16 GEOME1UY [On. I. 



with the ; end 



of the terminal side. The p,.int in which the lines in- 

 is (ailed the vertex of the angle. The angle is 

 positive, or +, if the rotation from the initial to the ter- 

 minal side is in c >ckwise direction: the angli 

 . if the rotation is clockwise. 

 : med by two directed straight lines in 

 which do not meet, is equal to the angle between two n 

 fleeting lines, which are respectively parallel t<> the -ivm 



lines. 



I r the measurement of angles there are two absolute 

 units: 



(1) The angular magnitude about a point in a plane, i.e., 

 a complete revolution. One fourth of a complete revolution 

 is called a right angle, ^ of a right angle is a degree (1), 

 g\y of a degree is a minute (I'), and ^ of a minute is a 

 second (1 



the angle whose subtending circular arc is equal 

 fh to the radius of that arc; this angle is callc 

 radian )l (r) $ ; it is independent of the length of the radius, 

 o. circumference _ semi-circumference __ *t f 11 tl t 



diameter radius 



the angle formed by a half rotation, i.e., 180, is TT radians; 



/22V r) 

 i.e., 180 = 7r (r) = f yj approximately ; 



= 57 17' 44. 8" approximately. 



IT 



A right angle is 90 or ( ^ 



When there is no danger of being misunderstood, the index 

 (r) is omitted, and ^ radians is written simply as ^, 

 not f? M 



