a]n ibn al-Fat[h.][370] of
[H.]arr[=a]n, and Ahmed ibn `Omar, al-Kar[=a]b[=i]s[=i].[371] In the
eleventh century come Al-B[=i]r[=u]n[=i][372] (973-1048) and `Ali ibn
A[h.]med, Ab[=u] 'l-[H.]asan, Al-Nasaw[=i][373] (c. 1030). The following
century brings similar works by Ish[=a]q ibn Y[=u]suf al-[S.]ardaf[=i][374]
and Sam[=u]'[=i]l ibn Ya[h.]y[=a] ibn `Abb[=a]s al-Ma[.g]reb[=i]
al-Andalus[=i][375] (c. 1174), and in the thirteenth century are
`Abdallat[=i]f ibn Y[=u]suf ibn Mo[h.]ammed, Muwaffaq al-D[=i]n Ab[=u]
Mo[h.]ammed al-Ba[.g]d[=a]d[=i][376] (c. 1231), and Ibn al-Bann[=a].[377]

The Greek monk Maximus Planudes, writing in the first half of the
fourteenth century, followed the Arabic usage in calling his work _Indian
Arithmetic_.[378] There were numerous other Arabic writers upon arithmetic,
as that subject occupied one of the high places among the sciences, but
most of them did not feel it necessary to refer to the origin of the
symbols, the knowledge of which might well have been taken for granted.

{94}

One document, cited by Woepcke,[379] is of special interest since it shows
at an early period, 970 A.D., the use of the ordinary Arabic forms
alongside the [.g]ob[=a]r. The title of the work is _Interesting and
Beautiful Problems on Numbers_ copied by A[h.]med ibn Mo[h.]ammed ibn
`Abdaljal[=i]l, Ab[=u] Sa`[=i]d, al-Sijz[=i],[380] (951-1024) from a work
by a priest and physician, Na[z.][=i]f ibn Yumn,[381] al-Qass (died c.
990). Suter does not mention this work of Na[z.][=i]f.

The second reason for not ascribing too much credit to the purely Arab
influence is that the Arab by himself never showed any intellectual
strength. What took place after Mo[h.]ammed had lighted the fire in the
hearts of his people was just what always takes place when different types
of strong races blend,--a great renaissance in divers lines. It was seen in
the blending of such types at Miletus in the time of Thales, at Rome in the
days of the early invaders, at Alexandria when the Greek set firm foot on
Egyptian soil, and we see it now when all the nations mingle their vitality
in the New World. So when the Arab culture joined with the Persian, a new
civilization rose and flourished.[382] The Arab influence came not from its
purity, but from its intermingling with an influence more cultured if less
virile.

As a result of this interactivity among peoples of diverse interests and
powers, Mohammedanism was to the world from the eighth