MifceUanea Curio fa. 



Thefe fame Limits^ are otherwife cxprelfed 

 by the Quantity <?, viz. | qy ^-y\ in the firfb 

 cafe, jy4 — \ qy in the fecond, andjy4 + f qy 

 in the third. But it may be, that the two 

 feller Qualities^ may not be far different from 

 one another, whence it comes to pa ft that 

 both of the Perpendiculars are greater than 

 the right Line G A, vm* when qq is greater 

 than f 7 f% but left than 7 ~ 7 p 3 \ the Center 

 falling within the fpace contain'd between 

 the Paraboloids of Fig. i. and 2. In this 

 cafe, if it be ~\- r, there can be but two 

 Roots, jy4 r h i qy of the great eft y being grea- 

 ter than r \ otherwife none. But if \ qy—y^ 

 pf the leaft y be greater than r mark'd with 

 the Sine — , but r be greater than f qy —y4- 

 of the meany^ then there will be four Roots; 

 but two only, if r be found greater than the 

 former, or left than the latter. But if in 

 the Equation it be "Y />, or if it be — p and 

 4q be greater than / 7 p ? , the Equation y 3 . *. 

 a ?> 4 is explicable by only one Root y - 7 

 that is, there can be but one Perpendicular 

 only let fall from the Center of the Circle. 

 Whence it > may be certainly concluded that 

 there can be but two Roots only in the 

 given Equation, the Sum of which, if it be 

 — r, is increased with the Quantity r \ but 

 if it be +-r, the Quantity y being obtain'd, 

 that Quantity r ought to be left than j4 in i 

 DS f° r ^ it be greater, the Equation pro-i 

 pos'd is abfurd and impoffible. 



'Twould be both tedious and needleft to 

 run over all Equations of this kind, fince 'tis 

 evident (from what has been already faid) 

 to thofe that are attentive, which are Ne- 

 gative 



