Newton's Construction of Conics


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Explanation


This applet requires Sun's Java VM 2 which your browser may perceive as a popup. Which it is not. If you want to see the applet work, visit Sun's website at https://www.java.com/en/download/index.jsp, download and install Java VM and enjoy the applet.


What if applet does not run?

Two pencils are called homographic if their lines are in a 1-1 correspondence that preserves the cross-ratio. The intersections of the corresponding lines of two homographic pencils form a conic that passes through the two pencil vertices. (There is a restriction that the line through the vertices does not correspond to itself.) One way to obtain homographic pencils is to move a point on a conic (a straight line, in particular). The point is connected to two fixed points - vertices of two pencils. The corresponding lines of the two pencils are inclined at fixed angles to the two "generating" lines that join the vertices to the variable point.

References

  1. G. Salmon, Treatise on Conic Sections, Chelsea Pub, 6e, 1960, p. 300
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Copyright © 1996-2018 Alexander Bogomolny
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