Unsurprisingly, an ellipse (meaning "oval") and ellipsis (the three-dot punctuation...) come from the same root. The plural of both is ellipses, anyway. They come from the Latin word ellipsis, which meant "omission" (the first because of some math-y thing to do with the base of a cone and the second because an ellipsis is, after all, an omission, implying something else). Ellipsis is from Ancient Greek elleipsis, which had about the same meaning, from elleipein, which literally translates to "to leave out". Here we can eliminate the prefix en, meaning "in", and we're left with the verb lepein, meaning "to leave". Most likely, lepein can be reconstructed to the Proto-Indo-European word leikw, also with a definition of "leave". So both a form of punctuation and a shape are leaving a lot out. Surprisingly, ellipse is used in literature far more than ellipsis or ellipses.
Adam Aleksic, a leading contender for valedictorian of his high school, is a 208-month-old boy with disturbing interests in etymology, vexillology, geography, and law. Adam would like to one day visit Tajikistan and just won an essay contest on linguistics!
The Etymology Nerd