QG-5: List of QG-Crosspoints
In next list sets of 3 lines are mentioned that concur.
All lines with points in the range QG-P1 – QG-P14, QA-P1 – QA-P21 and QL-P1 – QL-P23 have been taken into account.
Lines are defined by 2 points on it with lowest serial number.
There are regularly recurring crossing lines with these Crosspoints. This is an indication for the occurrence of Perspective Fields (see QG-PF1).
When the intersection points have fixed ratios of the distances to the defining points on the defining lines, then they are mentioned. There are many of them.
When there are no fixed ratios this is indicated by the remark “x : y”.
For point P on line P1.P2 the ratio d1 : d2 means that d(P,P1) : d(P,P2) = d1 : d2, where:
- d1 is positive when P is positioned wrt P1 at the same side of the line as P2. If not then d1 is negative.
- d2 is positive when P is positioned wrt P2 at the same side of the line as P1. If not then d1 is negative.
| Set of intersecting lines | Ratios | Comment |
|---|---|---|
| QG-P1.QG-P2 ^ QG-P10.QA-P14 ^ QG-P13.QA-P2 | x:y x:y x:y | |
| QG-P1.QG-P2 ^ QG-P12.QG-P14 ^ QL-P18.QL-P23 | x:y x:y x:y | point on QA-Co1 |
| QG-P1.QG-P4 ^ QG-P5.QG-P11 ^ QG-P6.QG-P9 | 3:2 4:1 4:1 | (simple coordinates) |
| QG-P1.QG-P5 ^ QG-P7.QG-P10 ^ QG-P11.QA-P1 | Infinity Point | |
| QG-P1.QG-P6 ^ QG-P5.QG-P8 ^ QG-P11.QA-P1 | 1:3 3:-1 2:-1 | point on QA-Co1 |
| QG-P1.QG-P6 ^ QG-P7.QG-P9 ^ QL-P2.QL-P7 | Infinity Point Steiner Line | |
| QG-P1.QG-P7 ^ QG-P4.QG-P10 ^ QG-P6.QA-P1 | 4:1 2:3 1:4 | |
| QG-P1.QG-P7 ^ QG-P5.QG-P10 ^ QG-P6.QG-P9 | 2:1 2:1 2:1 | (Centroid QG-P7/P9/P10), (Centroid QG-P1/P5/P6) |
| QG-P1.QG-P14 ^ QG-P2.QG-P3 ^ QG-P6.QL-P18 | Infinity Point (simple coordinates) | |
| QG-P1.QA-P5 ^ QG-P2.QA-P1 ^ QG-P8.QA-P20 | 1:1 2:1 -1:3 | point on Newton Line |
| QG-P1.QA-P5 ^ QG-P2.QA-P20 ^ QG-P4.QA-P10 | Infinity Point | |
| QG-P1.QA-P17 ^ QG-P4.QG-P12 ^ QG-P14.QA-P5 | x:y -2:3 x:y | |
| QG-P1.QA-P19 ^ QG-P2.QG-P3 ^ QG-P14.QA-P5 | x:y x:y x:y | point on QA-Cu4 |
| QG-P1.QA-P19 ^ QG-P2.QG-P12 ^ QG-P14.QA-P10 | x:y x:y 3:1 | |
| QG-P1.QA-P20 ^ QG-P2.QG-P3 ^ QG-P12.QA-P18 | x:y x:y x:y | |
| QG-P1.QA-P20 ^ QG-P2.QG-P12 ^ QG-P8.QA-P10 | point on QA-Cu2, Infinity Point, Newton Line | |
| QG-P1.QL-P9 ^ QG-P3.QL-P10 ^ QG-P5.QL-P17 | 2:-1 -1:2 x:y | point on QL-Ci1 |
| QG-P1.QL-P10 ^ QG-P3.QL-P9 ^ QG-P7.QL-P2 | Infinity Point (simple coordinates) | |
| QG-P1.QL-P12 ^ QG-P2.QG-P4 ^ QG-P3.QL-P18 | 6:-1 3: 2 3:2 | |
| QG-P2.QG-P4 ^ QG-P8.QA-P10 ^ QL-P12.QA-P25 | -1:2 3:-2 -3:4 | Only (Quasi-)Centroids involved |
| QG-P2.QG-P5 ^ QG-P7.QA-P5 ^ QG-P9.QA-P10 | -1:2 -1:2 3:-2 | |
| QG-P2.QG-P6 ^ QG-P5.QA-P5 ^ QG-P10.QA-P10 | -1:2 -1:2 3:-2 | |
| QG-P2.QG-P7 ^ QG-P5.QA-P5 ^ QG-P10.QA-P20 | Infinity Point | |
| QG-P3.QG-P7 ^ QG-P5.QL-P9 ^ QG-P10.QL-P11 | x:y x:y x:y | |
| QG-P4.QG-P9 ^ QG-P5.QG-P11 ^ QG-P6.QA-P1 | 4:3 4:3 8:-1 | |
| QG-P6.QG-P9 ^ QG-P7.QG-P8 ^ QG-P11.QA-P1 | 3:1 3:1 1:1 | |
| QG-P6.QL-P9 ^ QG-P7.QL-P2 ^ QG-P10.QL-P11 | x:y x:y x:y |
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