QL-L4: Morley Line


The Morley Line is the line through QL-P2 (Morley Point) and QL-P3 (Kantor-Hervey Point).
 
QL-L4-Morley Line-00

Coefficients: 
1st CT-coefficient:
+a4 (l - m) (l - n) (m - n) (l m + l n - m n)
+b4 (l - m) (l - n) (m - n) l m
+c4 (l - m) (l - n) (m - n) l n
+b2 c2 (n – m) U0
+a2 c2 ( l – n) (U0 – U1)
+a2 b2 (m – l) (U0 – U2)
where:
U0 = l (l2 m + l2 n - 4 l m n + m2 n + m n2)
U1 = (l - m) (l + m - 2 n) (l m + l n - m n)
U2 = (l – n) (l + n - 2 m) (l m + l n - m n)
1st DT-coefficient:
            l2 (m2-n2)3 SA2 - m2 (l2-n2)3 SB2 + n2 (l2-m2)3 SC2
   + (l2-m2) (l2-n2) (m2-n2) (2 l2 S2 - l2 SB SC - m2 SC SA- n2 SA SB)

Properties:

  • QL-L4 is parallel to QL-L1 (Newton Line).
  • QL-L4 is perpendicular to QL-L2 (Steiner Line) and QL-L3 (QL-Pedal Line).
  • QL-L4 is parallel to the Trilinear Polar of QL-P24 (note Eckart Schmidt).
  • The 3 QL-versions of QA-P15 lie on QL-L4 (Eckart Schmidt, August 24, 2012).

 

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