[2] Maximus Planudes (c. 1330) states that "the nine symbols come from the Indians." [Wäschke's German translation, Halle, 1878, 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.
[3] From the 1558 edition of The Grovnd of Artes, fol. C, 5. Similarly Bishop Tonstall writes: "Qui a 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, 3.] 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 Hebræis 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.]
[4] "... & que esto fu trouato di fare da gli Arabi con diece figure." [La prima parte del general trattato di nvmeri, et misvre, Venice, 1556, fol. 9 of the 1592 edition.]
[5] "Vom welchen Arabischen auch disz Kunst entsprungen ist." [Ain nerv geordnet Rechenbiechlin, Augsburg, 1514, fol. 13 of the 1531 edition. The printer used the letters rv for w in "new" in the first edition, as he had no w of the proper font.]
[6] Among them Glareanus: "Characteres simplices sunt nouem significatiui, ab Indis usque, siue Chaldæis asciti .1.2.3.4.5.6.7.8.9. Est item unus .0 circulus, qui nihil significat." [De VI. Arithmeticae practicae speciebvs, Paris, 1539, fol. 9 of the 1543 edition.]
[7] "Barbarische oder gemeine Ziffern." [Anonymous, Das Einmahl Eins cum notis variorum, Dresden, 1703, p. 3.] So Vossius (De universae matheseos natura et constitutione liber, Amsterdam, 1650, p. 34) calls them "Barbaras numeri notas." The word at that time was possibly synonymous with Arabic.
[8] His full name was ‛Abū ‛Abdallāh Moḥammed ibn Mūsā al-Khowārazmī. He was born in Khowārezm, "the lowlands," the country about the present Khiva and bordering on the Oxus, and lived at Bagdad under the caliph al-Māmūn. He died probably between 220 and 230 of the Mohammedan era, that is, between 835 and 845 A.D., although some put the date as early as 812. The best account of this great scholar may be found in an article by C. Nallino, "Al-Ḫuwārizmī" in the Atti della R. Accad. dei Lincei, Rome, 1896. See also Verhandlungen des 5. Congresses der Orientalisten, Berlin, 1882, Vol. II, p. 19; W. Spitta-Bey in the Zeitschrift der deutschen Morgenländ. Gesellschaft, Vol. XXXIII, p. 224; Steinschneider in the Zeitschrift der deutschen Morgenländ. Gesellschaft, Vol. L, p. 214; Treutlein in the Abhandlungen zur Geschichte der Mathematik, Vol. I, p. 5; Suter, "Die Mathematiker und Astronomen der Araber und ihre Werke," Abhandlungen zur Geschichte der Mathematik, Vol. X, Leipzig, 1900, p. 10, and "Nachträge," in Vol. XIV, p. 158; Cantor, Geschichte der Mathematik, Vol. I, 3d ed., pp. 712-733 etc.; F. Woepcke in Propagation, p. 489. So recently has he become known that Heilbronner, writing in 1742, merely mentions him as "Ben-Musa, inter Arabes celebris Geometra, scripsit de figuris planis & sphericis." [Historia matheseos universæ, Leipzig, 1742, p. 438.]
In this work most of the Arabic names will be transliterated substantially as laid down by Suter in his work Die Mathematiker etc., except where this violates English pronunciation. The scheme of pronunciation of oriental names is set forth in the preface.
[9] Our word algebra is from the title of one of his works, Al-jabr wa'l-muqābalah, Completion and Comparison. The work was translated into English by F. Rosen, London, 1831, and treated in L'Algèbre d'al-Khārizmi et les méthodes indienne et grecque, Léon Rodet, Paris, 1878, extract from the Journal Asiatique. For the derivation of the word algebra, see Cossali, Scritti Inediti, pp. 381-383, Rome, 1857; Leonardo's Liber Abbaci (1202), p. 410, Rome, 1857; both published by B. Boncompagni. "Almuchabala" also was used as a name for algebra.
[10] This learned scholar, teacher of O'Creat who wrote the Helceph ("Prologus N. Ocreati in Helceph ad Adelardum Batensem magistrum suum"), studied in Toledo, learned Arabic, traveled as far east as Egypt, and brought from the Levant numerous manuscripts for study and translation. See Henry in the Abhandlungen zur Geschichte der Mathematik, Vol. III, p. 131; Woepcke in Propagation, p. 518.