Lines

With Eukleides, the internal representation of lines is based on an abscissa, an ordinate and a polar angle. Therefore lines have an implicit orientation. Here are all the line valued functions:

• line(A, B)
• line(A, u)
• line(s)
• line(A, a)
  Line of polar angle a, containing point A.
• line(c, a)
  Tangent line of circle c at point of argument a (in respect of the center of c).
• line(cc, x)
  Tangent line of cc at point of argument x (in respect of the internal parametric representation). For parabolas, the representation is based on square function; for ellipses, on cosine and sine; for hyperbolas, on cosecant and tangent.
• parallel(l, A) or parallel(s, A)
• perpendicular(l, A) or perpendicular(s, A)
• bisector(s)
  Perpendicular bisector of segment s.
• bisector(A, B, C)
  Bisector of angle under ABC.
• bisector(l, l')
  Bisector of the sharp angle formed by l and l'.
• altitude(A, B, C)
  Altitude of triangle ABC containing vertex A.
• median(A, B, C)
  Median of triangle ABC containing vertex A.
• translation(l, u)
• reflection(l, l')
  Reflection in respect of line l'.
• rotation(l, A [, a])
  Rotation of center A and angle a (default: 180°).
• homothecy(l, A, x)
  Homothecy, i.e. expansion or dilation, of center A and ratio x.