Etymologie, Etimología, Étymologie, Etimologia, Etymology, (griech.) etymología, (lat.) etymologia, (esper.) etimologio
SA Saudi-Arabien, Arabia Saudita, Arabie saoudite, Arabia Saudita, Saudi Arabia, (esper.) Sauda Arabujo
Zahlen, Número, Nombre, Numero, Number, (esper.) nombroj, nombroteorio
Zahlentheorie, Teoría de números, Théorie des nombres, Teoria dei numeri, Number Theory
Algebraische Zahlentheorie, Teoría de números algebraicos, Théorie algébrique des nombres, Teoria algebrica dei numeri, Algebraic number theory

Arabic Numerals (W3)

Arabic Numerals are actually Indian numerals (1234567890). They were created by the Hindus about 400 BC but transfered to the western world by the Arabs, hence the misnomer. Today they are the internationally most common numerals. They replaced the roman numerals in Europe with the invention of printing with movable type in the 15th century and the spread of the decimal system in the 16th century.

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PREFACE

So familiar are we with the numerals that bear the misleading name of Arabic, and so extensive is their use in Europe and the Americas, that it is difficult for us to realize that their general acceptance in the transactions of commerce is a matter of only the last four centuries, and that they are unknown to a very large part of the human race to-day. It seems strange that such a labor-saving device should have struggled for nearly a thousand years after its system of place value was perfected before it replaced such crude notations as the one that the Roman conqueror made substantially universal in Europe. Such, however, is the case, and there is probably no one who has not at least some slight passing interest in the story of this struggle. To the mathematician and the student of civilization the interest is generally a deep one; to the teacher of the elements of knowledge the interest may be less marked, but nevertheless it is real; and even the business man who makes daily use of the curious symbols by which we express the numbers of commerce, cannot fail to have some appreciation for the story of the rise and progress of these tools of his trade.

This story has often been told in part, but it is a long time since any effort has been made to bring together the fragmentary narrations and to set forth the general problem of the origin and development of these [iv]numerals. In this little work we have attempted to state the history of these forms in small compass, to place before the student materials for the investigation of the problems involved, and to express as clearly as possible the results of the labors of scholars who have studied the subject in different parts of the world. We have had no theory to exploit, for the history of mathematics has seen too much of this tendency already, but as far as possible we have weighed the testimony and have set forth what seem to be the reasonable conclusions from the evidence at hand.

To facilitate the work of students an index has been prepared which we hope may be serviceable. In this the names of authors appear only when some use has been made of their opinions or when their works are first mentioned in full in a footnote.

If this work shall show more clearly the value of our number system, and shall make the study of mathematics seem more real to the teacher and student, and shall offer material for interesting some pupil more fully in his work with numbers, the authors will feel that the considerable labor involved in its preparation has not been in vain.

We desire to acknowledge our especial indebtedness to Professor Alexander Ziwet for reading all the proof, as well as for the digest of a Russian work, to Professor Clarence L. Meader for Sanskrit transliterations, and to Mr. Steven T. Byington for Arabic transliterations and the scheme of pronunciation of Oriental names, and also our indebtedness to other scholars in Oriental learning for information.

DAVID EUGENE SMITH
LOUIS CHARLES KARPINSKI

CONTENTS

• CHAPTER
• PRONUNCIATION OF ORIENTAL NAMES vi
• I. EARLY IDEAS OF THEIR ORIGIN 1
• II. EARLY HINDU FORMS WITH NO PLACE VALUE 12
• III. LATER HINDU FORMS, WITH A PLACE VALUE 38
• IV. THE SYMBOL ZERO 51
• V. THE QUESTION OF THE INTRODUCTION OF THE
• NUMERALS INTO EUROPE BY BOETHIUS 63
• VI. THE DEVELOPMENT OF THE NUMERALS AMONG THE ARABS 91
• VII. THE DEFINITE INTRODUCTION OF THE NUMERALS INTO EUROPE 99
• VIII. THE SPREAD OF THE NUMERALS IN EUROPE 128
• INDEX 153

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The Arabic numerals can be written and found more quickly, and with less danger of confusion or mistake, than any other symbols whatever. Therefore the Roman numerals, capitals and small letters, and similar symbols usually found in systems of classification are entirely discarded and by the exclusive use of Arabic numerals in their regular order throughout the shelves, classifications, indexes, catalogues and records, there is secured the greatest accuracy, economy, and convenience. This advantage is specially prominent in comparison with systems where the name of the author or the title must be written in calling for or charging books and in making references.
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Dates are all given in years of the common calendar, and Arabic numerals are uniformly used for all numbers.
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The numerals referred to here as 'Arabic' and 'Urdu' are those used when writing those languages. The Urdu numerals are also known as 'East Arab' numerals and differ slightly from those used in Arabic. In Arabic they are known as "Indian numbers" ("arqa-m hindiyyah").

The numerals 1, 2, 3, etc. are also known as "Arabic numerals", or "Hindu-Arabic numerals", "Indian numerals", "Hindu numerals", "European numerals", and "Western numerals". These numerals where first used in India in about 400 BC, were later used in Persia, then were brought to Europe by the Arabs. Hence the name "Arabic numerals".
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The Arabic numeral system

The Indian numerals discussed in our article Indian numerals form the basis of the European number systems which are now widely used. However they were not transmitted directly from India to Europe but rather came first to the Arabic/Islamic peoples and from them to Europe. The story of this transmission is not, however, a simple one. The eastern and western parts of the Arabic world both saw separate developments of Indian numerals with relatively little interaction between the two. By the western part of the Arabic world we mean the regions comprising mainly North Africa and Spain. Transmission to Europe came through this western Arabic route, coming into Europe first through Spain.

There are other complications in the story, however, for it was not simply that the Arabs took over the Indian number system. Rather different number systems were used simultaneously in the Arabic world over a long period of time. For example there were at least three different types of arithmetic used in Arab countries in the eleventh century: a system derived from counting on the fingers with the numerals written entirely in words, this finger-reckoning arithmetic was the system used for by the business community; the sexagesimal system with numerals denoted by letters of the Arabic alphabet; and the arithmetic of the Indian numerals and fractions with the decimal place-value system.
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Arabische Zahlen (W3)

In Europa wurde das indisch-arabische Zahlenrechnen (Dezimalsystem) erst durch den italienischen Kaufmann und Mathematiker Leonardo Fibonacci, genannt Leonardo von Pisa,(* Pisa um 1170, † ebd. nach 1240) bekannt. Er hatte auf Reisen nach Afrika, Byzanz und Syrien die arabische Mathematik kennengelernt und vermittelte sie in seinem Rechenbuch "Liber abaci" (lat. - Buch des Abakus) (1202, neubearbeitet 1228). Aber erst mit der Erfindung des Buchdrucks setzte sich das Rechnen mit den zehn Ziffern in Europa endgültig durch. In Deutschland war die Verbreitung des Dezimalsystems den Rechenbüchern des Adam Ries zu verdanken (1518).

Indische Zahlen und Arabische Zahlen
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Die wahren Urheber des Systems waren allerdings keineswegs Araber. Die Wiege unseres Zahlensystems stand in Indien. Von dort aus kam es in die Arabische Welt, von wo aus es über Spanien nach Europa gelangte. Zunächst wurde es als heidnische Hervorbringung verboten, setzte sich dann aber - nicht zuletzt durch die Werke Adam Rieses - langsam auch hier durch.

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Leonardo Fibonacci (1170-1250) führte Mitte des 12. Jahrhunderts das arabische Zeichensystem ein, das die römischen Zahlen ablöste.
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Arabische Ziffern (W3)

Bezeichnung für die heute gebräuchlichen zehn Zahlzeichen, einschliesslich der Null, von denen jedes ausser seinem absoluten noch einen relativen, von seiner jeweiligen Stellung abhängigen Wert hat. Die von den Arabern im 9. Jh. übernommene indische Erfindung bezeichnet die Zehner, Hunderter usw. wie die Einer durch Anhängen von Nullen (arab. 0 = zifr, zafar). Die Araber entwickelten die einfachen Rechnungsregeln, den Algorithmus, das Rechnen im Dezimalsystem, das im 13. Jh. v.a. über Italien Eingang in Europa fand. Die A. lösten die für das Rechnen unbequemeren röm. Zahlen im Gebiet der Schweiz zuerst bei den Daten ab. Sie erscheinen bereits im späten 14. Jh. im Verwaltungsschriftgut, teils noch im Wechsel mit röm. Zahlen, dienten aber vorerst noch nicht dem Rechnen. In der öffentl. Verwaltung (Jahresrechnungen, Zinsbücher, Urbare usw.) setzten sie sich unterschiedl. schnell durch, in Zürich z.B. Ende des 15. Jh., in St. Gallen um 1500, in Genf und Bellinzona um 1550, in Freiburg um 1590, in Bern 1650-90.
Autorin/Autor: Anne-Marie Dubler

Seit dem 13. Jahrhundert werden arabische Ziffern in Westeuropa verwendet. Sie lösten die römischen Zahlen hab. Vor allem durch die einfachere Schreibweise haben sie sich durchgesetzt.
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Arabische Ziffern 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 | Indo-arabische Ziffern

Die »Arabischen Ziffern« (typographische Bezeichnung) bzw. die »Indo-arabischen Ziffern« (mathematische Bezeichnung) lösten mit Beginn des 13. Jahrhunderts in Westeuropa die Römischen Zahlen sukzessive ab und ermöglichten durch ihre wesentlich einfachere und übersichtlichere Schreibweise - und natürlich der Null - die Weiterentwicklung der komplexen Mathematik und der Naturwissenschaften. Das Wissen über die indo-arabische Rechenkunst gelangte mit den Mauren (711-1492) nach Spanien und u.a. auch über den Geldumlauf und die Kreuzzüge (1095-1254) ins katholische Europa. Sehr frühe Abbildungen dieser arabischen Ziffern zeigt der spanische Codex Vigilanus (Escorial d, I, 2) aus dem Jahr 976.
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Indische Zahlendarstellung
(Weitergeleitet von Arabische Ziffern)

arabische/indische Ziffern
Die indischen Ziffern (in Europa auch als indisch-arabische Ziffern oder umgangssprachlich arabische Ziffern bekannt) sind eine Zahlschrift, in der Zahlen positionell auf der Grundlage eines Dezimalsystems mit neun aus der altindischen Brahmi-Schrift herzuleitenden Zahlzeichen und einem eigenen, oft als Kreis oder Punkt geschriebenen Zeichen für die Null dargestellt werden.

Inhaltsverzeichnis

• 1 Begriffsverwendung im Deutschen
• 2 Entstehung und Ausbreitung
• 2.1 Indien - vom Anfang zur Vollendung
• 2.1.1 ??? (sunya) - null
• 2.1.2 Brahmasphutasiddhanta
• 2.2 Weltweite Verbreitung
• 2.2.1 Arabische Verbreitung
• 2.2.1.1 al-Kitab al-muchta?ar fi ?isab al-dschabr wa-l-muqabala
• 2.2.1.2 Kitab al-dschabr wa-l-muqabala
• 2.2.2 Der Sprung ins Abendland
• 2.2.2.1 Liber abaci
• 3 Typographische Varianten
• 3.1 Indische Varianten
• 3.2 Arabische Varianten
• 3.3 Europäische Varianten
• 3.3.1 Versalziffern und Mediävalziffern
• 3.3.2 Weltweite Verbreitung der europäischen Variante
• 4 Quellen
• 5 Weblinks

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