364 GEOMETRY. 



cutting D e in e. Take the distance b a, and apply 

 it to the arc ef, from e tof. Lastly, through the 

 points, T),f, draw the line Dj and the angle e Df 

 will be equal to the angle b B a, as was required. 



Prob. 5. To divide a given angle, ABC, into 

 two equal angles. 



From the point B, with any radius, describe the 

 arc A C. From A and C with the same, or any 

 other radius, describe arcs cutting each in d. Draw 

 the line B d, and it will bisect the angle ABC, as 

 was required. 



Prob. 6. To lay down an angle of any number 

 of degrees. 



There are various methods of doing this. One 

 is by the use of an instrument called a protractor , 

 which is a semicircle of brass having its circumfer- 

 ence divided into degrees. Let A B be a given 

 line ; and let it be required to draw from the an- 

 gular point A, a line making with A B any number 

 of degrees, suppose 20. Lay the straight side of 

 the protractor along the line AB, and count 20 

 from the end B of the semicircle ; at C, which is 

 20 from B, make a mark ; then, removing the 

 protractor, draw the line A C, which makes with 

 A B the angle required. 



Or, it may be done by a divided line, usually 

 drawn upon scales, called a line of chords. Take 

 60 from the line of chords in the compasses ; and 

 setting one at the angular point B, Prob. 4, with 

 that opening as a radius, describe an arch, as a b : 

 then take the number of degrees you intend the 

 angle to be of, and set it from b to a, then is a B b, 

 the angle required. 



Prob. 7. Through a given point C, to draw a 

 line parallel to a given line A B. 



