The Hindu-Arabic Numerals

h a symbol exists. The importance of such a sign, the fact that it is a prerequisite to a place-value system, and the further fact that without it the H

eceding the Christian era. The symbol is or , and apparently it was not used in calculation. Nor does it always occur when units of any order are lacking; thus 180 is written with the meaning three sixties and no units, since 181 imm

symbol. Bayley mentions a grant of Jaika Rashtrakúta of Bharuj, found at Okamandel, of date 738 A.D., which contains a zero, and also a coin with indistinct Gupta date 707 (897 A.D.), but the reliability of Bayley's work is questioned. As has been noted, the appearance of the numerals in

s in his arithmetic[191] a distinct treatment of the properties of zero. He does not discuss a symbol, but he shows by his treatment that in some way zero had acquired a special significance not found in the Greek or other ancient arithmetics. A still more scientific treatment is given by Bhāskara,[192] although

used[195] and which most Arabs use to-day. There was also used for this purpose a cross, like our X, and this is occasionally found as a zero symbol.[196] In the Bakh?ālī manuscript above mentioned, the word ?ūnya, with the dot as its symbol, is used to denote the unknown quantity,

ndicate the absence of minutes (or seconds), is noted by Nallino.[202] Noteworthy is also the use of the for unity in the ?āradā characters of the Kashmirian Atharva-Veda, the writing being at least 400 years old. Bhāskara (c. 1150) used a small circle above a number to indicate subtraction, and in the Tartar writing a redundant word is removed by drawing an oval around it. It would be interesting to know whether our score mark , read "four in the hole," could trace its pedigree to the same sources. O'Creat[203] (c. 1130), in a lett

ed in a manuscript of 873 A.D.[208] Sometimes both the dot and the circle are used in the same work, having the same meaning, which is the case in an Arabic MS., an abridged arithmetic of Jamshid,[209] 982 A.H. (1575 A.D.). As given in this work the numerals are . The form for 5 varies, in some works becoming or ; is found in

call it. We speak of it to-day as zero, naught, and even cipher; the telephone operator often calls it O, and the illiterate

zephirum.[214] Maximus Planudes (1330), writing under both the Greek and the Arabic influence, called it tziphra.[215] In a treatise on arithmetic written in the Italian language by Jacob of Florence[216]

hili. In this statement Huswirt probably follows, as did many writers of that period, the Algorismus of Johannes de Sacrobosco (c. 1250 A.D.), who was also known as John of Halifax or John of Holywood. The commentary of Petrus de Dacia[223] (c. 1291 A.D.) on the Algorismus vulgaris of Sacrobosco was also widely used. The widespread use of this Englishman's work on arithmetic in the univers

medieval writers also spoke of it as the sipos,[232] and occasionally as the wheel,[233] circulus[234] (in German das Ringlein[235]), circular note,[236] theca,[237] long supposed to be from its resemblance to the Greek theta, but explained by Petrus de Dacia as being derived from the name of the iron[238] used to brand thieves and robbers with a circular mark placed on the forehead or on the cheek. It was also called omicron[239] (the Greek