Page:The Hindu-Arabic Numerals (1911).djvu/15

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EARLY IDEAS OF THEIR ORIGIN

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Others argued that they were probably invented by the Chaldeans or the Jews because they increased in value from right to left, an argument that would apply quite as well to the Roman and Greek systems, or to any other. It was, indeed, to the general idea of notation that many of these writers referred, as is evident from the words of England's earliest arithmetical textbookmaker, Robert Recorde (c. 1542): "In that thinge all men do agree, that the Chaldays, whiche fyrste inuented thys arte, did set these figures as thei set all their letters. for they wryte backwarde as you tearme it, and so doo they reade. And that may appeare in all Hebrewe, Chaldaye and Arabike bookes…where as the Greekes, Latines, and all nations of Europe, do wryte and reade from the lefte hand towarde the ryghte."^[1] Others, and

p. 3.] Willichius speaks of the "Zyphræ Indicæ," in his Arithmeticæ libri tres (Strasburg, 1540, p. 93), and Cataneo of "le noue figure de gli Indi,"' in his Le pratiche delle dve prime mathematiche (Venice, 1546, fol. 1). Woepcke is not correct, therefore, in saying ("Mémoire sur la propagation des chiffres indiens," hereafter referred to as Propagation [Journal Asiatique, Vol. I (6), 1863, p. 34]) that Wallis (A Treatise on Algebra, both historical and practical, London, 1685, p. 13, and De algebra tractatus, Latin edition in his Opera omnia, 1693, Vol. II, p. 10) was one of the first to give the Hindu origin.

↑ From the 1558 edition of The Grovnd of Artes, fol. C, 5. Similarly Bishop Tonstall writes: "Quia Chaldeis primum in finitimos, deinde in omnes pene gentes fluxit.…Numerandi artem a Chaldeis esse profectam: qui dum scribunt, a dextra incipiunt, et in leuam progrediuntur." [De arte supputandi, London, 1522, fol. B, 38.] Gemma Frisius, the great continental rival of Recorde, had the same idea: " Primùm autem appellamus dexterum locum, eo quòd haec ars vel à Chaldæis, vel ab Hebræeis ortum habere credatur, qui etiam eo ordine scribunt"; but this refers more evidently to the Arabic numerals. [Arithmeticæ practicæ methodvs facilis, Antwerp, 1540, fol. 4 of the 1563 ed.] Sacrobosco (c. 1225) mentions the same thing. Even the modern Jewish writers claim that one of their scholars, Māshāllāh (c. 800), introduced them to the Mohammedan world. [C. Levias, The Jewish Encyclopedia, New York, 1905, Vol. IX, p. 348.]

[2] From the 1558 edition of The Grovnd of Artes, fol. C, 5. Similarly Bishop Tonstall writes: "Quia Chaldeis primum in finitimos, deinde in omnes pene gentes fluxit.…Numerandi artem a Chaldeis esse profectam: qui dum scribunt, a dextra incipiunt, et in leuam progrediuntur." [De arte supputandi, London, 1522, fol. B, 38.] Gemma Frisius, the great continental rival of Recorde, had the same idea: " Primùm autem appellamus dexterum locum, eo quòd haec ars vel à Chaldæis, vel ab Hebræeis ortum habere credatur, qui etiam eo ordine scribunt"; but this refers more evidently to the Arabic numerals. [Arithmeticæ practicæ methodvs facilis, Antwerp, 1540, fol. 4 of the 1563 ed.] Sacrobosco (c. 1225) mentions the same thing. Even the modern Jewish writers claim that one of their scholars, Māshāllāh (c. 800), introduced them to the Mohammedan world. [C. Levias, The Jewish Encyclopedia, New York, 1905, Vol. IX, p. 348.]

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