284 EXAMPLES OF TANGENTS. 



Hence, by Art. 262, the equation to the tangent at the 

 point (re, y) is 



(y'-y] 

 which reduces by means of the given equation to 



Example (2). Suppose the equation to the curve to be 



f dy a - f v 



therefore -^- - e = - : 



ax c c 



and the equation to the tangent becomes 



The subtangent MT = j- = c, and is therefore constant in 



dx 

 this curve which is called the logarithmic curve. 



Example (3). The equation to the logarithmic spiral is 



dy ^ / dy 



x - 



therefore 



dy 



and the equation to the tangent is 



