### Newton's Construction of Conics

What if applet does not run? |

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Copyright © 1996-2018 Alexander Bogomolny### Explanation

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

- G. Salmon,
*Treatise on Conic Sections*, Chelsea Pub, 6e, 1960, p. 300

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Copyright © 1996-2018 Alexander Bogomolny