APPENDIX. 



I. 



A few Observations on the Numerical Contractions found 

 in some manuscripts of the Treatise on Geometry 

 by Boetius. 



The remarks which follow have not, as far as I am 

 aware, found a place in any prior publication ; I intend 

 them to form an appendix to the interesting chapter on 

 the same subject presented to the literary world by M. 

 Chasles. 



I could not have connected the following pages in the 

 form of a continuous history, without introducing much 

 that is already known ; I have, therefore, considered it 

 advisable to place my notes under distinct articles, with- 

 out any attempt at arrangement. 



1. It is very probable that the well-known passage on 

 the Abacus, in the first book of the Geometry of Boetius, 

 is an interpolation. For in a MS. once belonging to 

 Mr. Ames, no such passage appears ; and in another, now 

 in the library of Trinity College, it is also wanting : again, 

 no such contractions occur in any copy of the Treatise on 



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