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# Simon Stevin

In the DISME (1585) Simon Stevin suggested a way to write "broken numbers" (fractions) based on decimal fractions (that is fractions with 10, 100, 1'000, 10'000 etc.. for denominator)

So

"1 and 3/5" becomes "1 and 6/10" and it is written "1(int)6(dec)"

"2 and 3/4" becomes "2 and 75/100" and is written "2(int)7(dec)5(cent)".

Later on, in a new edition of his book, Simon Stevin introduced a new notation.

So

"6 and 35/100" becomes "6(0) 3(1) 5(2)"

A few decades later again, today's notation was reached:

6 and 35/100 is written 6,35 (6.35 in the English speaking world).

Source: http://www.ssis.unige.it/0607SostegnoLaviosa0607DDI_Lez2_lettura.pdf

Simon Stevin's father was Anthuenis (Anton) Stevin who, it is believed, was a cadet son of a mayor of Veurne. His mother was Cathelijne (or Catelyne) van der Poort who was the daughter of a burgher family of Ypres. Anthuenis and Cathelijne were not married but Simon's mother Cathelijne later married a man who was involved in selling carpets and in the silk trade. By marriage Cathelijne joined a family who were Calvinists. Nothing is known of Simon's early years or of his education although one assumes he was brought up in the Calvinist tradition.

Stevin became a bookkeeper and cashier with a firm in Antwerp. It is known that he spent some time between the years 1571 to 1577 travelling in Poland, Prussia and Norway. Then in 1577 he took a job as a clerk in the tax office at Brugge. After this he moved to Leiden in 1581 where he first attended the Latin school, then he entered the University of Leiden in 1583 (at the age of 35). Various theories have been put forward as to why he moved to Leiden. To understand these we need to look briefly at the history of the period.

The Union of Utrecht on 23 January 1579 was designed to form a block (known as the States-General) within the larger union of the Low Countries which would resist Spanish rule. It produced a union in the north Netherlands, still officially under the rule of the King of Spain, but distinct from the south. The strong reaction against the Spanish followed the start of a reign of terror by the Spanish occupation in the south beginning around 1567. The north was predominantly Calvinist and effectively ruled by William, Prince of Orange. In 1581 the States-General declared independence from Spain and a complex situation followed as foreign help was enlisted.

Stevin's move to the north Netherlands certainly coincided with their move to independence from the King of Spain. There were other possible reasons for Stevin to move, however, for we have already mentioned that Stevin was brought up in a Calvinist family after his mother remarried. Certainly Stevin was not alone in fleeing from the south Netherlands around this time, with many going to the north, but others fleeing to England or Germany. While Stevin was at the University of Leiden he met Maurits (Maurice), the Count Of Nassau, who was William of Orange's second son. The two became close friends and Stevin became mathematics tutor to the Prince as well as a close advisor. William of Orange was assassinated on 10 July 1584 at Delft by a Roman Catholic who believed that by assassinating William he would prevent the rebellion against Catholic Spain. William's eldest son Philip William was loyal to Spain so it was Maurits who was appointed stadholder of Holland and Zeeland, or the United Provinces of the Netherlands, in 1584.

With Prince Maurits now head of the army of the republic, and with Stevin as an advisor in his service, a series of military triumphs over the Spanish forces followed. Maurits understood the importance of military strategy, tactics, and engineering in military success. In 1600 he asked Stevin to set up an engineering school within the University of Leiden. It was a good political move to insist that the courses were taught there in the Dutch language. Certainly Prince Maurits saw his friend Stevin as having major importance in his success and the recent discovery of a journal in the Public Record Office of The Hague recording Stevin's salary as 600 Dutch guilders in 1604 confirms his high position.

It is believed that from 1604 Stevin was quartermaster-general of the army of the States-General. He invented a way of flooding the lowlands in the path of an invading army by opening selected sluices in dikes. He was an outstanding engineer who advised on building windmills, locks and ports. He advised Prince Maurits on building fortifications for the war against Spain and wrote detailed descriptions of the military innovations adopted by the army. These innovations would be copied by many other countries.

The army of the States-General reclaimed from Spanish rule essentially the territory which is today The Netherlands, and the States-General became officially recognized by England and France as an independent state. Prince Maurits wished to continue the war against Spain but, when Spain effectively recognised the United Provinces as independent and sovereign, there was little enthusiasm to continue the fight. The Twelve Years' Truce began in 1609.

Stevin bought a house at the Raamstraat in The Hague in 1612 for 3800 Dutch guilders (another sign of his high status and wealth). He married at a date given as 1610 by some sources and as 1614 by other sources. His wife was Catherine Krai, and they had four children named Frederic, Hendrik, Susanna and Levina. Hendrik, their second child, went on to attend the University of Leiden and, becoming a famous scientist in his own right, was the editor of his father's collected works.

The author of 11 books, Simon Stevin made significant contributions to trigonometry, mechanics, architecture, musical theory, geography, fortification, and navigation. His first book was Tafelen van Interest (Tables of interest) which he published in 1582. Prior to this, unpublished manuscript interest tables were in common use with bankers throughout Europe but had been treated as secret information not to be divulged. Before presenting the numerical tables, Stevin gave rules for simple and compound interest and also gave many examples of their use.

In Problemata geometrica (1583) Stevin presented geometry based largely on Euclid and Archimedes but the problems which he studied show that he was also influenced by Dürer. Stevin gave an interesting account in this work of constructions related to polygons and polyhedra, using the concept of similarity, and a study of regular and semi-regular polyhedra. It was written in Latin, and is the only one of his books to be first published in that language. He became a strong advocate of writing his scientific works in Dutch and he gives clear reasons for this choice in a text written in 1586.

In 1585 he published La Theinde (The tenth), a twenty-nine page booklet in which he presented an elementary and thorough account of decimal fractions. He wrote this small book for the benefit of:-

... stargazers, surveyors, carpet-makers, wine-gaugers, mint-masters and all kind of merchants.

Although he did not invent decimals (they had been used by the Arabs and the Chinese long before Stevin's time) he did introduce their use in mathematics in Europe. Stevin states that the universal introduction of decimal coinage, measures and weights would only be a matter of time (but he probably would be amazed to know that in the 21st century some countries still resist adopting decimal systems). Robert Norton published an English translation of La Theinde in London in 1608. It was titled Disme, The Arts of Tenths or Decimal Arithmetike and it was this translation which inspired Thomas Jefferson to propose a decimal currency for the United States (note that one tenth of a dollar is still called a dime). Stevin's notation was to be taken up by Clavius and Napier and it developed into that used today.

In the same year (1585) he published La pratique d'arithmétique and L'arithmétique which were the only texts he wrote first in French. In the latter Stevin presented a unified treatment for solving quadratic equations and a method for finding approximate solutions to algebraic equations of all degrees. He also made a strong plea that all numbers such as square roots, irrational numbers, surds, negative numbers etc should all be treated as numbers and not distinguished as being different in nature. Stevin's notion of a real number was accepted by essentially all later scientists. Particularly important was Stevin's acceptance of negative numbers but he did not accept the 'new' imaginary numbers and this was to hold back their development.

Inspired by Archimedes, Stevin wrote important works on mechanics. Mainly dealing with statics, his treatment appears in his book De Beghinselen der Weegconst published in 1586. It is famous for containing the theorem of the triangle of forces which gave impetus to statics. In the same year his treatise De Beghinselen des Waterwichts on hydrostatics contained notable improvements to the work of Archimedes on this topic. Many consider that he founded the science of hydrostatics with this work by showing that the pressure exerted by a liquid upon a given surface depends on the height of the liquid and the area of the surface.

Also in 1586 (3 years before Galileo) he reported that different weights fell a given distance in the same time. His experiments were conducted using two lead balls, one being ten times the weight of the other, which he dropped thirty feet from the church tower in Delft.

In De Hemelloop, published in 1608, he wrote on astronomy and strongly defended the sun centred system of Copernicus. Although he undertook his mathematical work earlier in his life, Stevin collected together some of his mathematical writings which he edited and published during the years 1605 to 1608 in Wiskonstighe Ghedachtenissen (Mathematical Memoirs). The collection included De Driehouckhandel (Trigonometry), De Meetdaet (Practice of measuring), and De Deursichtighe (Perspective). The work on perspective looks at a number of innovations such as the case of calculating the perspective for making a drawing on a canvas which is not perpendicular to the ground, and the case of inverse perspective. This calculates where the eye of the observer should be placed if an object and a perspective drawing of that object are given. Stevin, in his book Stelreghel (Algebra) used the notation +, - and √.

His other works included Vita Politica. Het Burgherlick leven (Civil life) published in 1590, De Sterktenbouwing (The construction of fortifications) published in 1594, De Havenvinding (Position finding) published in 1599, and the double work Castrametatio, dat is legermeting and Nieuwe Maniere van Stercktebou door Spilsluysen published in 1617.

In Het Burgherlick leven Stevin discusses how a citizen of a state should comply with the rules of the authorities (even when they appear unjust) and, in particular, he advises citizens how to behave in times of civil unrest. In De Sterktenbouwing Stevin takes an Italian method of fortification and modifies it for Dutch use. The ideas that he put forward in this treatise were clever but too expensive to implement. The work De Havenvinding literally means 'finding the harbour' and presents a method of finding the position of a ship by determining its longitude using the magnetic variation of the compass needle. Although theoretically sound, the method is impractical. In the first of the final double work that we mentioned above, Stevin describes the establishment, layout and setting up of a military camp. Particularly fascinating is his description of Prince Maurits camp which he set up prior to the Battle of Juliers in 1610. The second of the two works deals with sluices Stevin had designed to put into fortifications to keep a moat at the correct depth.

His contributions to music are contained in De Spiegheling der Singconst (Theory of the art of singing) which survived in manuscript until 1884 when it was published. This is usually seen as the first correct theory of the division of the octave into twelve equal intervals, see for example [1]. Cohen in [13] explains the importance of the problem to scientists of the period:-

Many pioneers of the Scientific Revolution, such as Galileo, Kepler, Stevin, Descartes, Mersenne, and others, wrote extensively about music theory. This was not a chance interest of a few individual scientists. Rather, it reflects a continuing concern of scientists from Pythagorean times onwards to solve certain quantifiable problems in music theory. One of the issues involved was technically known as 'the division of the octave', the problem, that is, with which notes to make music.

Cohen argues that this was not, as is commonly believed (see [1]), the purpose of Stevin's treatise:-

A careful analysis of the problem situation in the science of music around 1600, reveals that Stevin's treatise highlights a particular stage in the history of what has always been the core issue of the science of music, namely, the problem of consonance. This is the search for an explanation, on scientific principles, of Pythagoras' law: Why is it that those few musical intervals which affect our ear in a sweet and pleasing manner, correspond to the ratios of the first few integers?.

Article by: J J O'Connor

and E F Robertson

January 2004

Related pages

Decimals

Decimal worksheets

Decimal-to-fractions

Fractions-to-decimals

From Simon Stevin back to the decimals webpage.

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