[ 51 ] 
VIII. A fexso Observations on the Authenticity of the Pass- 
age in the Treatise of Boet ins de Geometria on Numerical 
Contractions. By J. O. Halliwell, Bsq^.^i F.S.A.^ 
F.R.A.S. ^'c:^ 
T VENTURE to add the following remarks to what I have 
^ previously written f, in consequence of a postscript by 
M. Libri, who wishes for more substantial evidence on the 
point of authenticity than has hitherto been produced. Such 
crude arguments as I am able to furnish must not by any 
means be considered as the result of a strict or lengthened 
inquiry, but are rather intended to show that the question is 
well worthy of much greater attention than has yet been paid 
to it. 
M. Libri was the first who conjectured that this passage 
might be an interpolation, and with some justice; for it may 
be reasonably asked, w'hy does not Boetius allude to the new 
system in his treatise on arithmetic. Again, from the abacal 
system employed in that treatise, I should be inclined to think 
that the articulate and composite divisions were certainly not 
introduced until after that period. 
In the library of Trinity College, Cambridge, there is a 
very beautiful quarto MS. ^ the eleventh century on vellum, 
containing the treatise of Boetius de Geometria plentifully il- 
lustrated with neat diagrams. This manuscript, one of the 
most ancient in this country, does not contain the disputed 
passage. M. Libri has challenged me to produce such an 
evidence ; accipe si vis — the manuscript may be found under 
the press mark R. xv. 14, and is briefly mentioned at p. 99 
of Bernard’s Catalogue, No. 491. 
It would, perhaps, be scarcely fair to make its extreme sin- 
gularity an argument against its authenticity, but we may 
be permitted to argue on the probability or improbability of 
such a passage being written at so early a period. Is it likely, 
that at a time when the arithmetic of the V^est was a mere 
geometrical adaptation of quantity, when Boetius himself re- 
cognised the Roman abacal system, and when it required no 
inconsiderable depth of foresight to appreciate the advantage 
of an arbitrary system of digital characters, that Boetius 
would have inserted so extended an innovation in a treatise 
written expressly on a science that has no immediate relation 
with that into which the improvement was introduced? At 
any rate it is a fair subject for discussion, whether we could 
reasonably suppose any writer fully acquainted with the merits 
* Communicated by the Author, 
t See p. 447 of the present volume. 
E 2 
