Baron of Merchiston. 175 



The simultaneous application to the same subject alone 

 ought to produce, for the strongest reasons, inventions at 

 the same time, or rather, of perceptions of the consequences 

 which present themselves mechanically as it were. Such 

 is the arithmetical triangle which refers to the powers of 

 numbers ; and this is so true, that from a remark which 

 has been communicated to me by my son, and of which I 

 append the proofs in a note which he has sent me, the 

 arithmetical triangle, with its use for the elevation to entire 

 powers, and for the extraction of their roots, is cited as a 

 very ancient invention in a work printed in China, in 1593, 

 when the Jesuits could only reach Canton with difficulty, 

 and were not acquainted with the arithmetical triangle, as 

 it was only discovered in Europe 60 years after. We see 

 from the same work, that the Chinese had been conducted, 

 at a very early period, to the principle of properties of 

 figures, to the summation of the series of natural numbers, 

 of their squares, and to different other properties which 

 have been discovered more slowly in Europe, probably by 

 a train of the same ideas. The author of the note remarks, 

 " that the formation of the binomial for entire powers 

 existed with the Arabs in 1430, who appear to have learned 

 it from the Hindoos ;" and he adds, " that the same notions 

 contained in the Chinese work bear marks of this origin, 

 from the fact, that among the different orders of numerical 

 units, which are all decimals, those of very high orders 

 are designated by the term of ' sands of the river Ganges.' " 

 These details of literary history have appeared sufficiently 

 curious of themselves, and besides, as connected with the 

 work of Napier and Pascal, in the invention of the arith- 

 metical triangle, to deserve a place here. Biot. 



Note. — The Royal Library contains, in the Chinese col- 

 lection, two copies of a work entitled, ' Souang-Fa-Tojrg- 

 Tsong,' or the principles of the art of calculation ; which, 

 according to the preface, was printed in 1593, under the 

 emperor Wan-ly, of the dynasty of Ming, who reigned in 

 China afer the expulsion of the Mongols. This work, 

 divided into several parts, contains a Chinese treatise on 

 arithmetic, a book upon geometrical figures, and upon 

 the principal figures of surveying, upon the extraction 



