On the USE of NEGATIVE QUANTITIES. 135 



cd, rather by induction, and analogy, than by mathematical de- 

 monftration. But fomething more than this is to be expected 

 from mathematicians ; and their knowledge of algebra will ftill 

 be confidered as imperfect, if there be any of its operations 

 which they cannot, in every letter and fign of it, explain as a 

 feries of juft reafoning, capable of being exprefled in common 

 language. Now, it does not appear that our inftructors in ma- 

 thematics have enabled us to do this in the cafes to which we 

 allude, that is, where negative quantities are found, without 

 any intimation of the quantities from which they are fubtract- 

 ed. In coniidering the abftract operations of addition, fub- 

 traction, multiplication, SsV. we may indeed take negative 

 quantities by themfelves : For here the meaning is obvious ; we 

 are examining, in what manner fuch operations will affect thofe 

 quantities, which are fubtracted from other quantities. But 

 when we come to apply thefe operations to the bufinefs of al- 

 gebra, the refolution of equations, it is not fo eafy to perceive, 

 nor does it appear to have been fufficiently explained, in what 

 light we are to confider negative quantities, or how mathemati^ 

 cians are to be juftified in the ufe which they make of them. 

 The very vague and unfatisfactory, and often myfterious ac- 

 counts of the matter, which are given even by writers of the 

 greateft eminence, ferve only to Ihew, that although they are 

 fatisfied of the certainty of the method, yet they perceive that 

 fomething ftill remains which ought to be explained, and of 

 which no good explanation has been given. 



Mr Baron MASERES, indeed, has publimed a large work, 



which he entitles, " A Diflertation, on the ufe of the negative 



' iign in algebra ; containing a demonftration of the rules ufu- 



' ally given concerning it, and mewing how quadratic and 



' cubic equations may be explained, without the conlideration 



' of negative roots." But this difTertation contributes little to 



remove the difficulties complained of. For even allowing the 



author to be right in his notion, that it would be better " if ne- 



" gative 



