Mtfcellanea Curioja. I 1 3 



falls in the fpace GNU, there are two 

 greater than j bat lefs than f i } but the 

 thmd is j — the two others, and confequent- v 

 ly lefs than ;\ b but nling the Limitation of 

 the Quantity />, the Roots are included in 

 narrower Bounds. For the greatcft Root is 



lefs than V f b* ip^ i £ but grater 



than V | ^ ~ f i i J but when | ^ is lefs 



than y, that jUwft becomes \/ J bz — jj> +*| 6. 



The Root is always lefs than \/i £ 2 — p 



~\- $ but greater than $ V $ ^-ffj ^ 

 but the leaft Root never exceeds this Limit y 

 but vanifhes with the Quantity q. 



In the fecond Formula^ according to* the 

 p'refcrib'd Laws, there arc two Affirmative 

 and one Negative Root; and the Center fal- 

 ling in the Space G P E, one of the Affirma- 

 tives is greater, and the other lefs than | fr, 

 but the greater exceeds not b *, but the Ne- 

 gative cannot be greater than V jbb—-jb J 

 and it is the difference of b and the Sum of 

 the Affirmative Roots. But the Center be- 

 ing poli ted in the Space £ N G a, either of 

 the Affirmatives is greater than § b, but lefs 



than \l \bb'Y \ b \ but the Negative is ever 

 lefs than f b. But the nearer Limits (from 



the Quantity ? given) are V % bb — p -f i by 

 of the gfeateft Affirmative Root than 

 Which it' is always lefs, as alfo greater 

 I than 



