ethius is speaking of angles, in his work on geometry, when
the text suddenly changes to a discussion of classes of numbers.[346] This
is followed by a chapter in explanation of the abacus,[347] in which are
described those numeral forms which are called _apices_ or
_caracteres_.[348] The forms[349] of these characters vary in different
manuscripts, but in general are about as shown on page 88. They are
commonly written with the 9 at the left, decreasing to the unit at the
right, numerous writers stating that this was because they were derived
from Semitic sources in which the direction of writing is the opposite of
our own. This practice continued until the sixteenth century.[350] The
writer then leaves the subject entirely, using the Roman numerals for the
rest of his discussion, a proceeding so foreign to the method of Boethius
as to be inexplicable on the hypothesis of authenticity. Why should such a
scholarly writer have given them with no mention of their origin or use?
Either he would have mentioned some historical interest attaching to them,
or he would have used them in some discussion; he certainly would not have
left the passage as it is.

{88}

FORMS OF THE NUMERALS, LARGELY FROM WORKS ON THE ABACUS[351]

a[352] [Illustration]
b[353] [Illustration]
c[354] [Illustration]
d[355] [Illustration]
e[356] [Illustration]
f[357] [Illustration]
g[358] [Illustration]
h[359] [Illustration]
i[360] [Illustration]

{89}

Sir E. Clive Bayley has added[361] a further reason for believing them
spurious, namely that the 4 is not of the N[=a]n[=a] Gh[=a]t type, but of
the Kabul form which the Arabs did not receive until 776;[362] so that it
is not likely, even if the characters were known in Europe in the time of
Boethius, that this particular form was recognized. It is worthy of
mention, also, that in the six abacus forms from the chief manuscripts as
given by Friedlein,[363] each contains some form of zero, which symbol
probably originated in India about this time or later. It could hardly have
reached Europe so soon.

As to the fourth question, Did Boethius probably know the numerals? It
seems to be a fair conclusion, according to our present evidence, that (1)
Boethius might very easily have known these numerals without the zero, but,
(2) there is no reliable evidence that he did know them. And just as
Boethius might have come in contact with them, so any other inquiring mind
might have done so