GEOMETRY. 



that will be similar to the given ellipsis A D B C, 

 which may be described by some of the foregoing 

 methods. 



Prob. 31. To describe a parabola. If a thread 

 equal in length to B C, be fixed at C, the end of 

 a square ABC, and the other end be fixed at F; 

 and if the side A B of the square be moved along 

 the line A D ; and if the point E be always kept 

 close to the edge B C of the square, keeping the 

 string tight, the point or pin E will describe a 

 curve E G I H, called a parabola. 



The focus of the parabola is the fixed point F, 

 about which the string revolves. 



The directrix is the line A D, which the side of 

 the square moves along. 



The axis is the line L K, drawn through the 

 focus F, perpendicular to the directrix. 



The vertex is the point I, where the line L K cuts 

 the curve. 



The latus rectum, or parameter* is the line G H 

 passing through the focus F, at right-angles to the 

 axis I K, and terminated by the curve. 



The diameter is any line M N, drawn parallel to 

 the axis I K. 



A double ordinate is a right line R S, drawn pa- 

 rallel to a tangent at M, the extreme of the dia- 

 meter M N, terminated by the curve. 



The abscissa is that part of a diameter contained 

 between the curve and its ordinate, as M N. 



Prob. 32. To describe a parabola, by finding 

 points in the curve ; the axis A B, or any diameter 

 being given, and a double ordinate C D. 



Through A draw E F parallel to C D ; through 

 C and D draw D F and C E parallel to A B, cut- 

 ting E F at E and F. Divide B C and B D, each 

 into any number of equal parts, as four j likewise 



