PROBLEMS, 



393 



PROBLEM III* 



To divide a right angle ABC into three equal parts^ 



From the centre B, with any 

 radius, describe the arc AC. From 

 the centre A, with the same radius, 

 cross the arc AC in n ; and with 

 the centre C, and the same radius, 

 cut the arc AC in w. Then 

 through the points m and n draw 

 B m and B n^ and they will trisect 

 the angle, as required. 



PROBLEM IV, 



To draiv a Line parallel to a given Line A B. 



Case i. — 'IVhcn the parallel Line is to be at a given Dis* 

 tance C. 



""■!> 



B 



From any two points m and 

 «, in the line AB, with a rad- 

 ius equal to C, describe the 

 arcs r and o. Draw C D to 

 touch these arcs, without cut- 

 ting • them, and it will be the 

 parallel required. 



Case l.-'—When the parallel Line is to pass through a given 

 Point C. 



From any point m^ in the ^ 



line AB, with the radius /tzC, ^1 "~ — " \ E 



describe the arc Qn. From / / 



the centre C, with the same A--, i ■— 4> 



radius, describe the arc mr. 



Take the arc Qn in the compasses, and apply it from >« to 



r. Through C and r draw DE, the parallel rL-quircd. 



Bub Note 



