

ANALVll' <,! OM 



[Ca IX. 



pre\ii.ns chapter, will he assumed in the following ,li s . 

 cussion. 



134. Construction of the parabola. The two conceptions 

 locus given in Article o.~> h-ad to t \\ o methods for con- 

 structing a curve, vi/., hy plotting points to he connected 

 by a smooth curve, and by the motion of a point constraint d 

 by some mechanical device to satisfy the law which defines 

 t lie eurve. These two methods may be used in constructing 

 a parabola. 



() By separate ;W//^. (liven the focus F and the ver 

 0, draw the axis OFX, the directrix D'J) cutting this axis 



in Z, and alsouserie 



pcrpcndiculiir to the axis at 

 M v M T M y etc., respectively. 

 With F as center and ZM l 

 as radius, describe arcs cut- 

 ting the line at M l in two 

 points f\-.nu\Q l ; similarly, 

 with F as center and ZM 2 as 

 radius, cut the line at 3/> in 

 P 2 and Q 2 ; and so on. Tho 

 points thus found evidently 

 satisfy the definition of the parabola (Art. 102). In this 

 way, as many points of the curve as are desired may be 

 found. If these be then connected by a smooth em \ 

 will be approximately the required parabola (cf. Note II, 

 Appendix). 



() By a continuously moving point. Let D'D be 

 directrix and F the focus. Plaee a right triangle 

 its longer Kid*' Klf in coincidence with the axis of 

 curve, and its shorter side KJ in coincide nee with the 

 trix. Let one end of a string of length Kll be fastened 



