de Spiegheling der singconst (ca 1605) published posthumously three hundred years later in 1884; however, due to insufficient accuracy of his calculation, many of the numbers (for string length) 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 (father of Galileo Galilei), a onetime pupil of Gioseffo Zarlino. 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 Pacioli and Gerolamo Cardano. 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. Decimal fractions Stevin wrote a 35-page booklet called De Thiende ("the art of tenths"), first published in Dutch in 1585 and translated into French as La 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, in whose trigonometrical tables (1612) it occurs, and it was accepted by John Napier 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 did not avoid fractional exponents; only negative exponents do not appear in his work. Stevin wrote on other