The Hindu-Arabic Numerals | Page 4

of Ancient Nations
he gives the sum of a geometric progression and shows how, in order to
avoid any possibility of error, the number may be expressed in three
different systems: with Indian symbols, in sexagesimal notation, and by
an alphabet system which will be touched upon later. He also speaks[19]
of "179, 876, 755, expressed in Indian ciphers," thus again attributing
these forms to Hindu sources.
Preceding Al-B[=i]r[=u]n[=i] there was another Arabic writer of the
tenth century, Mo[t.]ahhar ibn [T.][=a]hir,[20] author of the Book of the
Creation and of History, who gave as a curiosity, in Indian
(N[=a]gar[=i]) symbols, a large number asserted by the people of India

to represent the duration of the world. Huart feels positive that in
Mo[t.]ahhar's time the present Arabic symbols had not yet come into
use, and that the Indian symbols, although known to scholars, were not
current. Unless this were the case, neither the author nor his readers
would have found anything extraordinary in the appearance of the
number which he cites.
Mention should also be made of a widely-traveled student,
Al-Mas`[=u]d[=i] (885?-956), whose journeys carried him from
Bagdad to Persia, India, Ceylon, and even {8} across the China sea,
and at other times to Madagascar, Syria, and Palestine.[21] He seems to
have neglected no accessible sources of information, examining also
the history of the Persians, the Hindus, and the Romans. Touching the
period of the Caliphs his work entitled Meadows of Gold furnishes a
most entertaining fund of information. He states[22] that the wise men
of India, assembled by the king, composed the Sindhind. Further on[23]
he states, upon the authority of the historian Mo[h.]ammed ibn `Al[=i]
`Abd[=i], that by order of Al-Man[s.][=u]r many works of science and
astrology were translated into Arabic, notably the Sindhind
(Siddh[=a]nta). Concerning the meaning and spelling of this name
there is considerable diversity of opinion. Colebrooke[24] first pointed
out the connection between Siddh[=a]nta and Sindhind. He ascribes to
the word the meaning "the revolving ages."[25] Similar designations
are collected by Sédillot,[26] who inclined to the Greek origin of the
sciences commonly attributed to the Hindus.[27] Casiri,[28] citing the
T[=a]r[=i]kh al-[h.]okam[=a] or Chronicles of the Learned,[29]
refers to the work {9} as the Sindum-Indum with the meaning
"perpetuum æternumque." The reference[30] in this ancient Arabic
work to Al-Khow[=a]razm[=i] is worthy of note.
This Sindhind is the book, says Mas`[=u]d[=i],[31] which gives all that
the Hindus know of the spheres, the stars, arithmetic,[32] and the other
branches of science. He mentions also Al-Khow[=a]razm[=i] and
[H.]abash[33] as translators of the tables of the Sindhind.
Al-B[=i]r[=u]n[=i][34] refers to two other translations from a work
furnished by a Hindu who came to Bagdad as a member of the political
mission which Sindh sent to the caliph Al-Man[s.][=u]r, in the year of

the Hejira 154 (A.D. 771).
The oldest work, in any sense complete, on the history of Arabic
literature and history is the Kit[=a]b al-Fihrist, written in the year 987
A.D., by Ibn Ab[=i] Ya`q[=u]b al-Nad[=i]m. It is of fundamental
importance for the history of Arabic culture. Of the ten chief divisions
of the work, the seventh demands attention in this discussion for the
reason that its second subdivision treats of mathematicians and
astronomers.[35]
{10}
The first of the Arabic writers mentioned is Al-Kind[=i] (800-870
A.D.), who wrote five books on arithmetic and four books on the use of
the Indian method of reckoning. Sened ibn `Al[=i], the Jew, who was
converted to Islam under the caliph Al-M[=a]m[=u]n, is also given as
the author of a work on the Hindu method of reckoning. Nevertheless,
there is a possibility[36] that some of the works ascribed to Sened ibn
`Al[=i] are really works of Al-Khow[=a]razm[=i], whose name
immediately precedes his. However, it is to be noted in this connection
that Casiri[37] also mentions the same writer as the author of a most
celebrated work on arithmetic.
To Al-[S.][=u]f[=i], who died in 986 A.D., is also credited a large work
on the same subject, and similar treatises by other writers are
mentioned. We are therefore forced to the conclusion that the Arabs
from the early ninth century on fully recognized the Hindu origin of the
new numerals.
Leonard of Pisa, of whom we shall speak at length in the chapter on the
Introduction of the Numerals into Europe, wrote his Liber Abbaci[38]
in 1202. In this work he refers frequently to the nine Indian figures,[39]
thus showing again the general consensus of opinion in the Middle
Ages that the numerals were of Hindu origin.
Some interest also attaches to the oldest documents on arithmetic in our
own language. One of the earliest {11} treatises on algorism is a
commentary[40] on a set of verses called the Carmen de Algorismo,

written by Alexander de Villa Dei (Alexandra de Ville-Dieu), a
Minorite monk of about 1240 A.D. The