De Thiende


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 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, and 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 book De Thiende was expressed in The Princeton Companion to Mathematics:
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.