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ThreeDgeo1.omcd
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<OMOBJ xmlns:om="http://www.openmath.org/OpenMath"
xmlns="http://www.openmath.org/OpenMath">
<OMA>
<OMS cd="meta" name="CD"/>
<OMA>
<OMS cd="meta" name="CDComment"/>
<OMSTR>This document is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. The copyright holder grants you permission to redistribute this document freely as a verbatim copy. Furthermore, the copyright holder permits you to develop any derived work from this document provided that the following conditions are met. a) The derived work acknowledges the fact that it is derived from this document, and maintains a prominent reference in the work to the original source. b) The fact that the derived work is not the original OpenMath document is stated prominently in the derived work. Moreover if both this document and the derived work are Content Dictionaries then the derived work must include a different CDName element, chosen so that it cannot be confused with any works adopted by the OpenMath Society. In particular, if there is a Content Dictionary Group whose name is, for example, `math' containing Content Dictionaries named `math1', `math2' etc., then you should not name a derived Content Dictionary `mathN' where N is an integer. However you are free to name it `private_mathN' or some such. This is because the names `mathN' may be used by the OpenMath Society for future extensions. c) The derived work is distributed under terms that allow the compilation of derived works, but keep paragraphs a) and b) intact. The simplest way to do this is to distribute the derived work under the OpenMath license, but this is not a requirement. If you have questions about this license please contact the OpenMath society at http://www.openmath.org.</OMSTR>
</OMA>
<OMA>
<OMS cd="meta" name="CDName"/>
<OMSTR>ThreeDgeo1</OMSTR>
</OMA>
<OMA>
<OMS cd="meta" name="CDURL"/>
<OMSTR>http://nash.sip.ucm.es/LAD-3D/3DgeoCDs/ThreeDgeo1.ocd</OMSTR>
</OMA>
<OMA>
<OMS cd="meta" name="CDReviewDate"/>
<OMSTR>2017-12-31</OMSTR>
</OMA>
<OMA>
<OMS cd="meta" name="CDStatus"/>
<OMSTR>experimental</OMSTR>
</OMA>
<OMA>
<OMS cd="meta" name="CDDate"/>
<OMSTR>2008-01-21</OMSTR>
</OMA>
<OMA>
<OMS cd="meta" name="CDVersion"/>
<OMSTR>0</OMSTR>
</OMA>
<OMA>
<OMS cd="meta" name="CDRevision"/>
<OMSTR>3</OMSTR>
</OMA>
<OMA>
<OMS cd="meta" name="CDComment"/>
<OMSTR>Author: Jesús Escribano</OMSTR>
</OMA>
<OMA>
<OMS cd="meta" name="Description"/>
<OMSTR>This CD defines symbols for 3-dimensional Euclidean geometry</OMSTR>
</OMA>
<OMA>
<OMS cd="meta" name="CDDefinition"/>
<OMA>
<OMS cd="meta" name="Name"/>
<OMSTR>point</OMSTR>
</OMA>
<OMA>
<OMS cd="meta" name="Description"/>
<OMSTR>The symbol is used to indicate a point of 3-dimensional Euclidean geometry by a variable. The point may (but need not) be subject to constraints. The symbol takes the variable as the first argument and the constraints as further arguments.</OMSTR>
</OMA>
<OMA>
<OMS cd="meta" name="Example"/>
<OMSTR>Given two lines l and m, a point A on l and m is defined by:</OMSTR>
<OMA>
<OMS cd="ThreeDgeo1" name="point"/>
<OMV name="A"/>
<OMA>
<OMS cd="ThreeDgeo2" name="incident"/>
<OMV name="A"/>
<OMV name="l"/>
</OMA>
<OMA>
<OMS cd="ThreeDgeo2" name="incident"/>
<OMV name="A"/>
<OMV name="m"/>
</OMA>
</OMA>
</OMA>
</OMA>
<OMA>
<OMS cd="meta" name="CDDefinition"/>
<OMA>
<OMS cd="meta" name="Name"/>
<OMSTR>line</OMSTR>
</OMA>
<OMA>
<OMS cd="meta" name="Description"/>
<OMSTR>The symbol is used to indicate a line of 3-dimensional Euclidean geometry by a variable. The line may (but need not) be subject to constraints. The symbol takes the variable as the first argument and the constraints as further arguments.</OMSTR>
</OMA>
<OMA>
<OMS cd="meta" name="Example"/>
<OMSTR>Given points A and B in 3-dimensional space, a line l through A and B is defined by:</OMSTR>
<OMA>
<OMS cd="ThreeDgeo1" name="line"/>
<OMV name="l"/>
<OMA>
<OMS cd="ThreeDgeo2" name="incident"/>
<OMV name="A"/>
<OMV name="l"/>
</OMA>
<OMA>
<OMS cd="ThreeDgeo2" name="incident"/>
<OMV name="B"/>
<OMV name="l"/>
</OMA>
</OMA>
</OMA>
</OMA>
<OMA>
<OMS cd="meta" name="CDDefinition"/>
<OMA>
<OMS cd="meta" name="Name"/>
<OMSTR>segment</OMSTR>
</OMA>
<OMA>
<OMS cd="meta" name="Description"/>
<OMSTR>The symbol is used to indicate a segment of a line in 3-dimensional Euclidean geometry by a variable. The segment is contained in the affine part of the line. The symbol takes the variable as the first argument and the endpoints as second and third arguments.</OMSTR>
</OMA>
<OMA>
<OMS cd="meta" name="Example"/>
<OMSTR>The segment s with endpoints A and B is given by</OMSTR>
<OMA>
<OMS cd="ThreeDgeo1" name="segment"/>
<OMV name="s"/>
<OMV name="A"/>
<OMV name="B"/>
</OMA>
</OMA>
</OMA>
<OMA>
<OMS cd="meta" name="CDDefinition"/>
<OMA>
<OMS cd="meta" name="Name"/>
<OMSTR>endpoints</OMSTR>
</OMA>
<OMA>
<OMS cd="meta" name="Description"/>
<OMSTR>The symbol is used to indicate the set of the two endpoints of a segment in 3-dimensional Euclidean geometry by a variable. The symbol takes the variable as the first argument and the segment as second argument.</OMSTR>
</OMA>
<OMA>
<OMS cd="meta" name="Example"/>
<OMSTR>The set E of the two endpoints of a segment s is given by:</OMSTR>
<OMA>
<OMS cd="ThreeDgeo1" name="endpoints"/>
<OMV name="E"/>
<OMV name="s"/>
</OMA>
</OMA>
</OMA>
<OMA>
<OMS cd="meta" name="CDDefinition"/>
<OMA>
<OMS cd="meta" name="Name"/>
<OMSTR>midpoint</OMSTR>
</OMA>
<OMA>
<OMS cd="meta" name="Description"/>
<OMSTR>The symbol is used to indicate the midpoint of a segment in 3-dimensional Euclidean geometry by a variable. The symbol takes the variable as the first argument and the segment as second argument.</OMSTR>
</OMA>
<OMA>
<OMS cd="meta" name="Example"/>
<OMSTR>The midpoint M of the segment s is given by</OMSTR>
<OMA>
<OMS cd="ThreeDgeo1" name="midpoint"/>
<OMV name="M"/>
<OMV name="s"/>
</OMA>
</OMA>
</OMA>
<OMA>
<OMS cd="meta" name="CDDefinition"/>
<OMA>
<OMS cd="meta" name="Name"/>
<OMSTR>plane</OMSTR>
</OMA>
<OMA>
<OMS cd="meta" name="Description"/>
<OMSTR>The symbol is used to indicate a plane in 3-dimensional Euclidean geometry by a variable. The plane may (but need not) be subject to constraints. The symbol takes the variable as the first argument and the constraints as further arguments.</OMSTR>
</OMA>
<OMA>
<OMS cd="meta" name="Example"/>
<OMSTR>Given points A, B and C in 3-dimensional space, a plane p through A, B and C is defined by:</OMSTR>
<OMA>
<OMS cd="ThreeDgeo1" name="plane"/>
<OMV name="p"/>
<OMA>
<OMS cd="ThreeDgeo2" name="incident"/>
<OMV name="A"/>
<OMV name="p"/>
</OMA>
<OMA>
<OMS cd="ThreeDgeo2" name="incident"/>
<OMV name="B"/>
<OMV name="p"/>
</OMA>
<OMA>
<OMS cd="ThreeDgeo2" name="incident"/>
<OMV name="C"/>
<OMV name="p"/>
</OMA>
</OMA>
</OMA>
</OMA>
<OMA>
<OMS cd="meta" name="CDDefinition"/>
<OMA>
<OMS cd="meta" name="Name"/>
<OMSTR>circle</OMSTR>
</OMA>
<OMA>
<OMS cd="meta" name="Description"/>
<OMSTR>The symbol is used to indicate a circle in 3-dimensional Euclidean geometry by a variable. The circle may (but need not) be subject to constraints. The symbol takes the variable as the first argument and the constraints as further arguments.</OMSTR>
</OMA>
<OMA>
<OMS cd="meta" name="Example"/>
<OMSTR>The circle c with center at A and passing through the point B is given by:</OMSTR>
<OMA>
<OMS cd="ThreeDgeo1" name="circle"/>
<OMV name="c"/>
<OMA>
<OMS cd="ThreeDgeo2" name="circle_center"/>
<OMV name="c"/>
<OMV name="A"/>
</OMA>
<OMA>
<OMS cd="ThreeDgeo2" name="incident"/>
<OMV name="B"/>
<OMV name="c"/>
</OMA>
</OMA>
</OMA>
</OMA>
<OMA>
<OMS cd="meta" name="CDDefinition"/>
<OMA>
<OMS cd="meta" name="Name"/>
<OMSTR>sphere</OMSTR>
</OMA>
<OMA>
<OMS cd="meta" name="Description"/>
<OMSTR>The symbol is used to indicate a sphere in 3-dimensional Euclidean geometry by a variable. The sphere may (but need not) be subject to constraints. The symbol takes the variable as the first argument and the constraints as further arguments.</OMSTR>
</OMA>
<OMA>
<OMS cd="meta" name="Example"/>
<OMSTR>The sphere s with center at A and passing through the point B is given by:</OMSTR>
<OMA>
<OMS cd="ThreeDgeo1" name="sphere"/>
<OMV name="s"/>
<OMA>
<OMS cd="ThreeDgeo2" name="sphere_center"/>
<OMV name="s"/>
<OMV name="A"/>
</OMA>
<OMA>
<OMS cd="ThreeDgeo2" name="incident"/>
<OMV name="B"/>
<OMV name="s"/>
</OMA>
</OMA>
</OMA>
</OMA>
</OMA>
</OMOBJ>