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[[File:Parabola.svg|right|thumb|A [[parabola]], one of the simplest curves, after (straight) lines]]
Intuitively, a curve may be thought of as the trace left by a moving [[point (geometry)|point]]. This is the definition that appeared more than 2000 years ago in [[Euclid's Elements|Euclid's ''Elements'']]: "The [curved] line{{efn|In current mathematical usage, a line is straight. Previously lines could be either curved or straight.}} is […] the first species of quantity, which has only one dimension, namely length, without any width nor depth, and is nothing else than the flow or run of the point which […] will leave from its imaginary moving some vestige in length, exempt of any width."<ref>In (rather old) French: "La ligne est la première espece de quantité, laquelle a tant seulement une dimension à sçavoir longitude, sans aucune latitude ni profondité, & n'est autre chose que le flux ou coulement du poinct, lequel […] laissera de son mouvement imaginaire quelque vestige en long, exempt de toute latitude." Pages 7 and 8 of ''Les quinze livres des éléments géométriques d'Euclide Megarien, traduits de Grec en François, & augmentez de plusieurs figures & demonstrations, avec la corrections des erreurs commises és autres traductions'', by Pierre Mardele, Lyon, MDCXLV (1645).</ref>
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