''De Thiende'', published in 1585 in the

Dutch language Dutch ( ) is a West Germanic language spoken by about 25 million people as a first language and 5 million as a second language. It is the third most widely spoken Germanic language The Germanic languages are a branch of the Indo-Europea ...

Simon Stevin Simon Stevin (; 1548–1620), sometimes called Stevinus, was a Flemish mathematician, scientist and music theorist. He made various contributions in many areas of science and engineering, both theoretical and practical. He also translated vario ...

, is remembered for extending positional notation to the use of decimals to represent fractions. A French version, ''La Disme'', was issued the same year by Stevin. Stevin introduced the

decimal separator A decimal separator is a symbol used to separate the integer part from the fractional part of a number written in decimal form (e.g., "." in 12.45). Different countries officially designate different symbols for use as the separator. The choi ...

(0) between integer and fractional parts of a decimal number, calling it the "commencement". His notation included superfluous symbols (1) after or above the tenths place, (2) after or above the hundredths, and so on. Stevin also produced a French language version, and according to Sarton, "As the Flemish and French texts were both written by the author, edited by him, and published at almost the same time in the same printing shop, they have practically the same standing as original sources of STEVIN’s thought."

Decimal fractions

According to

George Sarton George Alfred Leon Sarton (; 31 August 1884 – 22 March 1956) was a Belgian-born American chemist and historian. He is considered the founder of the discipline of the history of science as an independent field of study. His most influential work ...

, "The ''Thiende'' was the earliest treatise deliberately devoted to the study of decimal fractions, and STEVIN's account is the earliest account of them. Hence, even if decimal fractions were used previously by other men, it was STEVIN – and no other – who introduced them into the mathematical domain. That important extension of the idea of number – the creation of the decimal number – was undoubtedly a fruit of his genius, and its occurrence can be very exactly dated – 1585."

(1935) "The first explanations of decimal fractions and measures (1585)"

Isis Isis (; ''Ēse''; ; Meroitic: ''Wos'' 'a''or ''Wusa''; Phoenician: 𐤀𐤎, romanized: ʾs) was a major goddess in ancient Egyptian religion whose worship spread throughout the Greco-Roman world. Isis was first mentioned in the Old Kin ...

23(1): 153–24
Jstor
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The Princeton Companion to Mathematics ''The Princeton Companion to Mathematics'' is a book providing an extensive overview of mathematics that was published in 2008 by Princeton University Press. Edited by Timothy Gowers with associate editors June Barrow-Green and Imre Leader, it ...

'' provides the following estimation of Stevin's contribution to positional notation: :"The Flemish mathematician and engineer Simon Stevin is remembered for his study of decimal fractions. Although he was not the first to use decimal fractions (they are found in the work of the tenth-century Islamic mathematician

al-Uqlidisi Abu'l Hasan Ahmad ibn Ibrahim Al-Uqlidisi ( ar, أبو الحسن أحمد بن ابراهيم الإقليدسي) was a Muslim Arab mathematician, who was active in Damascus and Baghdad. He wrote the earliest surviving book on the positional us ...

), it was his tract ''De Thiende'' (“The tenth”), published in 1585 and translated into English as ''Disme: The Art of Tenths, or Decimall Arithmetike Teaching'' (1608), that led to their widespread adoption in Europe. Stevin, however, did not use the notation we use today. He drew circles around the exponents of the powers of one tenth: thus he wrote 7.3486 as 7 3⁽¹⁾ 4⁽²⁾ 8⁽³⁾ 6⁽⁴⁾. In ''De Thiende'' Stevin not only demonstrated how decimal fractions could be used but also advocated that a decimal system should be used for weights and measures and for coinage."

Importance

The importance of Stevin's book ''De Thiende'' was expressed in ''

'': On the dedication, Sarton wrote, "The dedication 'To astrologers, landmeasurers, measurers of tapestry and wine casks, and steriometricians in general, mint-masters and merchants all, SIMON STEVIN, greetings' has such a queer ring that I wonder whether the author did not make it with his tongue in his cheek." Although Stevin is credited with introduction of decimal fractions in Europe through this book, there were predecessors: In particular, the book ''al-Fusul'' (952) by

Abu'l-Hasan al-Uqlidisi Abu'l Hasan Ahmad ibn Ibrahim Al-Uqlidisi ( ar, أبو الحسن أحمد بن ابراهيم الإقليدسي) was a Muslim Arab mathematician, who was active in Damascus and Baghdad. He wrote the earliest surviving book on the positional use ...

exhibited decimal fractions as well as a

Roshdi Rashed Roshdi Rashed (Arabic: رشدي راشد), born in Cairo in 1936, is a mathematician, philosopher and historian of science, whose work focuses largely on mathematics and physics of the medieval Arab world. His work explores and illuminates the un ...

(1996) ''Encyclopedia of the History of Arabic Science'', chapter 10: Numeration and Arithmetic, page 315,

Routledge Routledge () is a British multinational publisher. It was founded in 1836 by George Routledge, and specialises in providing academic books, journals and online resources in the fields of the humanities, behavioural science, education, law ...

References

{{reflist * Vera Sanford (translator
Stevin: On Decimal Fractions
pages 20 to 34 in

David Eugene Smith David Eugene Smith (January 21, 1860 – July 29, 1944) was an American mathematician, educator, and editor. Education and career David Eugene Smith is considered one of the founders of the field of mathematics education. Smith was born in Cortl ...

(1929) ''A Source Book in Mathematics'' via

Internet Archive The Internet Archive is an American digital library with the stated mission of "universal access to all knowledge". It provides free public access to collections of digitized materials, including websites, software applications/games, music, ...

External links

''La Thiende'' at britannica.com
16th-century books Mathematics textbooks Science and technology in the Dutch Republic