nL-n-Luc1 nL-Common Point of Perpendiculars On Omitted Line


From an n-Line n different (n-1)-Lines can be constructed by omitting one line.

Through the (n-1)L-versions of some central point perpendiculars are drawn to the omitted line. In special cases they will concur and so a new central nL-point is created

This method is used for nL-n-P4, nL-o-P1, nL-o-L2.

Examples
3L-point 4L-point 5L-point 6L-point higher

3L-n-P5

=X(5)

4L-n-P4/P10

= QL-P2

None

4L-e-P1

= QL-P3

5L-o-P1 (per definition)

(lies on 5L-o-L2)

None

QL-P20

= 4L-e-P1.4L-n-P5 (3:-1)

= QL-P3.QL-P30 (3:-1)

5L-o-P1.5L-n-P4 (3:-1)

(lies on 5L-o-L2)

5L-n-P4.5L-n-P10 (-5:6)

None

4L-n-P5

= QL-P30

5L-n-P4 (per definition)

(lies on 5L-o-L2)

None

5L-n-P5

6L-n-P4 (per definition) None

Other known 5L-points

None

Remarks:

QL-P3.QL-P30.QL-P20 is transformed into 5L-o-P1.5L-n-P4.XX preserving distance ratios,

where XX= 5L-o-P1.5L-n-P4 (3:-1).




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