Mifcellaned Cttriofa. 1 1 5 



i's affe&ed with the contrary Sine ; as I in- 

 timated above. 



The Demon {Ira t ion of all thefe things fol- 

 lows from hence, that where-ever the Cen- 

 ter of the Circle R falls upon the Curve 

 Lines UPX or UaL, the Circumference 

 of it touches the Parabola in a Point whole 

 diftance from the Axis is V f VH, and cuts 

 it on the other fide the Axis at the diftance 

 of 2 V f U H - 0 but when the Center falls on 

 the Line DPD, one of the Roots is == 0, 

 and confequently the Cubick Equation is re- 

 duced to a Quadratick one, or to ^2 hz. 

 -|- p z=z 0, the Roots of which give the Limits 

 when the Quantity q vanifhes ; and by how 

 much the iefs q becomes, by fo much the 

 nearer do the Roots approach to thefe Li- 

 mits. The Equation is alfo Quadratical^ 

 when the Center falls in the Axis-, that is, 

 when I q = g bp *— \ 7 in the firft Formula - 7 

 or \ q == 27 bi ~- \ bp, in the fecond *, in the 

 third 'tis impoilible but in the fourth, when 

 I q-=z\ 1 bl bpij in which cafe the lefs of 

 the Affirmative Roots is ' b, and the greater 



V 3 bb +p+ 3 b 7 but the Negative V I bb 



vfc f—'l In the firft Formula, the Roots 



are 3 b i and \ b^£ Vj kb ~ p But in the 



fecond, the Affirmatives are \ b y and V I bb 



*~p + 3 b, but the Negative V \bb —p-\b: 

 And thefe things may feem to fuffice in Cu~ 

 ticks } but becaufe of the excellent ufe of the 

 Method, by which, by the help of the Table 



I i of 



