1887.] «>57 [Taylor. 



Such action could not fail to meet with a response due to the importance 

 of the subject ; and if the great object be attained, to lead to results pro- 

 ductive of vast and lasting benefit to the human race. 



These suggestions are offered for the purpose of promoting discussion, 



investigation, and consideration of the subject in all its bearings, in the 



liope that when the time arrives in which a change must be made, and 



such a time will inevitably come, that a system may be adopted which 



has been, or can be demonstrated to possess the greatest advantages, and 



is admitted to be, of all schemes proposed, the truest, the wisest, the 



best. 



Note A. 



"The triumph of the art of calculation, and that to which mainly the 

 modern system of numerical computation owes its perfection, consists in the 

 'device of place,' by which all necessity for distinguishing the nature of the 

 units signified by any symbol is superseded. Like many other inventions of 

 the highest utility this, when known, appears to aiise so naturally and neces- 

 sarily out of the exigencies of the case, tiiat it must excite unqualified as- 

 tonishment how it could have remained so long undiscovered. » * * That 

 the honor of the invention of a system which produced such important 

 effects as well on the investigations of science as in the common concerns of 

 commerce, should be claimed by many contending nations, is what would 

 naturally be expected. * * * All Arabian authors on arithmetic appear 

 to agree that the first writer of that country upon this system of arithmetic 

 was ^lohamnied ben Mnza, the Khuwarezmite, who flourished about the year 

 DOO. This writer is celebrated for having introduced among his countrymen 

 many important parts of the science of the Hindoos, to the cultivation of 

 which he was devotedly attached; and among other branches of knowledge 

 thence derived, there is satisfactory evidence that this species of arithmetic 

 was one. From the time of Mohammed ben Muza the figures and modes of 

 calculation introduced by him were generally adopted by scientific writers 

 of Arabia, although a much longer period elapsed before they got into com- 

 mon popular use, even in that country. They were always distinguished by 

 the name Ilindasi, meaning the Indian mode of computation. * » At 

 the beginning of the eleventh century the use of the Arabic notation had be- 

 come universal in all the scientific works of Arabian writers, and more espe- 

 cially in their astronomical tables. The knowledge of it was of course com- 

 municated to all those people with whom the IMoors held that intercourse 

 which would lead to a community of scientific research. In the beginning of 

 the eleventh century the Moors were in possession of the southei n part of Spain, 

 where the sciences were then actively cultivated. In tins way the use of 

 the new arithmetic was received into Europe first in scientific treati.ses. A 

 translation of Ptolemy was published in Spain in 1130, in which this notation 

 was used ; and after this period it continued in general use for the purposes of 

 science. Xotwitiistanding the knowledge and practice of this superior notation 

 by scientific men, the lioman numerals continued to be used for purposes of 

 business and commerce for nearly three centuries, and it was only by slow and 

 gradual steps that the improved notation prevailed over its clumsy and incom- 

 modious predecessor. The first attempt to introduce it for the purposes of com- 

 merce was made by a Tuscan merchant, Leonardo Pisano, in 1202. Having 



