The Imaginary in Geometry 



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and the conies are line-pairs, but the red elements are self-con- 

 jugate. If we attempt in either of these cases to construct red 

 vectors other than those joining p x and p i we meet failure. The 

 cases are rather too exceptional, however, to possess interest. 



Fig. 38. 



Figs. 37 • • • 40 show constructions for new vectors given the 

 center of the line and a vector. Each line is an /-ray whose 

 center is the origin and the given vector is I. The vectors drawn 



Fig. 39. 



have one coordinate wholly real, the other wholly imaginary. 

 Observe that in fig. 37 the vectors with .r" = o are apparently as 

 they would be in ordinary rectangular coordinates ; but all the 

 other vectors, for example, those for which y" = o, are very 



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