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