Arabic numerals

“ Only as Western civilization is making its way into the commercial life of the East do the numerals as used by us find place, save as the Sanskrit forms appear in parts of India. It is therefore with surprise that the student of mathematics comes to realize how modern are these forms so common in the West, how limited is their use even at the present time, and how slow the world has been and is in adopting such a simple device as the Hindu-Arabic numerals. ”

“ It is with this unsatisfactory material, then, that we have to deal in searching for the early history of the Hindu-Arabic numerals, and the fact that many unsolved problems exist and will continue to exist is no longer strange when we consider the conditions. It is rather surprising that so much has been discovered within a century, than that we are so uncertain as to origins and dates and the early spread of the system. ”

“ As a matter of fact, one form of Arabic numerals, the one now in use by the Arabs, is attributed to the influence of Kabul, while the other, which eventually became our numerals, may very likely have reached Arabia by the other route. It is in Bagdad, [385] Dār al-Salām—"the Abode of Peace," that our special interest in the introduction of the numerals centers. Built upon the ruins of an ancient town by Al-Manṣūr [386] in the second half of the eighth century, it lies in one of those regions where the converging routes of trade give rise to large cities. ”

“ It should be stated definitely at the outset, however, that we are not at all sure that the most ancient forms of the numerals commonly known as Arabic had their origin in India. As will presently be seen, their forms may have been suggested by those used in Egypt, or in Eastern Persia, or in China, or on the plains of Mesopotamia. We are quite in the dark as to these early steps ”

“ The arithmetical or Arabic numerals are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. Properly they should be styled Hindu or Indian numerals; for the Arabs borrowed them, along with the decimal system of notation, from the Hindus. They were probably first introduced from the East into Italy about 1202; yet they did not come into general use before the invention of printing. Accounts were kept in Roman numerals up to the sixteenth century. Figures are usually made one en thick; but of late a broader figure is cast for newspaper use, which is two-thirds or six-sevenths of an em in width. ”

“ Taking the symbol for 1,000 twice, on the multiplicative principle, yielded 1,000,000. The Hindu-Arabic numerals, with the zero, began to spread among the Arabs in the ninth and tenth centuries, and they slowly displaced the Arabic and Greek numerals. ”

“ The Arabic numerals are used as in English.
S added to any word forms the plural, which is never formed in any other way. The first three vowels (a, e, i) added to any noun, form respectively its genitive, dative, and accusative; s added to these forms makes the plurals of the same cases. Man is therefore declined as follows:
Every noun in the language is declined in the same way, so that all declensions may be learned in one minute. ”

“ It is for many reasons improbable, rather than otherwise, that the Arabic numerals should have been freely used (if used at all) on ecclesiastical structures till long after the Reformation: indeed they are not so even yet.
But more. Even where there is authentic evidence of such symbols being used in ecclesiastical inscriptions, the forms of them will tell nothing. For generally in such cases an antique form of symbol would be assumed, if it were the alteration of a "learned clerk;" ”

“ 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. ”

“ Others, and [4] among them such influential writers as Tartaglia [4] in Italy and Köbel [5] in Germany, asserted the Arabic origin of the numerals, while still others left the matter undecided [6] or simply dismissed them as "barbaric." [7] Of course the Arabs themselves never laid claim to the invention, always recognizing their indebtedness to the Hindus both for the numeral forms and for the distinguishing feature of place value. ”

“ We give the credit of the invention to the Arabs by using the term Arabic numerals, while the Arabs call them Indian, and there is truth in both acknowledgments of the nations having been scholars in arithmetic one to the other. But this does not go to the root of the matter, and it is still unsettled whether ciphering was first devised in Asia, or may be traced further back in Europe to the arithmeticians of the school of Pythagoras. ”

“ There are no head-lines, the pages being numbered centrally in Arabic numerals. Beyond that upon the foot of the title-page, there is no imprint. The signatures are given in large Arabic numerals, each pair of half-sheets dividing one number between them; thus the first half-sheet is signed 1, the second 1*, the third 2, the fourth 2*, &c. The Register is therefore 1 to 7 (thirteen half-sheets, each 4 leaves) , followed by a single unsigned leaf (pp. 105–106) , the whole preceded by an unsigned half-sheet carrying the Title-page, Preface, and Table of Contents. ”

“ AT present the Hindu-Arabic numerals hold nearly unlimited sway in the realm of number. In China, in Japan, in southeast Asia, and in parts of India, it is true, they are employed only by the upper classes and by foreign traders; but all over Europe, in Australia, and in North America, they are supreme; while in South America and in Africa they are used wherever civilized men make arithmetical computation.
Scarcely ever has a more wonderful device been perfected. By means of these characters prodigious calculations can be made. ”

“ Erculio said in Arabic. Hearing that title, Daoud thought it even less likely that the little man was trying to trick him.
"I have been watching you since Lucera, My Lord," Erculio went on. "You have done well, even if it has been God's will that you should not succeed. You have been clever. But you should have taken the tawidh off before you surrendered. Do you think there are no Christians who can recognize Arabic numerals?" ”

“ They should never be used to record the publication date of a work, even if the source uses Roman numerals. They should not be used in page names to represent volume or issue numbers, in part because the trend in modern libraries has been to shift away from Roman numerals for these purposes, and to use Arabic numerals instead. ”

“ So, too, in Chaucer's explanation of the astrolabe, [478] written for his son Lewis, the number of degrees is expressed on the instrument in Hindu-Arabic numerals: "Over the whiche degrees ther ben noumbres of augrim, that devyden thilke same degrees fro fyve to fyve," and "... the nombres ... ben writen in augrim," meaning in the way of the algorism. Thomas Usk about 1387 writes: [479] "a sypher in augrim have no might in signification of it-selve, yet he yeveth power in signification to other." So slow and so painful is the assimilation of new ideas. ”

“ This theory of the very early introduction of the numerals into Europe fails in several points. In the first place the early Western forms are not known; in the second place some early Eastern forms are like the ġobār, as is seen in the third line on p. 69, where the forms are from a manuscript written at Shiraz about 970 A.D., and in which some western Arabic forms, e.g. for 2, are also used. Probably most significant of all is the fact that the ġobār numerals as given by Sacy are all, with the exception of the symbol for eight, either single Arabic letters or combinations of letters. ”

“ As to Germany, the fifteenth century saw the rise of the new symbolism; the sixteenth century saw it slowly [150] gain the mastery; the seventeenth century saw it finally conquer the system that for two thousand years had dominated the arithmetic of business. Not a little of the success of the new plan was due to Luther's demand that all learning should go into the vernacular. [606]
During the transition period from the Roman to the Arabic numerals, various anomalous forms found place. For example, we have in the fourteenth century cα for 104 ”

“ I know one case only too well of a man who learnt his Arabic numerals prematurely, before he had acquired any sound experimental knowledge of numerical quantity, and, as a consequence, his numerical ideas are incurably associated with the peculiarities of the figures. ”

“ It was due to him particularly that the Hindu signs came to be known in Europe as Arabic numerals.
The Hindu characters were now known, but they came into general use very slowly, for the same reason that the metric system is not adopted immediately nowadays. The Roman characters, computation on the abacus, and various devices held their own obstinately through force of custom. Moreover, before the era of printing no knowledge could be spread rapidly among the mass of the people, and for the most part the counting of the ordinary man could be done upon his fingers. ”

“ The introduction of myriads as in the Greek, and thousands as in Arabic and in modern numeration, is really a step away from a decimal scheme. So in the numbers below one hundred, in English, eleven and twelve are out of harmony with the rest of the -teens, while the naming of all the numbers between ten and twenty is not analogous to the naming of the numbers above twenty. To conform to our written system we should have ten-one, ten-two, ten-three, and so on, as we have twenty-one, twenty-two, and the like. The Sanskrit is consistent, the units, however, preceding the tens and hundreds. ”

“ According to Ball's 'Short Account of the History of Mathematics,' the arabic arithmetic was practically unknown in Europe until the end of the thirteenth century. At that date numbers were written in Roman numerals. When we see a date inscribed in Roman numerals upon the portal of a public building, we witness the persistence, in art, of the system which was in universal use for all the arithmetical purposes of the civilized world only a few centuries ago.
How simple to our minds to-day seems such a numerical problem as a determination of the number of seconds in a mean solar day. ”

“ The Anglo-Saxon letters are in like manner nothing but a barbarous imitation of old manuscript characters, and have no real connexion with the Anglo-Saxon language. Their use ought to be wholly abandoned (with the exception of those which are wanting in modern English) . Roman numerals, likewise, as being less clear and concise than Arabic numerals, especially for large numbers, ought to be discarded, except in cases where it is convenient to distinguish the volume from the page, and the book from the chapter. ”

“ Here is a new agent of civilization, to be felt in all the concerns of life, at home and abroad. It will be hardly less important than the Arabic numerals, by which the operations of arithmetic are rendered common to all nations. ”

“ The name algorism was applied for some five hundred years to the arithmetic which explained the method of reckoning with the Hindu-Arabic numerals. The word is a corruption from the name of Mohammed ben Musa, al-Khowarazmi, whose Arabic work on this subject was translated into Latin in the early twelfth century. Early manuscripts of Sacrobosco's classic are found in the Columbia Library as well as in the Plimpton collection. ”

“ IN this age the knowledge of arithmetic is so widespread that it is difficult to conceive that it is comparatively young. The three R's, Reading, 'Riting and 'Rithmetic, seems to our mind almost axiomatic and fundamental in regard to education. It is, therefore, very interesting to read in histories of arithmetic that the earliest known book which contains a systematic exposition of the decimal system of numeration was written in the seventh century, and that our familiar arabic numerals 1, 2, 3, 4, 5, 6, 7, 8, 9, can not be traced to an earlier century than the seventh. ”

“ Here he acquired a knowledge of the language and learning of the Arabians, particularly of their astronomy, geometry and arithmetic; and he is understood to have been the first that imparted to the north and west of Europe a knowledge of the Arabic numerals, a science, which at first sight might be despised for its simplicity, but which in its consequences is no inconsiderable instrument in subtilising the powers of human intellect. He likewise introduced the use of clocks. He is also represented to have made an extraordinary proficiency in the art of magic ”

“ Dates are always to be given in a catalogue in Arabic numerals. It is important that the date should be discovered when it does not occur on the title-page. The date may sometimes occur as a chronogram, which should not be overlooked. ”

“ Will you suffer me to add some further remarks on the subject of the Arabic numerals and cipher; as neither the querists nor respondents seem to have duly appreciated the immense importance of the step taken by introducing the use of a cipher. I would commence with observing, that we know of no people tolerably advanced in civilisation, whose system of notation had made such little progress, beyond that of the mere savage, as the Romans. The rudest savages could make upright scratches on the face of a rock, and set them in a row, to signify units ”