Editing Hyperbola (section)

==Etymology and history==
The word "hyperbola" derives from the [[Greek language|Greek]] {{lang|grc|ὑπερβολή}}, meaning "over-thrown" or "excessive", from which the English term [[hyperbole]] also derives. Hyperbolae were discovered by [[Menaechmus]] in his investigations of the problem of [[doubling the cube]], but were then called sections of obtuse cones.<ref>{{citation |title=Apollonius of Perga: Treatise on Conic Sections with Introductions Including an Essay on Earlier History on the Subject |last=Heath |first=Sir Thomas Little |publisher=Cambridge University Press |year=1896 |contribution=Chapter I. The discovery of conic sections. Menaechmus |pages=xvii–xxx |url=https://books.google.com/books?id=B0k0AQAAMAAJ&pg=PR17}}.</ref> The term hyperbola is believed to have been coined by [[Apollonius of Perga]] ({{circa|262|190 BC}}) in his definitive work on the [[conic section]]s, the ''Conics''.<ref>{{citation |title=A History of Mathematics |last1=Boyer |first1=Carl B. |last2=Merzbach |first2=Uta C. |author2-link=Uta Merzbach |publisher=Wiley |year=2011 |isbn=9780470630563 |page=73 |url=https://books.google.com/books?id=bR9HAAAAQBAJ&pg=RA2-PT73 |quote=It was Apollonius (possibly following up a suggestion of Archimedes) who introduced the names "ellipse" and "hyperbola" in connection with these curves.}}</ref>
The names of the other two general conic sections, the [[ellipse]] and the [[parabola]], derive from the corresponding Greek words for "deficient" and "applied"; all three names are borrowed from earlier Pythagorean terminology which referred to a comparison of the side of rectangles of fixed area with a given line segment. The rectangle could be "applied" to the segment (meaning, have an equal length), be shorter than the segment or exceed the segment.<ref>{{citation |pages=30–31 |last=Eves |first=Howard |title=A Survey of Geometry (Vol. One) |year=1963 |publisher=Allyn and Bacon}}</ref>