THE NON-LIVING WORLD 



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passes from our eye at A to O. Next we must plant 

 ourselves at B, and similarly observe the angle formed 

 by AB with a line from B to 0. Thus we may easily 

 obtain a triangle which will enable us to tell the dis- 

 tance of 0. To do this we must draw on paper a 

 straight line ab, and from its two ends draw two other 

 lines such that the angle formed at b by one of them 

 shall be the same as the angle we observed at the point 

 B, while the angle formed at a shall be equal to that 

 we observed at the station A. Let these lines be ax 



and ay respectively ; then if we prolong them enough 

 they will meet at some point p. Then the small triangle 

 on paper, apb, will be similar to (i.e., equiangular with) 

 the large triangle formed by the straight line AB and 

 the two lines respectively extending from A and B and 

 meeting at the distant object 0. Therefore the length 

 of AB must bear the same proportion to ap as the 

 line AB bears to AO and by measuring the actual 

 lengths of the three lines of the triangle apb and that 

 of the line AB, it is easy by the simple arithmetical 

 process known as " the rule of three," to ascertain the 



