GEOMETRY. 



divide C E and D F into the same number of equal 

 parts. Through the points 1, 2, 3, &c. in CD, 

 draw the lines 1 a, 2 b, 3 c, &c. parallel to AB; also 

 through the points 1, 2, 3, in C E and DF, draw 

 the lines 1 A, 2 A, 3 A, cutting the parallel lines 

 at the points a, b, c ; then the points a, b, c, are in 

 the curve of the parabola. 



Prob. 33. To describe an hyperbola. 



If B and C are two fixed points, and a rule 

 AB be made moveable about the point B, a 

 string ADC being tied to the other end of the 

 ruler, and to the point C ; and if the point A be 

 moved round the centre B, towards G, the angle 

 D of the string ADC, by keeping it always tight 

 and close to the edge of the rule A B, will describe 

 a curve D H G, called an hyperbola. 



If the end of the ruler at B were made moveable 

 about the point C, the string being tied from the 

 end of the ruler A to B, and a curve being de- 

 scribed after the same manner, is called an oppo- 

 site hyperbola. 



The foci are the two points B and C, about 

 which the ruler and string revolves. 



The transverse axis is the line IH, terminated 

 by the two curves passing through the foci, if con- 

 tinued. 



The centre is the point M, in the middle of the 

 transverse axis I H. 



The conjugate axis is the line N O, passing 

 through the centre M, and terminated by a circle 

 from H, whose radius is M C, at N and O. 



A diameter is any line V W, drawn through the 

 centre M, and terminated by the opposite curves. 



A conjugate diameter to another, is a line drawn 

 through the centre, parallel to a tangent with 



B B 3 



