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Two soloists in the universe--independent stars blinking light years apart--unexpectedly intersected paths across constellations.
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Sometimes he withdraws from the fray and engages in private discourse — as in the passage, at the end of the first movement of the Ninth, where a flute and a horn meander along fitfully intersecting paths, enacting the musical equivalent of a Beckett dialogue.
Similarly, neither path can intersect the normal path from a to y. If, for example, the path from q1 to x1 intersected the path from a to y, then by following the normal paths backwards we would have that either q1 lies on the path from a to y or else a lies on the path from q1 to x1.
It is nature bordered by high-rises, intersected by paths and roadways, basking under artificial light at night.
All non self-intersecting paths are those paths that do not contain loops (self-intersections).
So we've had intersecting paths.
As we twisted around hillocks and into dense woods, the intersecting paths quickly became a maze.
But given their intersecting paths, one wonders: Had Brown hired Jackson 24 years ago, would Jackson have ever coached Jordan?
Within hours of the assassination, Zapruder had given copies of his movie to two men, thus setting it off on divergent but intersecting paths.
For instance, one set of puzzles late in the game requires you to light the intersecting paths in a forest using as few lamps as possible.
In "MetaMaus," Spiegelman employs prose, drawings, documents, and photographs to trace the intersecting paths of history, family, and comics which led to the creation, twenty-five yeago agof of "Maus," his Pulitzer Prize-winning comic book about the Holocaust.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com