98 Mijcellanea Curiofa. 



by the addition of the Reclangle under r 

 and the Latus Redtum, if it be w r, or to 

 be diminimed by the fame Rectangle if it be 

 -f r. The Circle thus defcrib'd, and Perpen- 

 diculars let fall from its Interfe&ions with 

 the Parabola, to the Line DH, thofe that 

 are at the Left Hand as NO will always be 

 the Negative Roots of the Equation, and 

 thofe at the Right, the Affirmative. 



Cubick Equations are othervvife (and fome- 

 thing more limply) conftrutted according to 

 Schooten's Rule, in which alfo the Roots re- 

 fpecl: the Axis. But becaufe the Inventor 

 himfelf does neither explain the Inveftiga- 

 tion nor Demonftration, it will not be amifs 

 to fliew the Foundation of it here, and at 

 the fame time render the Geometrick Con- 

 ftru&ion more Elegant, and rid it of thofe 

 Cautions in which 'tis involv'd. 



This Rule is deriv'd from hence, that 

 every Cubick Equation may be reduced to 

 a Biquadratick one, in which the fecond 

 Term is wanting. Which is done, by mul- 

 tiplying the Equation propofed into 

 if it be ~Yb in the Equation, or into z.-\-b s=.^ 

 if it be — *b- r and the new Equation thus 

 form'd will have the fame Roots with the 

 Cubical one, and moreover another Equal to 



b<> if it be b in the Equation, or con- 

 trariwife. 



Let the- Equation x} -h b -\~dpz. -\-aaq 

 hp propofed to be conftru&ed ; multiply this 

 into and it makes 

 zf* — * & i b~\-apz. * 



*\-z. 3 b—bb^-YabpzL-^aaqb 



Here nm the- fecond Term is wanting, and 



the 



