Mtfcellanea Cur to fa. 87 



after the firft, does alfo double the number 

 of Figures, fo that it renders the ajfumed al- 

 together Seven-fold \ yet the firft Corredion 

 is abundantly fufficient for Arithmetical ufes, 

 for the moft part. 



But as to what is faid concerning the num- 

 ber of Places rightly taken in the Root, I 

 would have underftood fb, that when a is but 

 A part diftant from the true Root, then the 

 firft Figure is rightly afliitned } if it be within 

 t ~ Q part, then the two firft Figures are rightly 

 affiimed } if within to^e, and then the three 

 firft are fo •, which confequently manag'd ac- 

 cording to our Rule, do prefently become 

 nine Figures. 



It remains now that I add fomething con- 

 cerning our Rational Formula^ viz. e g£i — j^j" 



which feems expeditious enough, and is not 

 much Inferior to the former iince it will 

 triple the given Number of Places. Now 

 having formed an Equation from atke as 

 before, it will prefently appear, whether a be 

 taken greater or lefs than the Truth ; fince 

 s e ought always to have a Sign contrary to 

 the Sign of the difference of the Refolvend^ 

 and its Homogened produced from a. Then 

 fuppoling ~\zb-\-se-\-a~~ tee^o.^ the Divifor is 

 ss-tb y as often as t and b have the fame Signs; 

 -but it is ss-\-bt^ when they have different ones. 

 But it feems moft commodious for Pra&tce,to 



b tb 



write the Theorem thus,e 1=1 — — h — - fince 



this way the thing is done by one Multiplica- 

 tion and two Divifions,which otherwife would 

 require three Multiplications, and one Divi- 

 sion. G 4 Let 



