### Newton's Construction of Conics

What if applet does not run? |

### Conics

- Conic Sections
- Conic Sections as Loci of Points
- Construction of Conics from Pascal's Theorem
- Cut the Cone
- Dynamic construction of ellipse and other curves
- Joachimsthal's Notations
- MacLaurin's Construction of Conics
- Newton's Construction of Conics
- Parallel Chords in Conics
- Theorem of Three Tangents to a Conic
- Three Parabolas with Common Directrix
- Butterflies in a Pencil of Conics
- Ellipse
- Parabola
- G. Salmon,
*Treatise on Conic Sections*, Chelsea Pub, 6e, 1960, p. 300 - Conic Sections
- Conic Sections as Loci of Points
- Construction of Conics from Pascal's Theorem
- Cut the Cone
- Dynamic construction of ellipse and other curves
- Joachimsthal's Notations
- MacLaurin's Construction of Conics
- Newton's Construction of Conics
- Parallel Chords in Conics
- Theorem of Three Tangents to a Conic
- Three Parabolas with Common Directrix
- Butterflies in a Pencil of Conics
- Ellipse
- Parabola
|Activities| |Contact| |Front page| |Contents| |Geometry|

Copyright © 1996-2018 Alexander Bogomolny

|Activities| |Contact| |Front page| |Contents| |Geometry|

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

### Conics

- G. Salmon,

63407096 |