126 Mijcellanea Curio [a. 



impofiible. It happens alio that there are 

 four Affirmative Roots, when the Center G 

 is pofited in the little fpace UTS, Vmi 

 drawing RTS perpendicular upon the mid- 

 dle of the fuppofed Line AD. But this 

 eomes to pafs when p is greater than r 6 bb^ 



and %bb p V x^ bb —\ p greater than f 

 pb — i u bz — i q. In which cafe always two, 

 fometimes three of the Roots are greater 

 than % b. 



But 'tis to be noted here that that Limit 

 produced from the leafl y, is fometimes Ne- 

 gative, or lefs than nothing *, vit. as often 

 as the greateft of the three Perpendiculars is 

 greater than GD (Fig. 2.) If this happens^ 

 the Quantity 'V r may be diminiflfd to no- 

 thing from the Limit prefcribM, by the 

 middle y. But the defect of a Limit from the 

 ka.fi y, fhews how great — r may be in the 

 Equation, if there be three Affirmative R00H 

 and one Negative one ; which if it exceeds, 

 there can be but two, one Affirmatsve and 

 the other Negative. And all thefe things 

 rare demonftrated from hence, that the fore- 

 mention* d Limits of the Quantity r, are the dif- 

 ferences of the Squares of the Line G D, and the 

 Perpendiculars to the Curve of the Parabola, 



But becaufe of the perplexing Cautions ari- 

 flng from the diveriity of Sines with thefe E- 

 quations, 'tis better always to take away the 

 fecond Term, and then to inquire out the 

 number of Roots and the Sines, according to 

 the Rules already deliver'd ; especially if thofe 

 Quantities y are not much different from one 

 another* But of thefe four Affirmative Roots^ 



twd 



