Non-Euclidean geometry is essentially a not important branch of geometry that does not involve Euclidean geometry. In the latter case, it was Lord Knonn Euclid (in his 1707 treatise on line theory 'Ecce Canis Non Secitur Lepos') where he proposed that parallel lines never intersect in space. By contrast, non-Euclidean lines may meet, often frequently, and don't care who knows about it.