36 PHILOSOPHICAL TRANSACTIONS. [aNNO 1735. 



in Spain, which he afterwards carried into France, (De Algebra, c. 4, p. 17). 

 But the Doctor thinks those characters or figures were known for a long time 

 after only to such artists, and principally used by them in astronomical calcula- 

 tions ; the Roman numerals being still retained in common use to express 

 smaller numbers, (Ibid. p. 1 1, 15, l6.) Nor has he given the figures used by 

 any of those writers before Johannes de Sacro Bosco, who died in the year 

 1256; and Maximus Planudes, a Greek, who flourished after him ; which are 

 here copied from him, in fig. 4. 



Mr. David Casley, in his Catalogue of the Manuscripts of the King's Li- 

 brary, &c. has published a specimen of a manuscript from the Cottonian Library, 

 called Calendarium Rogeri Bacon, (Plate xv.) and dated I2g2. The figures in 

 this book are Arabian, and, as Mr. Casley says, the oldest that he remembers 

 to have met with in either of those libraries: for which reason they have a place 

 also in the table. 



It appeared exceedingly difficult, how to reconcile the opinions and observations 

 of these several writers, concerning the first use of the Arabian figures in these 

 western countries, with the time assigned even to the latest of the dates above- 

 mentioned. And it could not but seem very strange, that no date of any writ- 

 ing should have been produced in those figures, or any other use of them dis- 

 covered (except perhaps in some mathematical calculations, or books of arith- 

 metic) long before the 14th century ; and yet that a date should be found, so 

 carved in a piece of wood, before the middle of the I'ith century, for so com- 

 mon a purpose as the mantle-tree of a chimney. 



But on a closer examination of the characters, Mr. Ward found reason to 

 think, this was not really the case ; and that instead of 1 133, they ought to be 

 read 1233, what has been taken for a 1, being designed for a 2. This reading 

 seems to be confirmed by the shape of the two 33 that follow it, from which, 

 if the bottom curve towards the right hand (as it was often made formerly) was 

 taken off, the upper part would make the 2. Which agreement between those 

 figures is not only usual at present, but often found in manuscripts of the 14th 

 and 15th centuries. Though sometimes indeed it is otherwise ; and the 2 has 

 an angle at the top, when the 3 is round, which would not so well have suited 

 this square hand. The reason which occasioned the carrying this date so high, 

 has probably been the similitude between the small i over the preceding abre- 

 viated word domini and this 2. And he believes this date may claim the pre- 

 ference of being the oldest of the sort that has hitherto been discovered. 



The antiquity ascribed to the Colchester date, namely lOQO, has, it seems, 

 been occasioned by a mistake in the copy ; for the in the place of hundreds, 

 should have been made a 4, by drawing down an oblique stroke on each side 



