Simon Stevin

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Flemish mathematician and engineer (1548–1620)

Stevin was also known as Stevinus, the Latinized form of his name. Born in the city of Bruges, he worked for a time as a clerk in Antwerp, eventually working his way up to become quartermaster of the army under Prince Maurice of Nassau. While in this post he devised a system of sluices, which could flood the land as a defense should Holland be attacked.

Stevin was a versatile man who contributed to several areas of science. Mathematics owes to him the introduction of the decimal system of notating fractions. This system was perfected when John Napier invented the decimal point. Stevin helped to popularize the practice of writing scientific works in modern languages (in his case Dutch) rather than Latin, which for so long had been the traditional European language of learning. However such was the hold of the old ways that Willebrord Snell thought it was worthwhile to translate some of Stevin's work into Latin. To hydrostatics he contributed the discovery that the shape of a vessel containing liquid is irrelevant to the pressure that liquid exerts. He also did some experimental work in statics and in the study of the Earth's magnetism.

Simon Stevin (1548-1620) was an influential mathematician and engineer with a broad range of interests. He offered new insights and discoveries in the development of decimal numbers and the laws of inclines, gravity, hydrostatics, and fortification. Although Stevin never earned the same lasting reputation as Galileo or Isaac Newton, his contributions to the advancement of mathematical theory are noteworthy.

Very little regarding Stevin's early life is known with certainty. He noted in many of his books that he was a native of Bruges, a city in Flanders, which later became Belgium. According to the inscription on a later portrait, he was born in 1548. Records of his deeds name him as the son of wealthy parents, Antheunis Stevin and Cathelyne van der Poort. Conceived out of wedlock, he was most likely raised by his mother, but no information concerning his childhood is available.

In 1577, Stevin occupied an administrative position in the financial department of the government of Flanders. Prior to that, he was employed as a bookkeeper and cashier for the city of Antwerp. Reportedly he had traveled extensively through Poland, Prussia, and Norway from 1571 to 1577. By 1581 he had settled in the Dutch city of Leiden. Already in his 30s, Stevin finally began his formal education by enrolling in a Latin school and later entering the University of Leiden. He graduated on February 16, 1583, under the Latinized version of his name, Simon Stevinus.

After graduation, Stevin undertook numerous projects of mathematical writing and practical inventions. In 1584 he negotiated with the city of Delft to use an innovative system of drainage he developed. He also applied for patents for numerous inventions concerning drainage and dredging, along with an improved windmill and a mechanical roasting spit, which Stevin considered a toy.

From the beginning of his writings and engineering innovations, Stevin displayed a dual interest in pure thought and practical application. Although he asserted that knowledge with no use in practical living was not worth pursuing, he followed many of his practical projects to theoretical ends. He often went beyond the scope of his original plans, and in so doing enhanced the growth of mathematical understanding. His work was crucial to the development of mathematical theory in the late 16th century.

Published Important Mathematical Works

Stevin began publishing his writings on mathematics while still a student. In 1582 he employed a printing shop in Antwerp to produce Tables of Interest, which outlined the rules for computing interest and provided tables for understanding discounts and annuities. Until that time, the calculation of interest was a mathematical process known only to the banking industry, which guarded the formula closely to protect its financial interests. After the release of Tables of Interest, for the first time common people could calculate the interest costs and benefits of their investments.

In 1583, Stevin published Geometrical Problems. From the start, Stevin proved himself an innovator by publishing his books in Flemish. Writing in one's own language was highly unusual in a time when works of a scholarly nature were published in Latin. Over the next three years Stevin produced several of his most important mathematical works, including Dialectics (also known as Art of Demonstration ), The Dime, The Decimal, and L'Arithmetique.

Developed a System of Decimals

The Dime and The Decimal, both published in 1585, proved important in the advancement of the accepted use of a decimal system. The decimal system had been known for centuries, but Stevin's explanation provided an understandable and usable, albeit cumbersome, system of decimals. The common accepted practice among mathematicians at the time was to use fraction form with written notations. Although he fell short of devising a complete decimal system with a positional decimal point, Stevin provided the foundation on which other mathematicians would soon follow with these elaborations.

According to E. J. Duksterhuis in Simon Stevin: Science in the Netherlands Around 1600, other mathematicians were also gradually moving toward a decimal system. However, none of the advancements made were "comparable in importance and scope with the progress achieved by Stevin in The Dime. " Duksterhuis lists three points of special importance. First, Stevin invented a method of indicating the value of each digit without using fraction notation. Second, characteristic of Stevin's interest in the practical use of mathematics, he demonstrated useful applications for his system. Finally, Stevin presented his invention clearly and systematically so that it could be easily understood and followed by others.

Stevin's system of decimals was based on integers, which he called the units of commencement. Following from those were new units that Stevin named Prime, Second, Three, and so on. These were written by placing signs after the numbers. The sign consisted of a circled number, which designated the unit value. The system proved cumbersome in complex computations. Stevin recognized this and offered a shorter method of notation in which only one distinguishing sign was needed.

According to Stevin, the notation represented full integers, not fractions or parts of integers. In this sense, he did not set out to create decimal numbers. He believed that claiming integer status for all digits in the number was advantageous to its practical application. Mathematicians following Stevin, namely John Napier, soon adopted the use of a positional decimal point, thus eliminating the need for positional signs. In A History of Mathematics, Carl B. Boyer suggests that although highly trained mathematicians were familiar with a crude decimal system, "among the common people, however, and even among mathematical practitioners, decimal fractions became widely known only when Stevin undertook to explain the system in full and elementary detail. He wished to teach everyone."

Other Studies

In 1586 Stevin published several of his most famous writings: The Elements of the Art of Weighing, The Practice of Weighing, and The Elements of Hydrostatics. In The Elements of the Art of Weighing, Stevin again foreshadowed future mathematical discoveries while continuing the work of Greek scientist Archimedes in his discovery of the law of inclined planes. In describing his discovery, he drew a circle of connected, equal weights, called clootcrans, or a wreath of spheres. He was so elated with his discovery that he exclaimed, "What appears a wonder is not a wonder!" Like many in his day, Stevin believed the universe to be a vast array of mysteries that could be explained and understood through diligent study. Most of his subsequent publications included the circle of spheres and his newly adopted motto. Like his advancements in decimals, his discoveries of incline interaction grew out of his uncanny ability to circumvent detailed theory in favor of an understanding of the essence of the mathematical equation. During the 17th century, Sir Isaac Newton would fully develop the theoretical implications of Stevin's discovery.

Along with his contributions to the study of decimals and inclines, Stevin also made a significant advancement in hydrostatics, the study of the pressure that fluids extend or receive. Stevin discovered that the shape of the container does not affect the amount of pressure exerted by the compression of a fluid. Instead, it depends on the height of the liquid and the area of the surface. Always looking for applications for his discoveries, Stevin used his new understanding of hydrostatics to build advanced water mills in several locations and provided improvements to existing water mills.

There is also evidence that suggests that Stevin was the first to discover the law of gravity popularly attributed to Galileo. According to a report published in Flemish by Stevin in 1586, he and a friend dropped two balls of lead, one ten times the weight of the other, from a height of 30 feet. When the objects were dropped at the same time, Stevin discovered that the sounds of impact were simultaneous. This suggested that some force exerted the same pull on objects of different weights.

Civic Affairs and Defense

In 1588 Stevin turned his attention to civic matters, publishing the treatise Civic Life. In 1595 he returned to mathematics with the publication of the pamphlet Appendice Algebraique. In the same year, Stevin developed a name for himself in yet another field, publishing the highly regarded work The Art of Fortification.

By the end of the 16th century, Stevin came to work for Prince Maurice of Nassau as a private tutor. This job led to a new involvement in civic affairs. Stevin was appointed to an engineering position, and in 1603 named quartermaster of the States Army. At the beginning of the 16th century, the Low Countries (now the Netherlands and Belgium) were in turmoil. A revolutionary movement had begun in the 1580s in an attempt to achieve freedom from Spain. Prince Maurice became an influential leader of the resistance movement. He depended on his master tutor for direction and advice. Although Stevin's exact role in the rebellion is unknown, it is apparent that he deeply impacted the prince. In turn, his presence on numerous committees dealing with military matters influenced the activities of the forces. He was also employed to organize a school for engineers that ultimately was incorporated into the University of Leiden.

During his tenure with Maurice, Stevin compiled and wrote numerous textbooks for the prince's studies. Between 1605 and 1608, the works were published in an extensive volume entitled Mathematical Memoirs. He published only two more works in his lifetime. Released in a single volume in 1617, Marking Out of Army Camps and New Manner of Fortification dealt with practical issues Stevin encountered in his work as a civic servant. New Manner of Fortification offered an ingenious defense strategy of flooding the country in the case of an attack, a tactic suited for the water-logged states of the Low Countries. Although Stevin advocated for the creation of an office of Superintendent of Fortification and recommended himself to run it, his request was rejected.

During the final decades of his life, Stevin married a young woman named Catherine Cray, with whom he had four children before his death sometime during the first few months of 1620. His son Hendrick, who became a scientist, gathered his father's work and did much to preserve it for later generations.

Books

A Biographical Encyclopedia of Scientists, edited by John Daintith, Sarah Mitchell, and Elizabeth Tootill, Facts on File, 1981.

Boyer, Carl B., A History of Mathematics, John Wiley and Sons, 1968.

The Cambridge Dictionary of Scientists. edited by David Millar, John Millar, and Margaret Millar, Cambridge University Press, 1996.

Duksterhuis, E. J., Simon Stevin: Science in the Netherlands Around 1600, Martinus Nijhoff, 1970.

Online

"Simon Stevin," Math and Mathematicians: The History of Math Discoveries Around the World,http://www.galenet.com (January 18, 2001).

"Simon Stevin," Notable Mathematicians,http://www.galenet.com (January 18, 2001).

"Simon Stevin," World of Scientific Discovery,http://www.galenet.com (January 18, 2001).

"Simon Stevin," World of Invention,http://www.galenet.com(January 18, 2001).

"Stevin, Simon," Merriam-Webster's Biographical Dictionary,http://www.galenet.com (January 18, 2001).

Simon Stevin

Simon Stevin (1548/49 – 1620) was a Flemish mathematician and 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 ("the art of what is certain"), was not derived from Greek (via Latin).

Contents 1 Biography 2 Discoveries and inventions 2.1 Philosophy of science 2.2 Geometry and physics 2.3 Music theory 2.4 Bookkeeping 2.5 Decimal fractions 2.6 Neologisms 3 Publications 4 External links 5 References 6 Further reading 7 Trivia

Biography

Stevin was born in Bruges, Flanders (now Belgium) in the year 1548, to Antheunis Stevin and Cathelyne van der Poort. 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, he became advisor and tutor of Prince Maurice of Nassau, 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), and later quartermaster-general.

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

Statue of Stevin (detail)

Statue(detail):Inclined plane diagram

Discoveries and inventions

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 had been 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.

Philosophy of science

Stevin developed a theory about a bygone age of wisdom, for which even Hugo Grotius gave him great credit. Stevin's goal was to bring about a second age of wisdom, in which mankind would have recovered all of its earlier knowledge. He had deduced that the language spoken in this age would have had to be Dutch, because, as he had 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 and physics

Stevin's proof of the law of the equilibrium on an inclined plane

Stevin was the first to show how to model regular and semiregular polyhedra by delineating their frames in a plane. Stevin also distinguished stable from unstable equilibria. He proved the law of the equilibrium on an inclined plane, using an ingenious and intuitive diagram showing a rope containing evenly spaced beads draped over an inclined plane (see the illustration on the side). Physicist Richard Feynman discussed the diagram in his 'Lectures on Physics', and imagined that the diagram had been inscribed on Stevin's tombstone. In reality Stevin's grave does not exist.

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 downward pressure of a liquid is independent of the shape of the vessel, and depends only on its height and base.

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.^[1]

Music theory

Stevin was the first author in the West (1585, simultaneously with, and independently of, Zhu Zaiyu in China) to give a mathematically accurate specification for equal temperament. 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

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.

Decimal fractions

Stevin wrote a 36-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.

Decimal fractions had been employed for the extraction of square roots centuries before his time by Islamic mathematicians such as Al-Kashi^[2][3] 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.

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 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.

Neologisms

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' has no meaning). '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.

Publications

Amongst others, he published:

• Tafelen van Interest (Tables of interest) in 1582;
• 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;
• Wiskonstighe Ghedachtenissen (Mathematical Memoirs). 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).

External links

• O'Connor, John J.; Robertson, Edmund F., "Simon Stevin", MacTutor History of Mathematics archive, http://www-history.mcs.st-andrews.ac.uk/Biographies/Stevin.html .
•  "Simon Stevin". Catholic Encyclopedia. New York: Robert Appleton Company. 1913. http://en.wikisource.org/wiki/Catholic_Encyclopedia_(1913)/Simon_Stevin. 
• [1] contains an HTML version (including hyperlinks to explanations) of De Thiende and its translations into English, French and Swedish, and scans of these books
• [2] contains a lot more information about Simon Stevin
• [3] is the text of the Catholic Encyclopedia about Stevin. The author can hardly conceal his admiration, and for the rest the article is mostly a bibliography of Stevin's work.
• [4] is a short essay on Simon Stevin by S. Abbas Raza at 3 Quarks Daily
• [5] is an Internet bibliography regarding Simon Stevin.
• [6] treats Stevin's use of the rule of false position.
• http://www.newadvent.org/cathen/14293b.htm
• MathPages - Wonder En Is Gheen Wonder
• http://www.knaw.nl/publicaties/pdf/961083.pdf link to unpublished treatise of Simon Stevin on architecture, town planning and civil engineering - C. van den Heuvel. De Huysbou.

References

1. ^ Galileo Galilei: The Falling Bodies Experiment
2. ^ St Andrews School of Mathematics
3. ^ Flegg, Graham (2002). Numbers: Their History and Meaning. Dover Publications. p. 76. ISBN 0486421651, 9780486421650. 

•  "Stevinus, Simon". Encyclopædia Britannica (11th ed.). 1911. 

Further reading

• Virtually all of Stevin's writings have been published in five volumes with introduction and analysis in: E. J. Dijksterhuis, et al., ed (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. 
• C. van den Heuvel,: De Huysbou. A reconstruction of an unfinished treatise on architecture, and civil engineering by Simon Stevin, KNAW Edita, Amsterdam 2005, 545 pp. - The work is available on line - see external links

Trivia

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

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