Given a pentagon P1P2P3P4P5.
We denote the intersection of P1P3 and P2P5 by P12.
Similarly P23, P34, P45 and P51 are defined.
The 5 Newton lines of P1P12P2P4, P2P23P3P5, P3P34P4P1, P4P45P5P2 and P5P51P1P3 have a common point 5G-s-P1.
See Ref-34, Seiichi Kirikami, QFG#760.
We denote the intersection of P1P3 and P2P5 by P12.
Similarly P23, P34, P45 and P51 are defined.
The 5 Newton lines of P1P12P2P4, P2P23P3P5, P3P34P4P1, P4P45P5P2 and P5P51P1P3 have a common point 5G-s-P1.
See Ref-34, Seiichi Kirikami, QFG#760.
There is another way to construct this point:
Given a pentagon P1P2P3P4P5.
We denote the intersection of P1P3 and P2P5 by P12.
Similarly P23, P34, P45 and P51 are defined.
We denote the midpoints of PiPi+1 by Mi+3
We denote the midpoints of PiPi+2 by mi. The lines Mimi concur in 5G-s-P1.
See Ref-34, Seiichi Kirikami, QFG#726.
Given a pentagon P1P2P3P4P5.
We denote the intersection of P1P3 and P2P5 by P12.
Similarly P23, P34, P45 and P51 are defined.
We denote the midpoints of PiPi+1 by Mi+3
We denote the midpoints of PiPi+2 by mi. The lines Mimi concur in 5G-s-P1.
See Ref-34, Seiichi Kirikami, QFG#726.
Note that the Newton Line in the left figure coincides with the lines Mimi in the right figure.