108 APPENDIX. 



Arithmetic* by the same author; although, in the libraryf 

 just mentioned, there is a list of them, on a fly-leaf to 

 a MS. of that work, in a hand-writing of the fourteenth 

 century, which is thus headed : 



Primus igin ; andras ; ormis ; quarto subit arbas ; 



Quinque quinas ; termas ; zenis ; temenias ; celentis. 

 and over these names the contractions are written, as 

 well as Roman numerals explaining them. 



2. There are two MSS. in the Bodleian Library which 

 merit particular attention. One, MS. Hatton. 112, pos- 

 sesses two distinct treatises on arithmetic on this system : 

 the first is very extensive, but anonymous; the rubrication 

 to the preface of the other is as follows : Incipit pre- 



fatio libri Abaci quce junior Berhelinus edidit Parisiis, 

 Domino suo Amulio. In both these treatises, as well as 

 in the other MS., local position is clearly pointed out. 



3. VossiusJ attributes them to a Grecian origin; Huet 

 derives them from the Hebrew; and the Bodleian MSS. 

 refer them to Syria and Chaldea. It is scarcely neces- 

 sary to observe, that there is no connection between these 

 numerals and those among the contractions of Tyro and 

 Seneca. 



4. M. Chasles has confused the sipos and celentis, the 

 latter of which was seldom used as a cipher. In the 

 second Bodleian MS. we read, inscribitur et in ultimo 



figura 0, sipos nomine. Que licet numerum nullum 

 significet : turn ad alia qucedam utilis est. In the 



* Most of the MSS. of this work that I have examined are very old, 

 generally prior to the thirteenth century. Only one MS. that I am ac- 

 quainted with (Bib. Burn. 275.) contains Arabic numerals. It may also be 

 remarked here, that a treatise on arithmetic in verse, by one Leopald (Bib. 

 Arund. 339.) possesses numerals whose forms are, as far as 1 know, unique. 

 But this tract will receive its due attention in a proper place. 



f* R. xv. 16. There are also a few pages on arithmetic, which contain the 

 following account of its rise among the ancients : Hanc igitur artem nume- 

 randi apud Grecos Samius Pitagoras et Aristoteles scripserunt, diffusiusque 

 Nicomachus et Euclides ; licet et alii in eadem floreunt, ut Erastosthenes et 

 Crisippus. Apud Latinos primus Apuleius, delude Boecius. 



% Observationes ad Pomponiam Melam. 4to. Hag. Com. 1658, p. 64. 



Demonstratio Evangelica. Prop. iv. p. 173. E. 



