MENSURATION. 



I. Lines. 

 a. In a circle. 



r ^ radius of circle, 

 c = length of any chord, 

 s = arc subtended by c, 

 a =■ angle corresponding to s, 



h = height of arc s above r, or perpendicular distance from middle point of 

 arc to chord. 



Circumference = 2 tt r, 



77 = 3.14159265, log 77 = 0.49714987, 



2 TT = 6.28318 531, log 2 TT = 0.79 817 987. 



c = 2 r sin ^ a, s =^ r a. 



Length of perpendicular from center on chord 

 = r cos ^ a 



A = r (i — cos h a) 

 = 2 rsin^ J a 



=i.{(9v.vg+.He,)+,.,i. 



•^ — ^ == s"? •«■ (t^^ — ^0 "^ + • • • ) 



.= s{f+,(:o+...}. 



b. In regular polygon. 



r = radius of inscribed circle, 

 A'^ radius of circumscribed circle, 

 n = number of sides, 

 s = length of any side, 

 (3 = angle subtended by s, 

 p = perimeter of polygon. 



