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.
QL-P3.QL-P30.QL-P20 is transformed into 5L-o-P1.5L-n-P4.XX preserving distance ratios
(XX= 5L-o-P1.5L-n-P4 (3:-1))
This method is used for nL-n-P4, nL-o-P1, nL-o-L2.
Examples:
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3L-point
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4L-point
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5L-point
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6L-point
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3L-n-P5
=X(5)
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4L-n-P4/P10
= QL-P2
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None
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---
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---
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4L-e-P1
= QL-P3
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5L-o-P1 (per definition)
(lies on 5L-o-L2)
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None
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---
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= 4L-e-P1.4L-n-P5 (3:-1)
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5L-o-P1.5L-n-P4 (3:-1)
(lies on 5L-o-L2)
5L-n-P4.5L-n-P10 (-5:6)
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None
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---
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4L-n-P5
= QL-P30
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5L-n-P4 (per definition)
(lies on 5L-o-L2)
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None
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---
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5L-n-P5
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6L-n-P4 (per definition)
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None
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||
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Other known 5L-points
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None
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QL-P3.QL-P30.QL-P20 is transformed into 5L-o-P1.5L-n-P4.XX preserving distance ratios
(XX= 5L-o-P1.5L-n-P4 (3:-1))