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The Collaborative International Dictionary of English v.0.48: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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The Collaborative International Dictionary of English v.0.48: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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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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