used by different Nations, 303 



(by the latest comparisons of numerical hieroglyphics, and the 

 simple graphic method,) with our glorious progress in the 

 mathematical sciences. One of the greatest mathematicians 

 of our times and of all times, the author of the " Mecanique 

 Celeste*," says, " The idea of expressing all quantities by 

 nine figures, whereby is imparted to them both an absolute 

 value, and one by position, is so simple, that this very sim- 

 plicity is the reason for our not being sufficiently aware, how 

 much admiration it deserves. But it is this simplicity, and 

 the facility which calculations acquire by it, that raises the 

 arithmetical system of the Indians to the rank of the most 

 useful inventions. How difficult it was to discover such a 

 method may be inferred from the circumstance, that it has 

 escaped the talents of Archimedes and of Apollonius of Perga, 

 two of the most profound geniuses of antiquity." The fol- 

 lowing observations, I hope, will shew, that the Indian method 

 of calculation may very possibly have arisen by degrees out of 

 others, which were used earlier, and even now continue to be 

 used, in the eastern countries of Asia. 



As language, in general, affects the manner of writing, and 

 writing again reacts on language, but only under certain con- 

 ditions which have been inquired into by Silvestre de Sacy , and 

 my brother, so also the different modes of computation used 

 by different nations, and their numerical hieroglyphics, recipro- 

 cally -act upon one another. Yet no very great consequence 

 is to be attached to this alternate action. Numerical figures 

 do not always follow the same groups of unities like languages; 

 and moreover in languages we do not always discover the same 

 resting-points (tlie same quinary intermediate stops) as in 

 numerical signs. But if we bring together under one view, 

 the language (names of numbers) and the numerical figures used 

 in the remotest parts of the earth, as the common product of 

 human intelligence applied to quantitative relations, we discover 

 in the written numbers of one race, the isolated seeming pecu- 

 liarities of language of another race ; we may even add, that 



* Laplace, Expos6 du systeme du Monde (5th edit.), p. 325. The a.ssertion of 

 Delambre, (Histoire de I'Astron. Ancienne, t. i., p. 543,) hi his contest respecting 

 the nierit of the ancient Indian arithmetic, as it is explained in Bhascora Acharya's 

 Lileaoaii, is in very strange opposition to the opinion of Laplace. But language 

 ftlone can hardly prompt me to suppress the figures of the groups, 



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