Circular points 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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Circular \Cir"cu*lar\, a. [L. circularis, fr. circulus circle:
   cf. F. circulaire. See {Circle}.]
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   1. In the form of, or bounded by, a circle; round.
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   2. repeating itself; ending in itself; reverting to the point
      of beginning; hence, illogical; inconclusive; as, circular
      reasoning.
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   3. Adhering to a fixed circle of legends; cyclic; hence,
      mean; inferior. See {Cyclic poets}, under {Cyclic}.
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            Had Virgil been a circular poet, and closely adhered
            to history, how could the Romans have had Dido?
                                                  --Dennis.
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   4. Addressed to a circle, or to a number of persons having a
      common interest; circulated, or intended for circulation;
      as, a circular letter.
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            A proclamation of Henry III., . . . doubtless
            circular throughout England.          --Hallam.
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   5. Perfect; complete. [Obs.]
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            A man so absolute and circular
            In all those wished-for rarities that may take
            A virgin captive.                     --Massinger.
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   {Circular are}, any portion of the circumference of a circle.
      

   {Circular cubics} (Math.), curves of the third order which
      are imagined to pass through the two circular points at
      infinity.

   {Circular functions}. (Math.) See under {Function}.

   {Circular instruments}, mathematical instruments employed for
      measuring angles, in which the graduation extends round
      the whole circumference of a circle, or 360[deg].

   {Circular lines}, straight lines pertaining to the circle, as
      sines, tangents, secants, etc.

   {Circular note}{ or Circular letter}.
      (a) (Com.) See under {Credit}.
      (b) (Diplomacy) A letter addressed in identical terms to a
          number of persons.

   {Circular numbers} (Arith.), those whose powers terminate in
      the same digits as the roots themselves; as 5 and 6, whose
      squares are 25 and 36. --Bailey. --Barlow.

   {Circular points at infinity} (Geom.), two imaginary points
      at infinite distance through which every circle in the
      plane is, in the theory of curves, imagined to pass.

   {Circular polarization}. (Min.) See under {Polarization}.

   {Circular sailing} or {Globular sailing} (Naut.), the method
      of sailing by the arc of a great circle.

   {Circular saw}. See under {Saw}.
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