nL-o-L2: nL-Morley’s Line of Orthocenters

Morley describes this line in his paper: Orthocentric properties of the Plane n-line (Ref-49).

It is the line connecting nL-o-P1 (Morley’s 1st Orthocenter) and nL-n-P4 (Morley’s 2nd Orthocenter).

Let X be some point on (n-1)L-e-L2 with fixed ratio wrt (n-1)L-n-P5 and (n-1)L-e-P1. Then nL-o-L2 is the locus of the common intersection point of the perpendiculars through the n lower level versions of X to the omitted line (Level-up Construction nL-n-Luc1) preserving distance ratios.

In this way (n-1)L-e-P1 is transformed into nL-o-P1 and (n-1)L-n-P5 is transformed into nL-n-P4.

Correspondence with ETC/EQF

• When n=3, then 3L-o-L2 = X(4).X(4) = undefined line.

Properties

• These points lie on nL-o-L2 (all Orthocenters indeed):
• nL-o-P1 (nL-Morley’s 1st Orthocenter
• nL-n-P4 (nL-Morley’s 2nd Orthocenter)
• nL-n-P10 (nL-MVP Orthocenter)

Estimated human page views: 256