MATHEMATICS 



35 



axioms * of Euclid) being granted, the problem is solved 

 as follows, and the reader will see that the solution is 

 absolutely certain for any such possible triangle. 



Let us first draw a line (as from premiss i we can) 

 from a point marked A to a point marked B, and let 

 this be the given line whereon the equilateral triangle 

 is to be drawn. 



Now taking the point A as a centre, let us describe 

 round about it (as from premiss 2 we can) a circle, the 



FIG. 2. 



circumference of which shall pass through the point B 

 forming the circle BCDEF. Next, taking the point 

 B as a centre, let us describe round about it a circle, 

 the circumference of which shall pass through the point 

 A, forming the circle ACGHI. From the point C, 

 where these two circles intersect, let us draw two straight 

 lines, one from C to A and the other from C to B, as 

 we may do from premiss i. 



* See ante, p. 25. 



