#Euclid Book VI Proposition 2 states: If a straight line be drawn parallel to one of the sides of a triagle, it will cut the sides of the triangle proportionally; and, if the sides of the triangle be cut proportionally, the line joining the points of section will be parallel to the remaining side of the triangle. #Desargues' two triangle theorem represented as a graph. #The red and blue nodes represent points and lines. #A connection between nodes represents incidence. #The two node at the end are the colinear/concurrent #points/lines of the six coners/sides of the two triangles. #Note that this graph possess perfect symmetry. #The graph can be repositioned so any node can occupy #one of the "ends". # Xah # xah@xahlee.org # ∑ http://xahlee.org/ #Converted from Mathematica #by SaveToRotaterFormat.m 1. 0 0.5 0 0.86603 0.5 1. 2. 0.5 0.86603 0.5 2. -0.5 0.86603 0.5 0 -0.86603 0.5 1. 2. -1. 0 0.5 2. -0.5 -0.86603 0.5 0 0 -1. 1. 2. 0.5 -0.86603 0.5 2. 0 0 2. 0 0.86603 0.5 1. 2. 0 0 2. 0 -0.86603 0.5 1. 2. 0 0 2. 0 0 -1. 1. 2. 1. 0 0.5 0 1. 0 -0.5 2. 1. 0 0.5 0 -0.5 -0.86603 -0.5 2. 0.5 0.86603 0.5 0 0.5 0.86603 -0.5 2. 0.5 0.86603 0.5 0 0.5 -0.86603 -0.5 2. -0.5 0.86603 0.5 0 -0.5 0.86603 -0.5 2. -0.5 0.86603 0.5 0 1. 0 -0.5 2. -1. 0 0.5 0 -1. 0 -0.5 2. -1. 0 0.5 0 0.5 0.86603 -0.5 2. -0.5 -0.86603 0.5 0 -0.5 -0.86603 -0.5 2. -0.5 -0.86603 0.5 0 -0.5 0.86603 -0.5 2. 0.5 -0.86603 0.5 0 0.5 -0.86603 -0.5 2. 0.5 -0.86603 0.5 0 -1. 0 -0.5 2. 1. 0 -0.5 0 0.86603 0.5 -1. 2. 0.5 0.86603 -0.5 2. -0.5 0.86603 -0.5 0 -0.86603 0.5 -1. 2. -1. 0 -0.5 2. -0.5 -0.86603 -0.5 0 0 -1. -1. 2. 0.5 -0.86603 -0.5 2. 0 0 -2. 0 0.86603 0.5 -1. 2. 0 0 -2. 0 -0.86603 0.5 -1. 2. 0 0 -2. 0 0 -1. -1. 2. 0 0 2. -1. 1. 0 0.5 -1. 0.5 0.86603 0.5 -1. -0.5 0.86603 0.5 -1. -1. 0 0.5 -1. -0.5 -0.86603 0.5 -1. 0.5 -0.86603 0.5 -1. 0.86603 0.5 -1. -1. -0.86603 0.5 -1. -1. 0 -1. -1. -1. 0 0 -2. -3. 1. 0 -0.5 -3. 0.5 0.86603 -0.5 -3. -0.5 0.86603 -0.5 -3. -1. 0 -0.5 -3. -0.5 -0.86603 -0.5 -3. 0.5 -0.86603 -0.5 -3. 0.86603 0.5 1. -3. -0.86603 0.5 1. -3. 0 -1. 1. -3.