OF THE PARALLELOGRAM AND ITS INSCRIBED PARABOLA. 87 



therefore, by involving or squaring both sides of this equation, we 

 shall obtain 



and by extracting the sursolid root, we get 



= '1/0 



)*' (47). 



If m and n be equal to one another as in the preceding case, then 

 it is obvious that the equation becomes 



and if any other numerical ratio be proposed, such as 4 to 5; then 

 we shall have 



Thus for example; let the axis of the parabola remain as in the 

 foregoing question, and let it be required to find a point, through 

 which a line must be drawn parallel to the base, so that the pressure 

 on the part above the dividing line, may be to that below it in the 

 ratio of 4 to 5 ? 



Here we have 



= 20.967 feet. 



Hence it appears, that if a point be taken in the axis of the given 

 parabola at the distance of 20.967 feet from the vertex, and if through 

 that point, a line be drawn parallel to the base, the parabola will be 

 divided into two parts, on which the pressures are to one another 

 as 4 to 5. 



