query: Applying Playfair's axiom when the point does not lie on the given line
positive_passages.docid: 152685
positive_passages.text: Parallel postulate from Playfair's axiom
negative_passages.docid: 119978
negative_passages.text: Equidistant points on a polyline
negative_passages.docid: 153103
negative_passages.text: How to tell whether a point is to the right or left side of a line
negative_passages.docid: 38917
negative_passages.text: If point is zero-dimensional, how can it form a finite one dimensional line?
negative_passages.docid: 153767
negative_passages.text: Singular points and tangent lines
negative_passages.docid: 51393
negative_passages.text: Moving points onto lines (~neighborhood)
negative_passages.docid: 21661
negative_passages.text: How do I test for a player at specific coordinates?
negative_passages.docid: 121361
negative_passages.text: Showing that $\lnot Q \lor (\lnot Q \land R) = \lnot Q$ without a truth table
negative_passages.docid: 26356
negative_passages.text: Avoiding a spline dip
negative_passages.docid: 62260
negative_passages.text: Rational Coordinates with two intersecting lines
negative_passages.docid: 85274
negative_passages.text: Point reflection over a line
negative_passages.docid: 23219
negative_passages.text: The plane minus $n$ points deformation retracts onto...
negative_passages.docid: 57473
negative_passages.text: how to find a point in the path of a line
negative_passages.docid: 123208
negative_passages.text: Show that the Sorgenfrey line does not have a countable basis.
negative_passages.docid: 12449
negative_passages.text: How to formulate continuum hypothesis without the axiom of choice?
negative_passages.docid: 135957
negative_passages.text: Why in an inconsistent axiom system every statement is true? (For Dummies)
negative_passages.docid: 150707
negative_passages.text: Prove the statement 'World is not flat'