246 Notices respecting New Books. 



lations. But this is not its only value, for it fully explains some 

 early MSS. on aritlimetic; such as that known as the Metz MS., 

 (343 Arundel,) Chartres, (see Chasles, Jper^u His. de Meth. en 

 Geom., p. 467) and one or two others. Into this subject it would, 

 however, be impossible to enter in this place, though possibly some 

 of our correspondents may be led to consider this matter at greater 

 length*. 



IX. Carmen de Algorismo. This song is, by a MS. in the British 

 Museum, and by another in the French King's library, attributed to 

 Alexander de Villa Dei. Its chief value is its showing the opinion 

 that was currently entertained respecting the Indian origin of the 

 modern notation for numbers; and as MSS. of it are very nume- 

 rous it has often been quoted as an authority on that head. 



Perhaps there are no MSS. of the same description which has a 

 greater number of variations than those of this Carmen. There is 

 one in the Ashmolean, which contains from 20 to 30 lines more than 

 that here printed from, which is that in the author's library. It is 

 a general principle amongst antiquaries in cases of this kind to con- 

 sider the lines which one MS. has in excess over another as inter- 

 polations ; except, indeed, collateral evidence should support the au- 

 thenticity of the so suspected passages. As we have not collated 

 the Oxford MS. with this, we can of course offer no opinion on 

 the subject, and merely make the remark as a suggestion to those 

 who may feel disposed to assent to the superior authority of the Ox- 

 ford as compared with Mr. Halliwell's manuscript. 



X. Prefatio Danielis de Merlai ad librum de naturis superiorum et 

 inferiorum. 



Its value is of the same kind as the last. 



XI. Proposals for some inventions in the mechanical arts ; from 

 the Lansdowne Collection, dated 1583. 



Probably by William Bourne. 



XII. The preface to a calendar or almanac for the year 1430. 

 From the opening address and date, it would seem to have been 



written for the use of the queen of Henry VI. It is a fair sample 

 of such prefaces, being merely a set of directions for the use of the 

 dominical letters, &c., and, indeed, some parts of it are almost li- 

 terally identical with corresponding ones in Chaucer's preface to his 

 tract on the Astrolabe. 



XIII. Johannis Norfolk in artem progressionis summula. 



A curious specimen of ingenuity to evade the difficulties which 

 a more enlarged view of the nature of numbers could alone re- 

 move. It also contains the passage already quoted on a former 

 page : " Rex quondam Castellise." 



To the work are appended two tracts, one on the Numeral con- 

 tractions found in some manuscripts of the Treatise on Geometry by 

 Boetius ; and the other, of Notes on Antient Almanacs. 



* We have seen some of the earlier sheets of a work by Mr. Davies, in 

 which this view is taken and contended for : but as the work is not, that 

 we know of, published, we can give no account of it here. 



