# OpenMath Content Dictionary: plangeo6

Canonical URL:
http://www.openmath.org/cd/plangeo6.ocd
CD Base:
http://www.openmath.org/cd
CD File:
plangeo6.ocd
CD as XML Encoded OpenMath:
plangeo6.omcd
Defines:
are_on_conic, conic
Date:
2004-06-01
Version:
0 (Revision 4)
Review Date:
2006-06-01
Status:
experimental

This CD defines symbols for planar Euclidean geometry related to conics. amc: 18 March 2004 added are_on_conic

## conic

Description:

The symbol represents a conic. The conic may be subject to constraints.

Example:
The conic G, incident to A,B,C,D and E is given by
$\mathrm{conic}\left(G,\mathrm{incident}\left(G,A\right),\mathrm{incident}\left(G,B\right),\mathrm{incident}\left(G,C\right),\mathrm{incident}\left(G,D\right),\mathrm{incident}\left(G,E\right)\right)$
Signatures:
sts

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## are_on_conic

Description:

The symbol is a boolean n-ary function. Its arguments should be points. When applied to a sequence of points, its evaluated to true if and only if there is a conic on which all arguments lie.

Commented Mathematical property (CMP):
If G is the conic determined by A,B,C,D, and E, whereas F is a point incident with G, then A,B,C,D, E, and F are on a conic.
Formal Mathematical property (FMP):
$F\in \mathrm{conic}\left(G,\mathrm{incident}\left(G,A\right),\mathrm{incident}\left(G,B\right),\mathrm{incident}\left(G,C\right),\mathrm{incident}\left(G,D\right),\mathrm{incident}\left(G,E\right)\right)⇒\mathrm{are_on_conic}\left(A,B,C,D,E,F\right)$
Signatures:
sts

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