. The numeral forms given are those which have usually been
called Indian,[266] in opposition to [.g]ob[=a]r. In this document the dots
are placed below the characters, instead of being superposed as described
above. The significance was the same.

In form these [.g]ob[=a]r numerals resemble our own much more closely than
the Arab numerals do. They varied more or less, but were substantially as
follows:

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1[267][Illustration]
2[268][Illustration]
3[269][Illustration]
4[270][Illustration]
5[271][Illustration]
6[271][Illustration]

The question of the possible influence of the Egyptian demotic and hieratic
ordinal forms has been so often suggested that it seems well to introduce
them at this point, for comparison with the [.g]ob[=a]r forms. They would
as appropriately be used in connection with the Hindu forms, and the
evidence of a relation of the first three with all these systems is
apparent. The only further resemblance is in the Demotic 4 and in the 9, so
that the statement that the Hindu forms in general came from {70} this
source has no foundation. The first four Egyptian cardinal numerals[272]
resemble more the modern Arabic.

[Illustration: DEMOTIC AND HIERATIC ORDINALS]

This theory of the very early introduction of the numerals into Europe
fails in several points. In the first place the early Western forms are not
known; in the second place some early Eastern forms are like the
[.g]ob[=a]r, as is seen in the third line on p. 69, where the forms are
from a manuscript written at Shiraz about 970 A.D., and in which some
western Arabic forms, e.g. [symbol] for 2, are also used. Probably most
significant of all is the fact that the [.g]ob[=a]r numerals as given by
Sacy are all, with the exception of the symbol for eight, either single
Arabic letters or combinations of letters. So much for the Woepcke theory
and the meaning of the [.g]ob[=a]r numerals. We now have to consider the
question as to whether Boethius knew these [.g]ob[=a]r forms, or forms akin
to them.

This large question[273] suggests several minor ones: (1) Who was Boethius?
(2) Could he have known these numerals? (3) Is there any positive or strong
circumstantial evidence that he did know them? (4) What are the
probabilities in the case?

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First, who was Boethius,--Divus[274] Boethius as he was called in the
Middle Ages? Anicius Manlius Severinus Boethius[275] was born at Rome c.
475. He was a member of the distingu