pts in which they
occur.

In answer therefore to the second question, Could Boethius have known the
Hindu numerals? the reply must be, without the slightest doubt, that he
could easily have known them, and that it would have been strange if a man
of his inquiring mind did not pick up many curious bits of information of
this kind even though he never thought of making use of them.

Let us now consider the third question, Is there any positive or strong
circumstantial evidence that Boethius did know these numerals? The question
is not new, {84} nor is it much nearer being answered than it was over two
centuries ago when Wallis (1693) expressed his doubts about it[333] soon
after Vossius (1658) had called attention to the matter.[334] Stated
briefly, there are three works on mathematics attributed to Boethius:[335]
(1) the arithmetic, (2) a work on music, and (3) the geometry.[336]

The genuineness of the arithmetic and the treatise on music is generally
recognized, but the geometry, which contains the Hindu numerals with the
zero, is under suspicion.[337] There are plenty of supporters of the idea
that Boethius knew the numerals and included them in this book,[338] and on
the other hand there are as many who {85} feel that the geometry, or at
least the part mentioning the numerals, is spurious.[339] The argument of
those who deny the authenticity of the particular passage in question may
briefly be stated thus:

1. The falsification of texts has always been the subject of complaint. It
was so with the Romans,[340] it was common in the Middle Ages,[341] and it
is much more prevalent {86} to-day than we commonly think. We have but to
see how every hymn-book compiler feels himself authorized to change at will
the classics of our language, and how unknown editors have mutilated
Shakespeare, to see how much more easy it was for medieval scribes to
insert or eliminate paragraphs without any protest from critics.[342]

2. If Boethius had known these numerals he would have mentioned them in his
arithmetic, but he does not do so.[343]

3. If he had known them, and had mentioned them in any of his works, his
contemporaries, disciples, and successors would have known and mentioned
them. But neither Capella (c. 475)[344] nor any of the numerous medieval
writers who knew the works of Boethius makes any reference to the
system.[345]

{87}

4. The passage in question has all the appearance of an interpolation by
some scribe. Bo