of science ===
Stevin's aim was to bring about a second age of [[wisdom]], in which mankind would have recovered all of its earlier knowledge. He deduced that the language spoken in this age would have to be Dutch, because, as he showed [[empirical]]ly, in that language, more concepts could be indicated with [[monosyllabic]] words than in any of the (European) languages he had compared it with.<ref name=EB1911/> This was one of the reasons why he wrote all of his works in Dutch and left the translation of them for others to do. The other reason was that he wanted his works to be practically useful to people who had not mastered the common scientific language of the time, Latin. Thanks to Simon Stevin the [[Dutch language]] got its proper scientific vocabulary such as "[[:nl:wiskunde|wiskunde]]" (''"kunst van het gewisse of zekere"'' the art of what is known or what is certain) for [[mathematics]], "[[:nl:natuurkunde|natuurkunde]]" (the "art of nature") for [[physics]], "[[:nl:scheikunde|scheikunde]]" (the "art of separation") for [[chemistry]], "[[:nl:sterrenkunde|sterrenkunde]]" (the "art of stars") for [[astronomy]], "[[:nl:meetkunde|meetkunde]]" (the "art of measuring") for [[geometry]].

=== Geometry, physics and trigonometry ===
[[File:StevinEquilibrium.svg|thumb|Stevin's proof of the [[Inclined plane#History|law of equilibrium on an inclined plane]], known as the "Epitaph of Stevinus".]]
Stevin was the first to show how to model regular and semiregular [[polyhedra]] by delineating their frames in a plane. He also distinguished stable from unstable equilibria.<ref name=EB1911/>

Stevin contributed to [[trigonometry]] with his book, ''De Driehouckhandel''.

In ''The First Book of the Elements of the Art of Weighing, The second part: Of the propositions [The Properties of Oblique Weights], Page 41, Theorem XI, Proposition XIX'',<ref>[http://www.dwc.knaw.nl/pub/bronnen/Simon_Stevin-%5BI%5D_The_Principal_Works_of_Simon_Stevin,_Mechanics.pdf The Principal Works of Simon Stevin]</ref> he derived the condition for the balance of forces on [[inclined plane]]s using a diagram with a "wreath" containing evenly spaced round masses resting on the planes of a triangular prism (see the illustration on the side). He concluded that the weights required were proportional to the lengths of the sides on which they rested assuming the third side was horizontal and that the effect of a weight was reduced in a similar manner. It is implicit that the reduction factor is the height of the triangle divided by the side (the [[Sine#History|sine]] of the angle of the side with respect to the horizontal). The proof diagram of this concept is known as the "Epitaph of Stevinus". As noted by [[E. J. Dijksterhuis]], Stevin's proof of the equilibrium on an inclined plane can be faulted for using [[perpetual motion]] to imply a [[reductio ad absurdum]]. Dijksterhuis says Stevin "intuitively made use of the principle of [[conservation of energy]] ... long before it was formulated explicitly".<ref name=EJD/>{{rp|54}}

He demonstrated the resolution of forces before [[Pierre Varignon]], which had not been remarked previously, even though it is a simple consequence of the law of their composition.<ref name=EB1911/>

Stevin discovered the [[hydrostatic paradox]], which states that the pressure in a liquid is independent of the shape of the vessel and the area of the base, but depends solely on its height.<ref name=EB1911/>

He also gave the measure for the pressure on any given portion of the side of a vessel.<ref name=EB1911/>

He was the first to explain the [[tides]] using the [[Theory of tides|attraction of the moon]].<ref name=EB1911/>

In 1586, he [[Delft tower experiment|demonstrated]] that two objects of different weight fall with the same acceleration.<ref>Appendix to [[De Beghinselen Der Weeghconst]]</ref><ref>{{Cite book|url=https://books.google.com/books?id=YicuDwAAQBAJ&q=delft+tower+experiment&pg=PA26|title=Ripples in Spacetime: Einstein, Gravitational Waves, and the Future of Astronomy|last=Schilling|first=Govert|date=2017-07-31|publisher=Harvard University Press|isbn=9780674971660|language=en}}</ref>

=== Music theory ===
[[File:De Spiegheling der signconst.jpg|thumb|''Van de Spiegheling der singconst''.]]
The first mention of equal temperament related to the [[twelfth root of two]] in the West appeared in Simon Stevin's unfinished manuscript ''Van de Spiegheling der singconst ''(ca 1605) published posthumously three hundred years later in 1884;<ref>{{cite web |url=http://diapason.xentonic.org/ttl/ttl21.html |title=Van de spiegheling der singconst |publisher=Diapason.xentonic.org |date=2009-06-30 |access-date=2012-12-29 |archive-url=https://web.archive.org/web/20110717015203/http://diapason.xentonic.org/ttl/ttl21.html |archive-date=17 July 2011 |url-status=dead }}</ref> however, due to insufficient accuracy of his calculation, many of the numbers (for string length) he obtained were off by one or two units from the correct values.<ref>Christensen, Thomas S. (2006). ''The Cambridge History of Western Music Theory'', p.205, Cambridge University Press. {{ISBN|9781316025482}}.</ref> He appears to have been inspired by the writings of the Italian [[lutenist]] and musical theorist [[Vincenzo Galilei]] (father of [[Galileo Galilei]]), a onetime pupil of [[Gioseffo Zarlino]].

=== Bookkeeping ===

[[Double-entry bookkeeping]] may have been known to Stevin, as he was a clerk in [[Antwerp]] in his younger years, either practically or via the medium of the works of Italian authors such as [[Luca Pacioli]] and [[Gerolamo Cardano]]. However, Stevin was the first to recommend the use of impersonal [[account (accountancy)|accounts]] in the national household. He brought it into practice for Prince Maurice, and recommended it to the French statesman [[Maximilien de Béthune, duc de Sully|Sully]].<ref>Volmer, Frans. [https://egrove.olemiss.edu/acct_corp/168 "Stevin, Simon (1548–1620)."] In ''History of Accounting: An International Encyclopedia,'' edited by Michael Chatfield and Richard Vangermeesch. New York: Garland Publishing, 1996, pp. 565–566.</ref><ref name=EB1911/>

=== Decimal fractions ===<!-- This section is linked from [[Decimal]] -->

Stevin wrote a 35-page [[book]]let called ''[[De Thiende]]'' ("the art of tenths"), first published in Dutch in 1585 and translated into French as ''La Disme''. The full title of the English translation was ''[[Decimal arithmetic]]: Teaching how to perform all computations whatsoever by whole numbers without [[fraction (mathematics)|fraction]]s, by the four principles of common arithmetic: namely, [[addition]], [[subtraction]], [[multiplication]], and [[division (mathematics)|division]].'' The concepts referred to in the booklet included [[unit fractions]] and [[Egyptian fractions]]. [[Muslim mathematicians]] were the first to utilize [[decimal]]s instead of fractions on a large scale. [[Al-Kashi]]'s book, ''Key to Arithmetic'', was written at the beginning of the 15th century and was the stimulus for the systematic application of decimals to whole numbers and fractions thereof.<ref>{{MacTutor|id=Al-Kashi|title=Al-Kashi|date=July 2009}}</ref><ref>{{cite book |title=Numbers: Their History and Meaning |last=Flegg |first=Graham |year=2002 |publisher=[[Dover Publications]] |isbn=9780486421650 |pages=75–76}}</ref> But nobody established their daily use before Stevin. He felt that this innovation was so significant, that he declared the universal introduction of decimal coinage, measures and weights to be merely a question of time.<ref>{{Cite book | publisher = [[Facts on File]] | isbn = 0-8160-4955-6 | last = Tabak | first = John | title = Numbers: Computers, philosophers, and the search for meaning | year = 2004 | pages = [https://archive.org/details/numbers00john/page/41 41–42] | url-access = registration | url = https://archive.org/details/numbers00john/page/41 }}</ref><ref name=EB1911/>

His notation is rather unwieldy. The [[decimal mark|point]] separating the [[integer]]s from the decimal fractions seems to be the invention of [[Bartholomaeus Pitiscus]], in whose [[trigonometrical table]]s (1612) it occurs, and it was accepted by [[John Napier]] in his [[logarithm]]ic papers (1614 and 1619).<ref name=EB1911/>

{| class="wikitable floatright"
! style="background: #ececec; color: black; font-weight: bold; vertical-align: middle; text-align: right; " class="table-rh" | Number
|184.54290
|-
! style="background: #ececec; color: black; font-weight: bold; vertical-align: middle; text-align: right; " class="table-rh" | Simon Stevin's notation
|184⓪5①4②2③9④0
|}

Stevin printed little circles around the exponents of the different powers of one-tenth. That Stevin intended these encircled numerals to denote mere exponents is clear from the fact that he employed the same symbol for powers of [[algebra]]ic quantities. He did not avoid fractional exponents; only negative exponents do not appear in his work.<ref name=EB1911/>

Stevin wrote on other scientific subjects – for instance optics, geography, astronomy – and a number of his writings were translated into Latin by W. Snellius ([[Willebrord Snell]]). There are two complete editions in French of his works, both printed in Leiden, one in 1608, the other in 1634.<ref name=EB1911>{{EB1911|wstitle=Stevinus, Simon|inline=1}}</ref>

=== Mathematics ===
[[File:Stevin - Oeuvres mathematiques, 1634 - 4607786.tif|thumb|''Oeuvres mathematiques'', 1634]]
Stevin wrote his ''Arithmetic'' in 1594. The work brought to the western world for the first time a general solution of the [[quadratic equation]], originally documented nearly a millennium previously by [[Brahmagupta]] in India.

According to [[Bartel Leendert van der Waerden|Van der Waerden]], Stevin eliminated "the classical restriction of 'numbers' to integers (Euclid) or to rational fractions (Diophantos)...the real numbers formed a continuum. His general notion of a real number was accepted, [[tacit]]ly or explicitly, by all later scientists".<ref>{{cite book | last=van der Waerden | first=B. L. |author-link=Bartel van der Waerden| year=1985 | title=A History of Algebra. From al-Khwarizmi to Emmy Noether | url=https://archive.org/details/historyofalgebra0000waer | url-access=registration | page=[https://archive.org/details/historyofalgebra0000waer/page/69 69]| publisher= Springer-Verlag | location = Berlin|isbn=3-540-13610-X }}</ref> A recent study attributes a greater role to Stevin in developing the [[real number]]s than has been acknowledged by [[Karl Weierstrass|Weierstrass's]] followers.<ref>
Karin Usadi Katz and [[Mikhail Katz|Mikhail G. Katz]] (2011) A Burgessian Critique of Nominalistic Tendencies in Contemporary Mathematics and its Historiography. [[Foundations of Science]]. {{doi|10.1007/s10699-011-9223-1}}</ref> Stevin proved the [[intermediate value theorem]] for polynomials, anticipating [[Cauchy]]'s proof thereof. Stevin uses a [[divide and conquer algorithm|divide and conquer]] procedure, subdividing the interval into ten equal parts.<ref>Karin Usadi Katz and [[Mikhail Katz|Mikhail G. Katz]] (2011) Stevin Numbers and Reality. [[Foundations of Science]]. {{doi|10.1007/s10699-011-9228-9}} Online First. [https://doi.org/10.1007%2Fs10699-011-9228-9]</ref> Stevin's decimals were the inspiration for [[Isaac Newton]]'s work on [[infinite series]].<ref>{{citation
 | last1 = Błaszczyk | first1 = Piotr
 | last2 = Katz | first2 = Mikhail
 | author2-link = Mikhail Katz
 | last3 = Sherry | first3 = David
 | arxiv = 1202.4153
 | doi = 10.1007/s10699-012-9285-8
 | journal = [[Foundations of Science]]
 | title = Ten misconceptions from the history of analysis and their debunking
 | year = 2012| volume = 18
 | pages = 43–74
 | s2cid = 119134151
 }}</ref>

=== Neologisms ===

{{More citations needed section|date=October 2016}}

Stevin thought the [[Dutch language]] to be excellent for scientific writing, and he translated many of the mathematical terms to Dutch. As a result, Dutch is one of the few Western European languages that have many mathematical terms that do not stem from Greek or Latin. This includes the very name ''wiskunde'' (mathematics).

His eye for the importance of having the scientific language be the same as the language of the craftsman may show from the dedication of his book ''De Thiende'' ('The Disme' or 'The Tenth'): 'Simon Stevin wishes the stargazers, surveyors, carpet measurers, body measurers in general, coin measurers and tradespeople good luck.' Further on in the same pamphlet, he writes: "[this text] teaches us all calculations that are needed by the people without using fractions. One can reduce all operations to adding, subtracting, multiplying and dividing with integers."

Some of the words he invented evolved: 'aftrekken' (''subtract'') and 'delen' (''divide'') stayed the same, but over time 'menigvuldigen' became 'vermenigvuldigen' (''multiply'', the added 'ver' emphasizes the fact it is an action). 'Vergaderen' (''gathering'') became 'optellen' (''add'' lit. ''count up'').

Another example is the Dutch word for diameter: 'middellijn', lit.: line through the middle.

The word 'zomenigmaal' (''quotient'' lit. 'that many times') has been replaced by 'quotiënt' in modern-day Dutch.

Other terms did not make it into modern day mathematical Dutch, like 'teerling' (''[[Dice|die]]'', although still being used in the meaning as die), instead of cube.