Since Morley described the equivalents of a circumcenter (nL-n-P3), an orthocenter (nL-n-P4) and a Nine-point-center (nL-n-P5) in a general n-Line which also happen to be collinear it is evident that the connecting line of these points will be Morley’s Eulerline here coded nL-n-L1.
For the allocation of the centroid, circumcenter, orthocenter and nine-point center on the nL-Morley’s Eulerline see nL-n-P2.
Next figure gives an example of nL-n-L1 in a 5-Line.
For the allocation of the centroid, circumcenter, orthocenter and nine-point center on the nL-Morley’s Eulerline see nL-n-P2.
Next figure gives an example of nL-n-L1 in a 5-Line.
Correspondence with ETC/EQF:
When n=3, then nL-n-L1 = Triangle Eulerline X(3).X(4), with
• 3L-n-P2 = Centroid X(2)
• 3L-n-P3 = Circumcenter X(3)
• 3L-n-P4 = Orthocenter X(4)
• 3L-n-P5 = Nine-point Center X(5)
When n=3, then nL-n-L1 = Triangle Eulerline X(3).X(4), with
• 3L-n-P2 = Centroid X(2)
• 3L-n-P3 = Circumcenter X(3)
• 3L-n-P4 = Orthocenter X(4)
• 3L-n-P5 = Nine-point Center X(5)
When n=4, then nL-n-L1 = Quadrilateral Eulerline QL-P2.QL-P4, with
• 4L-n-P2 = Centroid-equivalent QL-P22
• 4L-n-P3 = Circumcenter-equivalent QL-P4
• 4L-n-P4 = Orthocenter-equivalent QL-P2
• 4L-n-P5 = Nine-point Center-equivalent QL-P30
• 4L-n-P2 = Centroid-equivalent QL-P22
• 4L-n-P3 = Circumcenter-equivalent QL-P4
• 4L-n-P4 = Orthocenter-equivalent QL-P2
• 4L-n-P5 = Nine-point Center-equivalent QL-P30