22 Ellery W. Davis 



to come into coincidence with the right is 



/ 



n — in 



I -j- nni 

 which is usually complex. 

 Return then to our problem, the distance from a point 



(J u y 1 )=P 1 to y = e**x. 



The perpendicular line though P l is x — x 1 = e i * (y — y t ) and 

 the distance sought is 



c '* x, 



d = 



Vi 



Vi + ^'' 



If the line is a circular ray the denominator vanishes and the 

 distance. becomes infinite unless the numerator vanishes also, that 

 is, unless P x is upon the ray. To see this otherwise, note that the 

 perpendicular to an /-ray through any point is an /-ray. If the 

 point is on the first ray it is of course no distance from it. If 



Fig. 22. 



the point is not on the ray it is necessary to go along the perpen- 

 dicular until / itself, common to the two rays, is reached. This 

 is an infinite distance as the construction in fig. 22 shows. In 

 particular, suppose the point is (2, i) the /-ray through it is 



y = i(x — 1) 

 22 



