GEOMETRY. 865 



Case 1. Take any point d, in A B ; upon d and 

 C, with the distance C d, describe two arcs, e C, 

 and df, cutting the line A B in e and d. Make 

 <//equaI to e C; through C andjfdraw Cf, and it 

 will be the line required. 



Case 2, When the parallel is to be at a given 

 distance from A B. From any two points, c and 

 d, in the line A B, with a radius equal to the given 

 distance, describe the arcs e and/V draw the line 

 C B to touch those arcs without cutting them, and 

 it will be parallel to A B, as was required. 



Prob. 8. To divide a given line A B into any 

 proposed number of equal parts. 



From A, one end of the line, draw A c, making 

 any angle with A B ; and from B, the other end, 

 draw B d, making the angle A B c? equal to B A c. 

 In each of these lines A c, B d, beginning at A and 

 B, set off as many equal parts of any length as A B 

 is to be divided into. Join the points C 5, 46, 

 37, &c., and A B will be divided as required. 



Prob. 9. To find the centre of a given circle, 

 that is, of any one already described. Draw any 

 chord A B, and bisect it with the perpendicular 

 C D. Bisect C D with the diameter E F, and the 

 intersection O will be the centre required. 



Prob. 10. To draw a tangent to a given circle 

 that shall pass through a given point, A. 



From the centre O, draw the radius O A. 

 Through the point A, draw D E perpendicular to 

 O A ; and it will be the tangent required. 



Prob. 11. To draw a tangent to a circle, or any 

 segment of a circle A B C, through a given point 

 B, without making use of the centre of the circle. 



Take any two equal divisions upon the circle 

 from the given point B, towards d and e, and draw 

 the chord e B. Upon B, as a centre with the dis- 



