VOL. XLIIX.] PHILOSOPHICAL TRANSACTIONS. 47 



the Indians about the year QOO ; when, having subdued Persia, Carmania, and 

 the coast of India, they opened a commerce with that country. On the contrary. 

 Dr. Wallis, as our author remarks, has shown, that these figures were known to 

 the Europeans, and used by them in books of astronomy and arithmetic, long be- 

 fore the time assigned by Kircher. But, as Dr. Wallis suspects, that the cha- 

 racters found in some old editions of Boethius De G«ometria, very like the 

 Arabian figures, are different from the original, or other ancient manuscripts of 

 that work ; our author acquaints us, that he himself saw in the public library of 

 the university at Altorf a copy of it, which by the form of the letters appeared to 

 him to have been written in the 8th or Qth century ; and that both the shape and 

 situation of the numeral characters were the same, as in the first edition printed at 

 Venice in 14Q2. He thinks therefore, that they might be the same, as in the 

 original of Boethius ; and endeavours to show, that they were then used in much 

 the same manner as the Arabian figures now are, in sums of multiplication and 

 division. And from thence he concludes, that such characters must have been 

 known in Europe as early as the beginning of the 6th century ; since Boethius was 

 put to death by Theodoricus king of the Goths, in the year 524. As to the ob- 

 jection, which may be made to this opinion, from the silence of writers concern- 

 ing it for several ages after Boethius; he observes, that the same has happened in 

 other instances of a like nature. Though he supposes, that both the characters 

 themselves, and the use of them, were a secret at that time, known only to phi- 

 losophers and men of learning, and not introduced into the common affairs of 

 life ; and that the first invention of them was owing to the eastern nations, whence 

 they came to the Greeks, among whom the Pythagoreans were particularly re- 

 markable for concealing their knowledge from the vulgar, and imparting it only to 

 their followers. 



With this learned dissertation, he sent also to Dr. Mortimer a small brass qua- 

 drant, with the numbers engraven on it in Arabian figures, and the date when it 

 was made, namely, 1306. In this quadrant, all the figures agree with those of 

 Johannes de Sacro Bosco, except the 2 ; which in him is inverted thus, z, but on 

 the quadrant has the present form. 



Observations on the late Comet, made at Sherborn and Oxford; ivith the Elements 

 for computing its Motions. By the Rev. Joseph Betls, M. yi. N°474, p. Ql. 



The comet which appeared towards the end of Dec. 1743, and in the follow- 

 ing months January and February, 1744, was first seen in England, at the ob- 

 servatory of the Earl of Macclesfield, Dec. 23, between 5 and 6 o'clock in the 

 evening. It formed, at that time, an obtuse-angled triangle, with a. of Andro- 

 meda, and y Pegasi, the comet being at the obtuse angle; and its passage over 

 the meridian was observed at S*" 32*", mean Oxford time. 



> 



