Mr. Bui-ch's Method of Drawing Hyperbolas. 373 



mine, however, by several years, as lie states that he first 

 used it in 1885, while it first occurred to me in 1893. In 

 the present note I only wish to call attention to the fact that 

 the particular construction described is only one example of 

 a general class of solutions of this character, and to describe 

 two or three others which are, I think, equally simple and 

 convenient. 



In general, if in any two similar triangles two dissimilar 

 sides are kept constant and the other sides varied, it is evident 

 that these two varying sides, which are proportional to the 

 two fixed sides, will be asymptotic coordinates of an hyperbola 

 of which the modulus is the product of the two constant sides. 

 The simplicity of the corresponding graphical or mechanical 

 tracing of the curve depends simply upon our choice of tri- 

 angles and choice of sides. In the method of construction 

 which I most frequently employ, the two similar triangles 

 have a common vertex at the origin o, fig. 1, and the two 



sides ob, bo and od, de parallel to the asymptotes of the re- 

 quired hyperbola. Then if we put 



ob = x, 



de=y f 



bc=l, 

 we have at once 



xy = od. 



Hence if we draw a series of triangles in each of which be 



