364f GEOMETRY. 



cutting T) e in e. Take the distance b c/, and apply 

 it to the arc ej", from e tof. Lastly, through the 

 points, T),J] draw the line D^ and the angle e T>f 

 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 2^rottYwtor, 

 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 « B ^, 

 the angle required. 



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

 line parallel to a given line A B. 



