On the Formation of the Paraboloid. 



189 



-section of the axis beyond the base-line, will be the required 

 focal distance of the parabola. 



Fig. 5. 



Fig. 6. 



Fig. 7. 



To those not possessing the requisite tools, this method of 

 cutting out a template, of course, cannot be available. The plan 

 of drawing with a square and piece of string, described in all 

 elementary works on geometry, is so irregular in its action as 

 to be useless for small parabolas; bisection must therefore be 

 resorted to, which, by careful manipulation, gives a very true 

 figure. This operation depends upon the following property 

 of a parabola : that any point, taken on the axis at a distance 

 beyond the vertex equal to the distance of the focus within it, 

 to any transverse line on the axis, will be equidistant from the 

 same line to the focus. Proceed as follows: 



