Simon Stevin

Encyclopedia

**Simon Stevin**was a Flemish

Flemish people

The Flemings or Flemish are the Dutch-speaking inhabitants of Belgium, where they are mostly found in the northern region of Flanders. They are one of two principal cultural-linguistic groups in Belgium, the other being the French-speaking Walloons...

mathematician

Mathematician

A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....

and military engineer

Engineer

An engineer is a professional practitioner of engineering, concerned with applying scientific knowledge, mathematics and ingenuity to develop solutions for technical problems. Engineers design materials, structures, machines and systems while considering the limitations imposed by practicality,...

. He was active in a great many areas of science and engineering, both theoretical and practical. He also translated various mathematical terms into Dutch

Dutch language

Dutch is a West Germanic language and the native language of the majority of the population of the Netherlands, Belgium, and Suriname, the three member states of the Dutch Language Union. Most speakers live in the European Union, where it is a first language for about 23 million and a second...

, making it one of the few European languages in which the word for mathematics

Mathematics

Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...

,

*wiskunde*("the art of what is certain"), was not derived from Greek

Greek language

Greek is an independent branch of the Indo-European family of languages. Native to the southern Balkans, it has the longest documented history of any Indo-European language, spanning 34 centuries of written records. Its writing system has been the Greek alphabet for the majority of its history;...

(via Latin

Latin

Latin is an Italic language originally spoken in Latium and Ancient Rome. It, along with most European languages, is a descendant of the ancient Proto-Indo-European language. Although it is considered a dead language, a number of scholars and members of the Christian clergy speak it fluently, and...

).

## Biography

Stevin was born in BrugesBruges

Bruges is the capital and largest city of the province of West Flanders in the Flemish Region of Belgium. It is located in the northwest of the country....

, Flanders (now Belgium

Belgium

Belgium , officially the Kingdom of Belgium, is a federal state in Western Europe. It is a founding member of the European Union and hosts the EU's headquarters, and those of several other major international organisations such as NATO.Belgium is also a member of, or affiliated to, many...

) around the year 1548, to unmarried parents, Antheunis (Anton) Stevin and Catelyne van der Poort. His father is believed to have been a cadet

Cadet (genealogy)

In genealogy, a cadet is a younger son, as opposed to the firstborn heir. Compare puisne.- Etymology :The word is recorded in English since 1634, originally for a young son, identical to the French, which is itself derived from the gascon Occitan capdet "captain, chief", in turn from the Late...

son of a mayor of Veurne

Veurne

Veurne is a city and municipality in the Belgian province of West Flanders. The municipality comprises the town of Veurne proper and the settlements of Avekapelle, Booitshoeke, Bulskamp, De Moeren, Eggewaartskapelle, Houtem, Steenkerke, Vinkem, Wulveringem, and Zoutenaaie.-Origins in the 15th...

, while his mother Cathelijne (or Catelyne) was the daughter of a burgher

Burgher

Burgher may refer to:* A citizen of a borough or town, especially one belonging to middle class* A resident of a burgh* A formally defined class in medieval German cities, usually the only group from which city officials could be drawn...

family from Ypres

Ypres

Ypres is a Belgian municipality located in the Flemish province of West Flanders. The municipality comprises the city of Ypres and the villages of Boezinge, Brielen, Dikkebus, Elverdinge, Hollebeke, Sint-Jan, Vlamertinge, Voormezele, Zillebeke, and Zuidschote...

. 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 in the Calvinist faith. Very little has been recorded about his life. Even the exact date of birth and the date and place of his death (The Hague

The Hague

The Hague is the capital city of the province of South Holland in the Netherlands. With a population of 500,000 inhabitants , it is the third largest city of the Netherlands, after Amsterdam and Rotterdam...

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

Poland

Poland , officially the Republic of Poland , is a country in Central Europe bordered by Germany to the west; the Czech Republic and Slovakia to the south; Ukraine, Belarus and Lithuania to the east; and the Baltic Sea and Kaliningrad Oblast, a Russian exclave, to the north...

, Denmark

Denmark

Denmark is a Scandinavian country in Northern Europe. The countries of Denmark and Greenland, as well as the Faroe Islands, constitute the Kingdom of Denmark . It is the southernmost of the Nordic countries, southwest of Sweden and south of Norway, and bordered to the south by Germany. 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

William the Silent

William I, Prince of Orange , also widely known as William the Silent , or simply William of Orange , was the main leader of the Dutch revolt against the Spanish that set off the Eighty Years' War and resulted in the formal independence of the United Provinces in 1648. He was born in the House of...

's second son, Maurits (Maurice), the Count Of Nassau. 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

Public works

Public works are a broad category of projects, financed and constructed by the government, for recreational, employment, and health and safety uses in the greater community...

), and later quartermaster-general of the army of the States-General.

In Bruges

In Bruges

In Bruges is a 2008 black comedy crime film written and directed by Martin McDonagh. The film stars Colin Farrell and Brendan Gleeson as two hitmen in hiding, with Ralph Fiennes as their gangster boss. The film takes place—and was filmed—within the Belgian city of Bruges. In Bruges was...

there is a Simon Stevin Square which contains his statue by Eugène Simonis

Eugène Simonis

Louis-Eugène Simonis was a Belgian sculptor.-Career:Simonis studied under François-Joseph Dewandre at the Academie Royale des Beaux-Arts in Liège and at the age of nineteen went to Italy, where he continued his studies in Bologna and Rome. When he returned to Belgium he accepted an instructor...

, which includes his 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 yachtLand sailing

Land sailing, also known as sand yachting or land yachting, is the act of moving across land in a wheeled vehicle powered by wind through the use of a sail. The term comes from analogy with sailing. Historically, land sailing was used as a mode of transportation or recreation...

, 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

Maurice of Nassau, Prince of Orange

Maurice of Nassau, Prince of Orange was sovereign Prince of Orange from 1618, on the death of his eldest half brother, Philip William, Prince 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 GrotiusHugo Grotius

Hugo Grotius , also known as Huig de Groot, Hugo Grocio or Hugo de Groot, was a jurist in the Dutch Republic. With Francisco de Vitoria and Alberico Gentili he laid the foundations for international law, based on natural law...

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, physics and trigonometry

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 an ingenious and intuitive 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

Trigonometry

Trigonometry is a branch of mathematics that studies triangles and the relationships between their sides and the angles between these sides. Trigonometry defines the trigonometric functions, which describe those relationships and have applicability to cyclical phenomena, such as waves...

. His book,

*De Driehouckhandel*, included Plane Trigonometry.

He demonstrated the resolution of forces before Pierre Varignon

Pierre Varignon

Pierre Varignon was a French mathematician. He was educated at the Jesuit College and the University in Caen, where he received his M.A. in 1682. He took Holy Orders the following year....

, 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, the area of the base, and 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

Theory of tides

The theory of tides is the application of continuum mechanics to interpret and predict the tidal deformations of planetary and satellite bodies and their atmospheres and oceans, under the gravitational loading of another astronomical body or bodies...

.

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

### Music theory

The first mention of equal temperament related to Twelfth root of two in the West appeared in Simon StevinSimon Stevin

Simon Stevin was a Flemish mathematician and military engineer. He was active in a great many areas of science and engineering, both theoretical and practical...

's unfinished manuscript

*Van de Spiegheling der signconst*(ca 1605) published posthumously three hundred years later in 1884http://diapason.xentonic.org/ttl/ttl21.html; 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.. He appears to have been inspired by the writings of the Italian lutenist and musical theorist Vincenzo Galilei

Vincenzo Galilei

Vincenzo Galilei was an Italian lutenist, composer, and music theorist, and the father of the famous astronomer and physicist Galileo Galilei and of the lute virtuoso and composer Michelagnolo Galilei...

(father of Galileo Galilei

Galileo Galilei

Galileo Galilei , was an Italian physicist, mathematician, astronomer, and philosopher who played a major role in the Scientific Revolution. His achievements include improvements to the telescope and consequent astronomical observations and support for Copernicanism...

), a onetime pupil of Gioseffo Zarlino

Gioseffo Zarlino

Gioseffo Zarlino was an Italian music theorist and composer of the Renaissance. He was possibly the most famous music theorist between Aristoxenus and Rameau, and made a large contribution to the theory of counterpoint as well as to musical tuning.-Life:Zarlino was born in Chioggia, near Venice...

.

### 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 PacioliLuca Pacioli

Fra Luca Bartolomeo de Pacioli was an Italian mathematician, Franciscan friar, collaborator with Leonardo da Vinci, and seminal contributor to the field now known as accounting...

and Gerolamo Cardano

Gerolamo Cardano

Gerolamo Cardano was an Italian Renaissance mathematician, physician, astrologer and gambler...

. 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

Maximilien de Béthune, duc de Sully

Maximilien de Béthune, first Duke of Sully was the doughty soldier, French minister, staunch Huguenot and faithful right-hand man who assisted Henry IV of France in the rule of France.-Early years:...

.

### Decimal fractions

Stevin wrote a 36-page bookBook

A book is a set or collection of written, printed, illustrated, or blank sheets, made of hot lava, paper, parchment, or other materials, usually fastened together to hinge at one side. A single sheet within a book is called a leaf or leaflet, and each side of a leaf is called a page...

let 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. 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

Bartholomaeus Pitiscus

Bartholomaeus Pitiscus was a 16th century German trigonometrist, astronomer and theologian who first coined the word Trigonometry....

, in whose trigonometrical tables (1612) it occurs and it was accepted by John Napier

John Napier

John Napier of Merchiston – also signed as Neper, Nepair – named Marvellous Merchiston, was a Scottish mathematician, physicist, astronomer & astrologer, and also the 8th Laird of Merchistoun. He was the son of Sir Archibald Napier of Merchiston. John Napier is most renowned as the discoverer...

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.

### Mathematics

Stevin wrote his*Arithmetic*in 1594. The work contains the first general solution of the quadratic equation

Quadratic equation

In mathematics, a quadratic equation is a univariate polynomial equation of the second degree. A general quadratic equation can be written in the formax^2+bx+c=0,\,...

.

According to van der Waerden

Bartel Leendert van der Waerden

Bartel Leendert van der Waerden was a Dutch mathematician and historian of mathematics....

(1985, p. 69), Stevin's "general notion of a real number

Real number

In mathematics, a real number is a value that represents a quantity along a continuum, such as -5 , 4/3 , 8.6 , √2 and π...

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. Stevin proved the intermediate value theorem

Intermediate value theorem

In mathematical analysis, the intermediate value theorem states that for each value between the least upper bound and greatest lower bound of the image of a continuous function there is at least one point in its domain that the function maps to that value....

for polynomials, anticipating Cauchy's proof thereof. Stevin uses a divide and conquer

Divide and conquer

Divide and conquer may refer to:* Divide and rule, in politics, sociology and economics, a strategy to gain or maintain power...

procedure subdividing the interval into ten equal parts.

### Neologisms

Stevin thought the Dutch languageDutch language

Dutch is a West Germanic language and the native language of the majority of the population of the Netherlands, Belgium, and Suriname, the three member states of the Dutch Language Union. Most speakers live in the European Union, where it is a first language for about 23 million and a second...

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.

Dice

A die is a small throwable object with multiple resting positions, used for generating random numbers...

His books were bestsellers.

## Trivia

The student association of mechanical engineering at the Technische Universiteit EindhovenEindhoven University of Technology

The ' is a university of technology located in Eindhoven, Netherlands. The motto of the university is: Mens agitat molem . The university was the second of its kind in the Netherlands, only Delft University of Technology existed previously. Until mid-1980 it was known as the...

, W.S.V. Simon Stevin 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

Laurence Sterne

Laurence Sterne was an Irish novelist and an Anglican clergyman. He is best known for his novels The Life and Opinions of Tristram Shandy, Gentleman, and A Sentimental Journey Through France and Italy; but he also published many sermons, wrote memoirs, and was involved in local politics...

's

*The Life and Opinions of Tristram Shandy Gentleman*.

Quote:

*A man in anger is no clever dissembler*

## Publications

Amongst others, he published:-
*Tafelen van Interest*(Tables of interest) in 1582 with present valuePresent valuePresent value, also known as present discounted value, is the value on a given date of a future payment or series of future payments, discounted to reflect the time value of money and other factors such as investment risk...

problems of simple and compound interestCompound interestCompound interest arises when interest is added to the principal, so that from that moment on, the interest that has been added also itself earns interest. This addition of interest to the principal is called compounding...

and interest tables that had previously been unpublished by bankers; -
*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 equationsAlgebraic geometryAlgebraic geometry is a branch of mathematics which combines techniques of abstract algebra, especially commutative algebra, with the language and the problems of geometry. It occupies a central place in modern mathematics and has multiple conceptual connections with such diverse fields as complex...

; -
*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 findingNavigationNavigation is the process of monitoring and controlling the movement of a craft or vehicle from one place to another. It is also the term of art used for the specialized knowledge used by navigators to perform navigation tasks...

) published in 1599; -
*De Hemelloop*in 1608 in which he voiced support for the CopernicanNicolaus CopernicusNicolaus Copernicus was a Renaissance astronomer and the first person to formulate a comprehensive heliocentric cosmology which displaced the Earth from the center of the universe....

theory. -
*Wiskonstighe Ghedachtenissen*(Mathematical Memoirs). This included earlier works like*De Driehouckhandel*(TrigonometryTrigonometryTrigonometry is a branch of mathematics that studies triangles and the relationships between their sides and the angles between these sides. Trigonometry defines the trigonometric functions, which describe those relationships and have applicability to cyclical phenomena, such as waves...

),*De Meetdaet*(Practice of measuringMeasurementMeasurement is the process or the result of determining the ratio of a physical quantity, such as a length, time, temperature etc., to a unit of measurement, such as the metre, second or degree Celsius...

), and De Deursichtighe (PerspectivePerspective (graphical)Perspective in the graphic arts, such as drawing, is an approximate representation, on a flat surface , of an image as it is seen by the eye...

); -
*Castrametatio, dat is legermeting and Nieuwe Maniere van Stercktebou door Spilsluysen*(New ways of building of sluiceSluiceA sluice is a water channel that is controlled at its head by a gate . For example, a millrace is a sluice that channels water toward a water mill...

s) published in 1617; -
*De Spiegheling der Singconst*(Theory of the art of singing).

## Further reading

- Virtually all of Stevin's writings have been published in five volumes with introduction and analysis in: 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: .
- A recent work on Simon Stevin in Dutch is: .
- A recent work on Simon Stevin in English is: 545 pp – The work is available on line – see external links

## External links

- Simon Stevin's De Thiende en vertalingen, contains an HTML version (including hyperlinks to explanations) of
*De Thiende*and its translations into English, French and Swedish, and scans of these books - Honkblad van Simon Stevin (1548–1620) contains a lot more information about Simon Stevin
- Newadvent.org 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.
- 3 Quarks Daily is a short essay on Simon Stevin by S. Abbas Raza at
*3 Quarks Daily* - Simonstevin.be is an Internet bibliography regarding Simon Stevin.
- Loci: Convergence treats Stevin's use of the rule of false position.
- Catholic Enxyclopedia
- MathPages –
*Wonder En Is Gheen Wonder* - KNAW.nl link to unpublished treatise of Simon Stevin on architecture, town planning and civil engineering – C. van den Heuvel. De Huysbou.