448 Mr. Halliwell on the Boetian and Arabic Numerals. 



The names alone are almost sufficient to show that the 

 origin of these numerals is Eastern, if not from the Arabic ; 

 but it appears to me that sufficient attention has not been paid 

 to the variations of the forms of the figures in different manu- 

 scripts. Now, in the tract de ratione abaci, we have invariably 

 two lists of forms, and these again vary in MSS. of different 

 ages. Let us make a brief comparison of a few of them. 



1. In all the manuscripts to which I have referred, igin is 

 the same, and agrees with the common middle-Arabic form. 



2. Andras does not vary to any extent, but how easily is 

 it convertible to the Arabic form ! 



3. Ornus in MS. Lansd. 842, is the same with ornus in 

 MS. Arund. 343 transvejsed, and this is an example of a cu- 

 rious result of practice, the truth of which I hope to be able 

 to establish universally. In MS. Harl. 3595, of the tenth 

 century, we find two forms of ornus very nearly identical with 

 the Arabic. 



4. The form of arbas is not so readily convertible to the 

 Arabic, but a bisection of this character in its second place 

 in MS. Harl. 3595, and in MS. Lansd. 842, would make the 

 loop of the middle-Arabic figure. 



5. Quinas, as given in MS. Arund. 343, is identical with 

 the middle- Arabic form. In MS. Harl. 3595, and in many 

 other early manuscripts, this character is transversed. 



6. Chalcus is evidently convertible to the common form by 

 the mere obtainable effect of convenient expression. 



7. Zenis, as given in the MS. Arundel. 343, 'when trans- 

 versed, is identical with the middle-Arabic form. Examples of 

 it, in that state, may be seen in MS. Lansd. 842, and MS. 

 Harl. S595. 



8. Zemenias agrees in form with the common character. 



9. Celentis agrees, by transversion, with the common form. 

 The second form of this figure in MS. Lansd. 842 is trans- , 

 versed. 



I am almost inclined to believe from these examples, and 

 from others equally conclusive which can be brought forward, 

 that, in the case of middle numerals, transversion is invariably 

 true in the change of form they underwent, provided that any 

 reasonable theory is thereby supported. Perhaps also we 

 may arrive at an additional argument from the Eastern manner 

 of writing from the right to the left ; for what is more pro- 

 bable than, supposing the case of a Latin scribe copying the 

 numerals from the Arabic, that he should turn them Jipside 

 down, for the facility thus afforded by that means of copying 

 them in the proper order ? Thus would the transversion be 

 satisfactorily accounted for, and without a conjecture so vie- 



