him to Mr. Strachey's Bija Ganita, and to Sir E. Colebrooke's Algebra of
the Hindus, from the Sanscrit of Brahmegupta. Perhaps a few sentences
may sufficiently point out where the difficulty lies. In the beginning
of the sixth century, the celebrated Boethius described the present
system as an invention of the Pythagoreans, meaning, probably, to
express some indistinct notion of its coming from the east. The figures
in MS. copies of Boethius are the same as our own for 1, 8, and 9; the
same, but inverted, for 2 and 5; and are not without vestiges of
resemblance in the remaining figures. In the ninth century we come to
the Arabian Al Sephadi, and derive some information from him; but his
figures have attracted most notice, because though nearly all of them
are different from those found in Boethius, they are the same as occur
in Planudes, a Greek monk of the fourteenth century, who says of his own
units, "These nine characters are Indian," and adds, "they have a tenth
character called [Greek: tziphra], which they express by an 0, and which
denotes the absence of any number." The date of Boethius is obviously
too early for the supposition of an Arabic origin; but it is doubted
whether the figures are of his time, as the copyists of a work in MS.
were wont to use the characters of their own age in letters, and might
do so in the case of figures also.

H.W.

* * * * *

ROMAN NUMERALS.

There are several points connected with the subject of numerals that are
important in the history of practical arithmetic, to which neither
scientific men nor antiquaries have paid much attention. Yet if the