igofi Henderson — Graphic Representation. 125 



Pascalian points (the intersections of pairs of lines each 

 through two of the points 1, 2, 3, 4, 5, 6) which lie on the 

 Pascalian lines be, ca, ab, gh, hf,fg respectively; the point 

 abc is the intersection of the Pascalian lines be, ca, ab, and 

 the point fg/i is the intersection of the Pascalian lines gh, hf, 

 fg, the points in question being" two of the points S (Steiner's 

 twenty points, each the intersection of three Pascalian lines).* 



§ 2. The question with which I concern myself in the 

 present paper is: — May such a beautiful theorem be repre- 

 sented to the eye in such a way as to show clearly the entire 

 configuration? After some labor and thought, I am able to 

 answer this question in the affirmative. The accompanying 

 plate (Plate I.), drawn to scale with great precision, repre- 

 the sents ultimate result of the investigation. 



The initial problem was so to choose the two triads of 

 planes as to give the point of projection a position that 

 might be readily representable on a diagram, showing also 

 the two triads of planes. Choosing to use quadriplanar co-or- 

 dinates, I found it desirable for the point to coincide with 

 one of the four vertices A, B, C, and D of the fundamental 

 tetrahedron ABCD. The point was finally chosen, from 

 various considerations into which I shall not enter at present, 

 to coincide with the vertex D. The question that next pre- 

 sented itself was what plane to choose as the plane of projec- 

 tion. The plane ABC was finally chosen as the most econom- 

 ical position for the plane of projection, as will appear later. 



I now proceed to an analysis of the problem. The planes 

 were chosen in the following manner: 



a: w = 



b: 256* — 384 j — 96 z + 459^ = 



e: 96* — 64^ — 256^+153^ = 

 and 



/: 32 x + 27 w = 



f: 64 y — 51 w = 



: • 32 z — 17 w = 



♦It is to be understood that a point or line and its projection have the 

 same designation, and that the meet of a line such as [1] with the plane of 

 projection is denoted by 1. 



