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belonging to the early part of the fifteenth century, and 

 containing the following articles : 



" 1. A brief treatise on arithmetic. 



" This unfortunately commences imperfectly in the ac- 

 count of the rule of duplation ; ' In duplation only one order 

 of figures is necessary : in the three preceding kinds, we com- 

 menced from the right and from a smaller figure ; but in this 

 this, and the following kinds, we commence from the left and 

 from a larger figure. For if you wish to double from the 

 first figure, it happens that you must double it twice. And 

 if you can in any other manner commence from the right 

 hand, the operation and construction will be much more diffi- 

 cult. If, therefore, you wish to double any number, that 

 number must be written by its differences, and the last 

 number must be doubled. From that duplation, therefore, 

 either results a digit, an article, or a composite. If a digit, 

 it must be written in the place of the other blotted out. If 

 an article, a must be written in the place of the other 

 blotted out, and the article must be removed towards the 

 left hand. If a composite number, the digit which is a part 

 of that composite must be written in the place of the other 

 blotted out, and the article be removed to the left hand. 

 This being done, the last figure must be doubled, and what- 

 ever thence arises must be dealt with as before ; but if a 

 cipher turns up, it must be left untouched. We prove du- 

 plation by means of mediation.' 



" This extract will be sufficient to give an idea of the whole 

 tract. After this rule, follow those of multiplication, division, 

 and progression in their proper order. For the comprehen- 

 sion of the uninitiated in the old arithmetic, it may be neces- 

 sary to state, that a digit is any number below ten, an article 

 is ten, or any multiple of ten, and that all other numbers are 

 composites, or composed of an article and some digit. My 

 friend Mr. Wright, gives it as his opinion, that this tract is 

 a translation from the Latin or French. 



