754 



PROCEEDINGS OF THE AMERICAN ACADEMY. 



Take two lines AC and BD passing through F. Since all points of 

 BD are at the same distance from A and all points of AC at the same 

 distance from D, and AB = — BA, 



AB = AD = CD. 



Figure 7. 



Therefore the distance from any point of a line through F to any point 

 of another line through F is constant. The distance between two 

 points depends only on the lines joining them to F. 



Figure 8. 



Take any line CD, not passing through F, as a scale. Let distances 

 along this line be proportional to the corresponding vectors. Then 

 any distance AB is equal to the distance CD into which it projects 



