De Thiende, published in 1585 in the Dutch language by Simon Stevin, 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 between integer and fractional parts of a decimal number, calling it the "commencement". His notation included superfluous symbols after or above the tenths place, 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 in the 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, "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, an its occurrence can be very exactly dated – 1585." The Princeton Companion to Mathematics provides the following estimation of Stevin's contribution to positional notation:
Importance
The importance of Stevin's bookDe Thiende was expressed in The Princeton Companion to Mathematics: "The idea of extending the decimal place-value system to include fractions was discovered by several mathematicians. The most influential of these was Simon Stevin, a Flemish mathematician and engineer who popularized the system in a booklet called De Thiende, first published in 1585. By extending place value to tenths, hundredths, and so on, Stevin created the system we still use today. More importantly, he explained how it simplified calculations that involved fractions, and gave many practical applications. The cover page, in fact, announces that the book is for astrologers, surveyors, measurers of tapestries." 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 by Abu'l-Hasan al-Uqlidisi exhibited decimal fractions as well as a decimal separator.
