"Alii referunt ad Phoenices inventores arithmeticae, propter eandem
commerciorum caussam: Alii ad Indos: Ioannes de Sacrobosco, cujus
sepulchrum est Lutetiae in comitio Maturinensi, refert ad Arabes." [Ramus,
_Arithmeticae libri dvo_, Basel, 1569, p. 112.]
Similar notes are given by Peletarius in his commentary on the arithmetic
of Gemma Frisius (1563 ed., fol. 77), and in his own work (1570 Lyons ed.,
p. 14): "La valeur des Figures commence au coste dextre tirant vers le
coste senestre: au rebours de notre maniere d'escrire par ce que la
premiere prattique est venue des Chaldees: ou des Pheniciens, qui ont ete
les premiers traffiquers de marchandise."
[2] Maximus Planudes (c. 1330) states that "the nine symbols come from the
Indians." [Waeschke's German translation, Halle, 1878, p. 3.] Willichius
speaks of the "Zyphrae Indicae," in his _Arithmeticae 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 ("Memoire 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: "Primum autem appellamus dexterum
locum, eo quod haec ars vel a Chaldaeis, vel ab Hebraeis ortum habere
credatur, qui etiam eo ordine scribunt"; but this refers more evidently to
the Arabic numerals. [_Arithmeticae practicae 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,
M[=a]sh[=a]ll[=a]h (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.]
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