CHAP. I.] STATION POINTER 23 



cumference of a circle, the size of which depends on the angle 

 observed. 



To draw this circle, we take advantage of the fact that the 

 angle at the centre of any segment is double the angle at the 

 circumference. (Euclid III. 20.) We lay off, therefore, from 

 either end of the line whose subtended angle we have observed, 

 the complement of the angle. The point where these lines 

 meet is the centre of the circle, which we describe with the 

 distance from this centre to either end of the line, as a radius. 



Thus if our observed angle is 64°, we lay off A G, B G each 

 making an angle of 26° with A B, and describing the circle with 

 centre G and radius A G or G B, we get the circle we want,, for 



AGB=180°-(B AG+GB A) 

 = 180° -52°. 

 = 128°. 

 And as AG B = 2 AE B, 



the angle A E B and all other angles on the circumference will 

 be 64°. 



If the angle observed is more than 90°, we describe the circle 

 by laying off the number of degrees over 90°, on the opposite 



I 

 I 

 I 

 I 

 \ 



\ 



\A' 



D 



side of the line to that on which we know we are, and proceed 

 as before. 



If we can obtain, besides the angle subtended by A B, the 

 one subtended by B C, another line, one of whose ends is 

 identical with A B, we can draw another circle on whose cir- 

 cumference we must also be, and the intersection of these 



