[ 395 ] 



all which we may fee the utility of fo adapting the pro- 

 duds to each other, that they may differ in their lowell terms 

 only. 



6. It is ufeful, when one of the produds only confifls en- 

 tirely of compound fadors, that the fecond terms of thefe fadors 

 be as fmall numbers as poffible ; for the continual produd of 

 all thefe fecond terms conftitutes in this cafe the difference of 

 the produds. This precaution is alfo ufeful, when both produds 

 confift entirely of compound fadors, and their lowefl terms are, 

 at the fame time, affeded with contrary figns. For the differ- 

 ence of the produds in this cafe is equal to the fum of two 

 numbers which are produced by the continual multiplication of 

 the fecond terms of the fadors of each produd refpedivcly, no 

 regard being paid to their figns. 



Substitute in the above produds of two dimenfions, i for a^ 

 and — I for 3 (by which means we fhall have ab = — i, and a ■{■ b 

 = o) the produds will then be x^ — i, and *r% whofe difference 

 is unity and which confift of but three different fadors x — r, 

 K+ I and X. 



The logarithms of any two of thefe fadors being given that 



of the third may be found by the application of the above 



d . . . , I 

 mentioned feries ; — being m this cafe equal to — ^ 



'5 D 2. But 



