Parabola studied by Menaechmus who was a disciple of Platoand Eudoxus. He attempted to duplicate the cube, namely to findthe cube that has twice the volume of a cube is given. Therefore he tried to solve x ^ 3 = 2 by the method of geometry.
Even the method of geometric construction of a ruler andcompass can not solve this (but Menaechmus did not know this).Menaechmus solved it by finding the intersection of twoparabolas x ^ 2 = y and y ^ 2 = 2 x
Euclid wrote about the dish and it was given its present name byApollonius. The focus of the parabola and the directory is offered by Pappus.
Pascal argued parabola as projections of circles and Galileoshowed that projectiles follow parabolic paths.
Gregory and Newton put forward as the property of a parabolathat bring parallel rays of light to focus.
Parabola with a pedal point as a pedal point is cissoid. Pedal of the parabola with focus as pedal point is a straight line. With afoot pedal directrix as it is right to point strophoid (an obliquestrophoid to himpunaniap another point of the directrix). Pedalwhen the pedal curve of the image focal point in the directrix isTrisectrix of Maclaurin.
Evolute Neile's parabola is a parabola. From that point on theevolute three normals can be drawn to a parabola, while only onenormal can be drawn to a parabola from a point below theevolute. If the focus of the parabola is taken as a center ofinversion, invert dish to cardioid. If the node is taken as a center of inversion parabolic, reverse parabolas keCissoid of Diocles.The caustic of a parabola with a beam perpendicular to the axis of the parabola is Tschirnhaus's Cubic.
sources:
http://www-history.mcs.st-and.ac.uk/Curves/Parabola.html
http://xsquared.wikispaces.com/Parabola+History
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