ThreeDgeo1.ocd

<CD xmlns="http://www.openmath.org/OpenMathCD">
<CDComment>

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          this document, and maintains a prominent reference in the 
          work to the original source.
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          document is stated prominently in the derived work.  Moreover if
          both this document and the derived work are Content Dictionaries
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          Dictionary Group whose name is, for example, `math' containing
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</CDComment>

<CDName>ThreeDgeo1</CDName>
<CDURL>http://nash.sip.ucm.es/LAD-3D/3DgeoCDs/ThreeDgeo1.ocd</CDURL>
<CDReviewDate>2017-12-31</CDReviewDate>
<CDStatus>experimental</CDStatus>
<CDDate>2008-01-21</CDDate>
<CDVersion>0</CDVersion>
<CDRevision>3</CDRevision>
<CDComment>
  Author: Jesús Escribano
</CDComment>

<Description> 
This CD defines symbols for 3-dimensional Euclidean geometry
</Description> 

<CDDefinition>
<Name>point</Name>
<Description>
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.
</Description>


<Example> Given two lines l and m, a point A on l and m is defined by:

<OMOBJ xmlns="http://www.openmath.org/OpenMath" version="2.0">
  <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>
</OMOBJ>

</Example>

</CDDefinition>

<CDDefinition>
<Name>line</Name>
<Description> 
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.
</Description>

<Example> Given points A and B in 3-dimensional space, a line l through A and B
is defined  by: 

<OMOBJ xmlns="http://www.openmath.org/OpenMath" version="2.0">
  <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>
</OMOBJ>
</Example>

</CDDefinition>

<CDDefinition>
<Name>segment</Name>
<Description> 
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.
</Description>

<Example> The segment s with endpoints A and B is given by

<OMOBJ xmlns="http://www.openmath.org/OpenMath" version="2.0">
  <OMA>
    <OMS cd="ThreeDgeo1" name="segment"/>
    <OMV name="s"/>
    <OMV name="A"/>
    <OMV name="B"/>
  </OMA>
</OMOBJ>

</Example>

</CDDefinition>

<CDDefinition>
<Name>endpoints</Name>
<Description>	
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.

</Description>
	
<Example> The set E of the two endpoints of a segment s is given by:

<OMOBJ xmlns="http://www.openmath.org/OpenMath" version="2.0">
  <OMA>
    <OMS cd="ThreeDgeo1" name="endpoints"/>
    <OMV name="E"/>
    <OMV name="s"/>
  </OMA>
</OMOBJ>

</Example>

</CDDefinition>

<CDDefinition>
<Name>midpoint</Name>
<Description> 
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.

</Description>

<Example> 
The midpoint M of the segment s is given by

<OMOBJ xmlns="http://www.openmath.org/OpenMath" version="2.0">
  <OMA>
    <OMS cd="ThreeDgeo1" name="midpoint"/>
    <OMV name="M"/>    
    <OMV name="s"/>
  </OMA>
</OMOBJ>

</Example>

</CDDefinition>

<CDDefinition>
<Name>plane</Name>
<Description> 
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.
</Description>

<Example> Given points A, B and C in 3-dimensional space, a plane p through A, B and C is defined  by: 

<OMOBJ xmlns="http://www.openmath.org/OpenMath" version="2.0">
  <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>
</OMOBJ>
</Example>

</CDDefinition>

<CDDefinition>
<Name>circle</Name>
<Description> 
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.
</Description>

<Example> 
The circle c with center at A and passing through the point B is given by:

<OMOBJ xmlns="http://www.openmath.org/OpenMath" version="2.0">
  <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>
</OMOBJ>

</Example>

</CDDefinition>

<CDDefinition>
<Name>sphere</Name>
<Description> 
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.
</Description>

<Example> 
The sphere s with center at A and passing through the point B is given by:

<OMOBJ xmlns="http://www.openmath.org/OpenMath" version="2.0">
  <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>
</OMOBJ>

</Example>

</CDDefinition>

</CD>