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Lineas were one-dimensional, geometrical creatures which existed in the Euclidean Plane, resembling straight lines.
Nature
Lineas appeared as straight lines of various lengths. They moved about “like a worm or snake”.
Unlike the wild Ambagesques, Lineas were tame, well-mannered creatures with a somewhat sluggish disposition, and were popular pets among Geometrons. Walking one's Linea required no leash, as “the end of the Linea itself [could] be held, while the front move[d] along”. (PROSE: The Euclidean Plane)