422 Mr. Lubbock o« the Perspective 



a hyperbola. Thus to a spectator in an amphitheatre the 

 inner benches are in the picture elhpses, the bench on which 

 he is seated is a parabola, or nearly so, and the outer benches 

 are hyperbolas. 



The following construction obtains generally for curves of 

 the second order: 



Let any straight line AGB (fig. 3.) be bisected in G, at G 

 draw GC perpendicular to AB, cutting W in C, in VV 



Fiff. 4. 



take any point D, and make DV = DV = DK. Join AV, 



BV the locus of the intersection of the lines AV, BV is a 



curve of the second order. 



If VV is parallel to AB, and 



KC>GA, the curve is an ellipse, 

 KC = GA, the curve is an parabola, 

 KC< GA, the curve is an hyperbola. 

 It is easy to show that if VV is the vanishing line of any 



plane, the vanishing point V" of a line perpendicular to this 



plane is found by taking in OC, fig. 2. 



V" O = ~> A being, as before, the 



distance of the picture. 



Spherical triangles may be solved gra- 

 phically by perspective by means of the 

 preceding theorems ; but this application 

 is without practical utility, and is too 

 simple to require development. 



In crystallography, it might be con- 

 venient to mark the angles contained 

 by planes at the vanishing point of the 

 lines which result from their intersec- 

 tion, or any point in them lines pro- 

 duced, as in (fig. 4.) which is Stilbite, 

 Jogyj Pag^ 37.) 



(Phillips's Minera- 

 The 



