circle at infinity

Infinity \In*fin"i*ty\, n.; pl. {Infinities}. [L. infinitas;
   pref. in- not + finis boundary, limit, end: cf. F.
   infinit['e]. See {Finite}.]
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   1. Unlimited extent of time, space, or quantity; eternity;
      boundlessness; immensity. --Sir T. More.
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            There can not be more infinities than one; for one
            of them would limit the other.        --Sir W.
                                                  Raleigh.
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   2. Unlimited capacity, energy, excellence, or knowledge; as,
      the infinity of God and his perfections. --Hooker.
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   3. Endless or indefinite number; great multitude; as an
      infinity of beauties. --Broome.
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   4. (Math.) A quantity greater than any assignable quantity of
      the same kind.
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   Note: Mathematically considered, infinity is always a limit
         of a variable quantity, resulting from a particular
         supposition made upon the varying element which enters
         it. --Davies & Peck (Math. Dict.).
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   5. (Geom.) That part of a line, or of a plane, or of space,
      which is infinitely distant. In modern geometry, parallel
      lines or planes are sometimes treated as lines or planes
      meeting at infinity.
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   {Circle at infinity}, an imaginary circle at infinity,
      through which, in geometry of three dimensions, every
      sphere is imagined to pass.

   {Circular points at infinity}. See under {Circular}.
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