368 MifceUanea Curiofa, 



Here it is to be noted, that if - — — be an 

 1 2. 



odd Number, the Sign of the Root found muft; 



be contrary to it. 



Let an Equation be propos'd 5 y — 207 3 -h 



16 y * = 6, whence n =2: 5", and a = 6, and tht 



Root will be =s J^-K^J? Mh ' * Jj; or 



becaufe 6 -I- ^35* = 11. 9 16 whole Logarithm 

 is 1.0761304, and its Fifch part is 0.2.1515611 

 whofe Arithmetical Complement is 9.7847439. 

 The Numbers belonging to thefe Logarithms are 

 1.641? and 0.6091, whofe half Sum is 1. 145*3 



But if it happen that a is lefs than Unity then 

 the Second Form, as being more convenient, 

 ought to be pitch'd on. So if the Equation had 



been 5 y — xo y^> -J- i6y* =. then y will 



04 



64 4096 * 64 4096 



and if the Root of the Fifth Power can by any 

 means be Extracted the tt ue and poffible Root 

 of the Equation, will thence Emerge, tho' the 

 Expreflion feems to infinuate an lmpoffibility. 

 But the Root of the Fifth Power of the Binomial 



% i VriZJ hL + JL V~T S and fo the 

 64 4096 44 * 



fame Root of the Binomial. 



ll+VEia ; s i._±^=Tythe half 

 64 4090 4 4 



Sum of which Roots is ss == 7. But 



4 



