Circle at infinity
(gcide) | 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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