Editing Parabola (section)

== History ==
[[File:Leonardo parabolic compass.JPG|thumb|180px|Parabolic compass designed by [[Leonardo da Vinci]]]]
The earliest known work on conic sections was by [[Menaechmus]] in the 4th century BC. He discovered a way to solve the problem of [[doubling the cube]] using parabolas. (The solution, however, does not meet the requirements of [[compass-and-straightedge construction]].) The area enclosed by a parabola and a line segment, the so-called "parabola segment", was computed by [[Archimedes]] by the [[method of exhaustion]] in the 3rd century BC, in his ''[[The Quadrature of the Parabola]]''. The name "parabola" is due to [[Apollonius of Perga|Apollonius]], who discovered many properties of conic sections. It means "application", referring to "application of areas" concept, that has a connection with this curve, as Apollonius had proved.<ref>{{cite web |url=http://www.maa.org/press/periodicals/convergence/can-you-really-derive-conic-formulae-from-a-cone-deriving-the-symptom-of-the-parabola |title=Can You Really Derive Conic Formulae from a Cone? – Deriving the Symptom of the Parabola – Mathematical Association of America |access-date=30 September 2016}}</ref> The focus–directrix property of the parabola and other conic sections was mentioned in the works of [[Pappus of Alexandria|Pappus]].

[[Galileo Galilei|Galileo]] showed that the path of a projectile follows a parabola, a consequence of uniform acceleration due to gravity.

The idea that a [[parabolic reflector]] could produce an image was already well known before the invention of the [[reflecting telescope]].<ref>{{cite book
|title=Reflecting Telescope Optics: Basic design theory and its historical development
|edition=2
|first1=Ray N.
|last1=Wilson
|publisher=Springer
|year=2004
|isbn=3-540-40106-7
|page=3
|url=https://books.google.com/books?id=PuN7l2A2uzQC}} [https://books.google.com/books?id=PuN7l2A2uzQC&pg=PA3 Extract of page 3].
</ref> Designs were proposed in the early to mid-17th century by many [[mathematician]]s, including [[René Descartes]], [[Marin Mersenne]],<ref>''Stargazer'', [https://books.google.com/books?id=2LZZginzib4C&pg=PA115&dq=mersenne+zucchi+parallel#PPA115,M1 p.&nbsp;115].</ref> and [[James Gregory (mathematician)|James Gregory]].<ref>''Stargazer'', [https://books.google.com/books?id=2LZZginzib4C&pg=PA132&dq=Gregory++telescope+French+convex pp.&nbsp;123, 132].</ref> When [[Isaac Newton]] built the [[Newton's reflector|first reflecting telescope]] in 1668, he skipped using a parabolic mirror because of the difficulty of fabrication, opting for a [[spherical mirror]]. Parabolic mirrors are used in most modern reflecting telescopes and in [[satellite dish]]es and [[radar]] receivers.<ref>{{cite web
|url        = http://farside.ph.utexas.edu/teaching/316/lectures/node136.html
|title      = Spherical Mirrors
|first      = Richard
|last       = Fitzpatrick
|date       = July 14, 2007
|work       = Electromagnetism and Optics, lectures
|publisher  = [[University of Texas at Austin]]
|at         = Paraxial Optics
|access-date = October 5, 2011}}</ref>
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