Simon Stevin

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Simon Stevin

Simon Stevin (1548 – 1620) was a Flemish mathematician and military engineer. He was active in a great many areas of science and engineering, both theoretical and practical. He also translated various mathematical terms into Dutch, making it one of the few European languages in which the word for mathematics, wiskunde (wis + kunde i.e. "the art of what is certain"), was not derived from Greek (via Latin).

Biography[edit]

Stevin was born in Bruges, Flanders (now Belgium) around the year 1548, to unmarried parents, Stevo (Anton) Antheunis and Catelyne van der Poort. His father is believed to have been a cadet son of a mayor of Veurne which draws some Croatian origin, while his mother Cathelijne (or Catelyne) was the daughter of a burgher family from Ypres. Simon's mother Cathelijne was later married to a man who was involved in the carpet and silk trade. Through her marriage Cathelijne became a member of a family who were Calvinists and it is presumed that Simon was brought up in the Calvinist faith.[1] Very little has been recorded about his life. Even the exact date of birth and the date and place of his death (The Hague or Leiden) are uncertain. It is known that he left a widow with two children; and one or two hints scattered throughout his works inform us that he began life as a merchant's clerk in Antwerp, that he travelled in Poland, Denmark and other parts of Northern Europe. After his travels, in 1581, while in his thirties, he moved to Leiden where he attended the Latin school and at the age of 35 (1583) entered the University of Leiden where he befriended William of Orange's second son, Maurits (Maurice), the Count Of Nassau.[1] Following William of Orange's assassination and Prince Maurice of Nassau's assumption of his father's office, he became an advisor and tutor of Maurice, who asked his advice on many occasions, and made him a public officer – at first director of the so-called "waterstaet" (the government authority for public works) from 1592, and later quartermaster-general of the army of the States-General.[2]

In Bruges there is a Simon Stevin Square which contains his statue by Eugène Simonis, which includes his inclined plane diagram.

Discoveries and inventions[edit]

Wind chariot or land yacht (Zeilwagen) designed by Simon Stevin for Prince Maurice of Orange (Engraving by Jacques de Gheyn).

His claims to fame are varied. His contemporaries were most struck by his invention of a so-called land yacht, a carriage with sails, of which a little model was preserved in Scheveningen until 1802. The carriage itself had been lost long before. Around the year 1600 Stevin, with Prince Maurice of Orange and twenty-six others, made use of it 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.

Management of waterways[edit]

Stevin's work in the waterstaet involved improvements to the sluices and spillways to control flooding. Windmills 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 the efficiency of the windmills used in pumping water out of the polders by three times.[3] He received a patent on his innovation in 1586.[2]

Philosophy of science[edit]

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 had to be Dutch, because, as he showed empirically, in that language, more concepts could be indicated with monosyllabic words than in any of the (European) languages he had compared it with. This was one of the reasons why he wrote all of his works in Dutch and left translations to others. 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.

Geometry, physics and trigonometry[edit]

Stevin's proof of the 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.

In The Principal Works of Simon Stevin, Vol. I, Ch II, Bk I, Th XI, he derived the condition for the balance of forces on inclined planes 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's implicit that the reduction factor is the height of the triangle divided by the side (the sine of the angle of the side with respect to the horizontal). Stevin also made contributions to trigonometry. His book, De Driehouckhandel, included Plane Trigonometry. The proof diagram of this concept is known as the "Epitaph of Stevinus". Although Stevin's conclusion is correct his proof has certain logical defects as pointed out by Dijksterhuis[4]

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.

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.

He also gave the measure for the pressure on any given portion of the side of a vessel.

He was the first to explain the tides using the attraction of the moon.

In 1586, he demonstrated that two objects of different weight fall down with exactly the same acceleration.[5][6]

Music theory[edit]

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;[7] however, due to insufficient accuracy of his calculation, many of the numbers he obtained were off by one or two units from the correct values.[8] 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[edit]

Bookkeeping by double entry may have been known to Stevin, as he was a clerk in Antwerp in his younger years, either practically or through 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 accounts in the national household. He brought it into practice for Prince Maurice, and recommended it to the French statesman Sully.[9]

Decimal fractions[edit]

Stevin wrote a 35-page booklet called De Thiende ('the art of tenths'), first published in Dutch in 1585 and translated into French as Disme. The full title of the English translation was Decimal arithmetic: Teaching how to perform all computations whatsoever by whole numbers without fractions, by the four principles of common arithmetic: namely, addition, subtraction, multiplication, and division. The concepts referred to in the booklet included unit fractions and Egyptian fractions. Muslim mathematicians were the first to utilize decimals 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.[10][11] 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.[12]

His notation is rather unwieldy. The point separating the integers from the decimal fractions seems to be the invention of Bartholomaeus Pitiscus, in whose trigonometrical tables (1612) it occurs and it was accepted by John Napier in his logarithmic papers (1614 and 1619).

Stevin-decimal notation.png

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 very same symbol for powers of algebraic quantities. He didn't avoid fractional exponents; only negative exponents don't appear in his work.

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.

Mathematics[edit]

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 van der Waerden (1985, p. 69), Stevin's "general notion of a real number was accepted, tacitly or explicitly, by all later scientists". A recent study attributes a greater role to Stevin in developing the real numbers than has been acknowledged by Weierstrass's followers.[13] Stevin proved the intermediate value theorem for polynomials, anticipating Cauchy's proof thereof. Stevin uses a divide and conquer procedure subdividing the interval into ten equal parts.[14] Stevin's decimals were the inspiration for Isaac Newton's work on infinite series.[15]

Neologisms[edit]

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 a lot of mathematical terms that do not stem from 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 craftsmen 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' became 'optellen' (add).

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

The word 'zomenigmaal' (quotient lit. 'that many times') has become the perhaps less poetic 'quotiënt' in modern day Dutch.

Other terms did not make it into modern day mathematical Dutch, like 'teerling' (die, although still being used in the meaning as die), instead of cube. His books were bestsellers.

Trivia[edit]

The student association of mechanical engineering at the Technische Universiteit Eindhoven, W.S.V. Simon Stevin,[16] is named after Simon Stevin. In Stevin's memory, the association calls its bar "De Weeghconst" and owns a self-built fleet of land yachts.

Stevin, cited as Stevinus, is one of the favorite authors – if not the favorite author – of Uncle Toby Shandy in Laurence Sterne's The Life and Opinions of Tristram Shandy Gentleman.

Quote: A man in anger is no clever dissembler.[17]

Publications[edit]

The Moers fortifications designed by Simon Stevin.

Amongst others, he published:

  • Tafelen van Interest (Tables of interest) in 1582 with present value problems of simple and compound interest and interest tables that had previously been unpublished by bankers;[1]
  • Problemata geometrica in 1583;
  • De Thiende (La Theinde, The tenth) in 1585 in which decimals were introduced in Europe;
  • La pratique d'arithmétique in 1585;
  • L'arithmétique in 1585 in which he presented a uniform treatment for solving algebraic equations;
  • De Beghinselen Der Weeghconst in 1586, accompanied by De Weeghdaet;
  • De Beghinselen des Waterwichts (Principles on the weight of water) in 1586 on the subject of hydrostatics;
  • Vita Politica. Named Burgherlick leven (Civil life) in 1590;
  • De Stercktenbouwing (The construction of fortifications) published in 1594;
  • De Havenvinding (Position finding) published in 1599;
  • De Hemelloop in 1608 in which he voiced support for the Copernican theory.
  • Wiskonstighe Ghedachtenissen (Mathematical Memoirs, Latin: Hypomnemata Mathematica). This included earlier works like De Driehouckhandel (Trigonometry), De Meetdaet (Practice of measuring), and De Deursichtighe (Perspective);
  • Castrametatio, dat is legermeting and Nieuwe Maniere van Stercktebou door Spilsluysen (New ways of building of sluices) published in 1617;
  • De Spiegheling der Singconst (Theory of the art of singing).
  • "Œuvres mathématiques..., Leyde, 1634[18]

References[edit]

  1. ^ a b c O'Connor, John J.; Robertson, Edmund F. (January 2004), "Simon Stevin", MacTutor History of Mathematics archive, University of St Andrews .
  2. ^ a b Sarton, George (1934). "Simon Stevin of Bruges (1548-1620)". Isis 21 (2): 241–303. doi:10.1086/346851. 
  3. ^ The Story of Science: Power, Proof & Passion - EP4: Can We Have Unlimited Power?
  4. ^ E.J.Dijksterhuis : Simon Stevin 1943 (In Dutch).
  5. ^ Appendix to De Beghinselen Der Weeghconst
  6. ^ "Galileo Galilei: The Falling Bodies Experiment". Juliantrubin.com. Retrieved 2012-12-29. 
  7. ^ "Van de spiegheling der singconst". Diapason.xentonic.org. 2009-06-30. Retrieved 2012-12-29. 
  8. ^ Thomas S. Christensen, The Cambridge history of western music theory p205, Cambridge University Press
  9. ^ Volmer, Frans. "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.
  10. ^ O'Connor, John J.; Robertson, Edmund F. (July 2009), "Al-Kashi", MacTutor History of Mathematics archive, University of St Andrews .
  11. ^ Flegg, Graham (2002). Numbers: Their History and Meaning. Dover Publications. pp. 75–76. ISBN 9780486421650. 
  12. ^ Tabak, John (2004). Numbers: Computers, philosophers, and the search for meaning. Facts on File. pp. 41–42. ISBN 0-8160-4955-6. 
  13. ^ Karin Usadi Katz and 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
  14. ^ Karin Usadi Katz and Mikhail G. Katz (2011) Stevin Numbers and Reality. Foundations of Science. doi:10.1007/s10699-011-9228-9 Online First. [1]
  15. ^ Błaszczyk, Piotr; Katz, Mikhail; Sherry, David (2012), "Ten misconceptions from the history of analysis and their debunking", Foundations of Science, arXiv:1202.4153, doi:10.1007/s10699-012-9285-8 
  16. ^ simonstevin.tue.nl
  17. ^ Crone et al., eds. 1955–1966, Vol. I, p.11
  18. ^ http://architectura.cesr.univ-tours.fr/Traite/Notice/B250566101_11463.asp?param=

Further reading[edit]

  • Virtually all of Stevin's writings have been published in five volumes with introduction and analysis in: Crone, Ernst; Dijksterhuis, E. J.; Forbes, R. J. et al., eds. (1955–1966). The Principal Works of Simon Stevin. Lisse: Swets & Zeitlinger.  The Principal Works are available online at The Digital Library of the Royal Netherlands Academy of Arts and Sciences.
  • Another good source about Stevin is the French-language bundle: Bibliothèque royale de Belgique, ed. (2004). Simon Stevin (1548–1620): L'émergence de la nouvelle science. Turnhout: Brepols. .
  • A recent work on Simon Stevin in Dutch is: Devreese, J. T. en Vanden Berghe, G. (2003). Wonder en is gheen wonder. De geniale wereld van Simon Stevin 1548–1620. Leuven: Davidsfonds. .
  • A recent work on Simon Stevin in English is: Devreese, J. T. en Vanden Berghe, G. (2007). Magic is no magic. The wonderful World of Simon Stevin 1548–1620. Southampton: WITpress. 
  • van den Heuvel, C. (2005). De Huysbou. A reconstruction of an unfinished treatise on architecture, and civil engineering by Simon Stevin. Amsterdam: KNAW Edita.  545 pp – The work is available on line – see external links
  • van der Waerden, B. L. (1985). A history of algebra. From al-Khwarizmi to Emmy Noether. Berlin: Springer-Verlag. 

External links[edit]