De Thiende

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I. De Thiende
Preserved copies, reprints and translations

Of the works of Simon Stevin De Thiende is his best-known in history of mathematics. In this book a new method to write decimal fractions is given, not by means of a numerator and a denominator (the latter of the form 10ⁿ) but in a positional system as was known already for whole numbers, written in Hindu-Arabic numerals. After this Stevin also treats for his new decimal fractions the fundamental arithmetical operations and from this treatment it becomes clear that all these operations can be performed now more easily and can be more conveniently arranged than before, when the older notation was used.

Herewith the importance of Stevin's invention is very briefly denoted. But his ideas were more far-reaching for in an ‘Aenhangsel’ (Appendix, pp. 22-36) he, moreover, points out how in practical computations his invention can give the best results. He then proposes to stick to the customary units for money, weights and measures but to take new subdivisions in tenths, hundredths and so on. Everyone who is familiar at all with those subdivisions

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in Stevin's days will agree that this proposal was indeed very clever and we cannot but admire Stevin not only because of the fact that he introduced the arithmetical operations with his new decimals but also fully saw the possible practical advantages.

At this time only a few copies of the original edition of De Thiende (1585) still are extant. E.J. Dijksterhuis mentions (a, p. 37) 3 copies viz. in Rotterdam, Gemeente Bibliotheek (Municipal Library), and in Antwerp, Stads-bibliotheek (Municipal Library) and Museum Plantin-Moretus. He also makes mention (a, p. 34) of investigations in connection with preserved copies of Stevin's works, made by Th. Morren in the beginning of this century. With the help of the results of these investigations - which can be consulted in the Gemeente Archief (the Archives) in the Hague - we were able to trace another copy of the original edition of De Thiende, viz. in the Stadt- und Universitätsbibliothek (Municipal and University Library) at Bern. From personal investigations it has become clear to us that there is another copy in the British Museum in London¹⁾.

The book was reprinted for the first time²⁾ in

1) In 1924 H. Bosnians (p. 4) also mentioned a copy in the University Library at Louvain. Now this copy has been lost.

2) D.E. Smith b), I, p. 564, gives in his chronological list for the year 1590; ‘Stevin. Decimal fractions’. This is not right. Nothing is said by D.E. Smith about the 1585-edition.

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Rotterdam in 1621. This reprint, edited by Jan van Waesbergen, differs from the original edition in this that the decimal signs are not printed in a circle but between two vertical lines³⁾.

A.J.J. van de Velde mentions (p. 24), as a separate edition De Thiende ... Leiden, Jan Cloesz van Dorp, 1626⁴⁾.

In works of Ezechiël De Decker the book was reprinted twice, viz. in Eerste deel van de nieuwe telkonst 1626 and in Nieuwe Rabattafels 1630, both printed at Gouda by Pieter Rammaseyn. A facsimile with an introduction by H. Bosmans appeared in 1924⁵⁾.

A new facsimile with an introduction by D.J. Struik and with an English translation occurs in the second volume, part I, of The principal works of Simon Stevin 1958⁶⁾.

Simon Stevin himself translated De Thiende into French. Under the title of La Disme, this translation appeared, also in the year 1585 and at Leyden, as part of his La Pratique d' Arithmetique (pp. 132 up to 160 inclusive). At the foot of the title-page of La Disme we read:

premierement descripte en Flameng, conuertie en François par Simon Stevin de Bruges, (written first in Flemish and now done into French by Simon Stevin of Bruges).

3) A copy is in the University Library in Amsterdam (Sign. 2007 E 48). This book which is not mentioned in existing bibliographies on Simon Stevin (E.J. Dijksterhuis, A.J.J. van de Velde) seems to be a very rare edition which up to the present day has remained unknown.

4) Not mentioned by E.J. Dijksterhuis.

5) In the Municipal Library in Antwerp is a copy (Sign. G. 15330) of a facsimile printed by J.E. Buschman for the ‘Maatschappij der Antwerpse Bibliophielen’ (Society of Antwerp bibliophiles). Only 15 copies were printed. This is a separate print of the Bosmans edition.

6) The facsimile is not entirely complete since the ‘Extract vande Privilegie’ following after page 36 is missing. The translation in English is the one of R. Norton, edited in London 1608. The translations of our quotations from the Dutch text, following below, are copied from Norton's translation occurring in The principal works of Simon Stevin. The translations of our quotations from the French La Disme are from V. Sanford's translation in D.E. Smith, a).

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This makes it evident that the Dutch text is the older⁷⁾.

The explanatory notes in the margins of some pages of De Thiende are lacking in La Disme⁸⁾. Further the Dutch text has (p. II):

Alle voorgestelde heel ghetal, noemen vvy Beghin,...
(Every (whole) number propounded is called commencement,...)

but for this we read in La Disme:

Toute nombre propose se dict Commencement,...
(Any given number is called the unit,...)

so the adjective ‘heel’ (whole) is not translated into French⁹⁾.

This La Disme also occurs in L' Arithmetique de Simon Stevin de Bruges, Reveuë, corrigee & augmentee de plusieurs traictez et annotations par Albert Girard Samielois ... Leyden 1625 and in Les Oeuvres Mathematiques de Simon Stevin de Bruges. Par Albert Girard, Leyden 1634.

G.A. Sarton wrote an extensive introduction to a facsimile of La Disme in ‘Isis’ 1935.

As translations or adaptations of De Thiende E.J. Dijksterhuis also states (a, pp. 37, 38):

7) Some confusion could arise whether the Dutch or the French text is the older for on pp. 13, 15, 16 and 18 of De Thiende Stevin refers to L'Arithmetique.

8) See about these explanatory notes p. 15, 16 below. In the French text these notes would have been superfluous.

9) In the English translation by R. Norton of the Dutch text the word ‘heel’ is not translated either. But from what will be explained below it will become clear that it is of essential importance te denote the whole numbers, the integers (and not numbers in general) with ‘commencement’.
The German translation by H. Gericke and K. Vogel has: ‘Jede vorgelegte ganze Zahl’, so ‘heel’ is translated. We only point to this difference between the Dutch and the French texts. But there are still other, though minor, differences.

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De la Londe, Traité de l'arithmétique dixme, Liège 1605.

Robert Norton, Dime: The Art of Tenths, or Decimall Arithmetic, London 1608.

Henry Lyte, The Art of tenths, or decimall arithmeticke, London 1619.

In A source book in mathematics 1929 (second edition 1959) published by D.E. Smith occurs an English translation of La Disme.

Quite recently, in 1965, a German translation appeared by H. Gericke and K. Vogel.