Arabic Numerals (W3)Die "Arabischen Ziffern" (eigentlich: "arabisch-indische Ziffern"), engl. "Arabic Numerals", stammen aus Indien. Nur die "Null" wurde von den Arabern "erfunden".
Der eigentliche Vorteil des indisch-arabischen Ziffernsystems ist nicht das Dezimalsystem sondern die Schreibweise als Stellenwertsystem. Die Platzierung einer Ziffer innerhalb einer Zahl an der Stelle n (von rechts) verleiht ihr einen 10**(n-1)-fachen Wert.
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.
Karpinski, Louis Charles, 1878-1956: The Hindu-Arabic Numerals (English) (as Author)
Smith, David Eugene, 1860-1944: The Hindu-Arabic Numerals (English) (as Author)
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
- 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
In der "Dewey Decimal Classification" findet man den Hinweis:
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.
Dates are all given in years of the common calendar, and Arabic numerals are uniformly used for all numbers.
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".
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.