, reaching
Boethius in Athens or in Rome, and to the schools of Spain, being
discovered in Africa and Spain by the Arabs even before they themselves
knew the improved system with the place value.

{65}

A recent theory set forth by Bubnov[249] also deserves mention, chiefly
because of the seriousness of purpose shown by this well-known writer.
Bubnov holds that the forms first found in Europe are derived from ancient
symbols used on the abacus, but that the zero is of Hindu origin. This
theory does not seem tenable, however, in the light of the evidence already
set forth.

Two questions are presented by Woepcke's theory: (1) What was the nature of
these Spanish numerals, and how were they made known to Italy? (2) Did
Boethius know them?

The Spanish forms of the numerals were called the _[h.]ur[=u]f
al-[.g]ob[=a]r_, the [.g]ob[=a]r or dust numerals, as distinguished from
the _[h.]ur[=u]f al-jumal_ or alphabetic numerals. Probably the latter,
under the influence of the Syrians or Jews,[250] were also used by the
Arabs. The significance of the term [.g]ob[=a]r is doubtless that these
numerals were written on the dust abacus, this plan being distinct from the
counter method of representing numbers. It is also worthy of note that
Al-B[=i]r[=u]n[=i] states that the Hindus often performed numerical
computations in the sand. The term is found as early as c. 950, in the
verses of an anonymous writer of Kairw[=a]n, in Tunis, in which the author
speaks of one of his works on [.g]ob[=a]r calculation;[251] and, much
later, the Arab writer Ab[=u] Bekr Mo[h.]ammed ibn `Abdall[=a]h, surnamed
al-[H.]a[s.][s.][=a]r {66} (the arithmetician), wrote a work of which the
second chapter was "On the dust figures."[252]

The [.g]ob[=a]r numerals themselves were first made known to modern
scholars by Silvestre de Sacy, who discovered them in an Arabic manuscript
from the library of the ancient abbey of St.-Germain-des-Pres.[253] The
system has nine characters, but no zero. A dot above a character indicates
tens, two dots hundreds, and so on, [5 with dot] meaning 50, and [5 with 3
dots] meaning 5000. It has been suggested that possibly these dots,
sprinkled like dust above the numerals, gave rise to the word
_[.g]ob[=a]r_,[254] but this is not at all probable. This system of dots is
found in Persia at a much later date with numerals quite like the modern
Arabic;[255] but that it was used at all is significant, for it is hardly
likely that t