infinity \infin"ity\, n.; pl. infinities. l. infinitas;
   pref. in- not + finis boundary, limit, end: cf. f.
   infinit'e. see finite.
   1913 webster
   1. unlimited extent of time, space, or quantity; eternity;
      boundlessness; immensity. --sir t. more.
      1913 webster

            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.
      1913 webster

   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.
      1913 webster
see also:
infinities finite circle at infinity circular points at infinity circular