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1 definition found
 for Osculating circle of a curve
From The Collaborative International Dictionary of English v.0.48 :

  Circle \Cir"cle\ (s[~e]r"k'l), n. [OE. cercle, F. cercle, fr. L.
     circulus (Whence also AS. circul), dim. of circus circle,
     akin to Gr. kri`kos, ki`rkos, circle, ring. Cf. Circus,
     Circum-.]
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     1. A plane figure, bounded by a single curve line called its
        circumference, every part of which is equally distant from
        a point within it, called the center.
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     2. The line that bounds such a figure; a circumference; a
        ring.
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     3. (Astron.) An instrument of observation, the graduated limb
        of which consists of an entire circle.
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     Note: When it is fixed to a wall in an observatory, it is
           called a mural circle; when mounted with a telescope
           on an axis and in Y's, in the plane of the meridian, a
           meridian circle or transit circle; when involving
           the principle of reflection, like the sextant, a
           reflecting circle; and when that of repeating an
           angle several times continuously along the graduated
           limb, a repeating circle.
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     4. A round body; a sphere; an orb.
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              It is he that sitteth upon the circle of the earth.
                                                    --Is. xi. 22.
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     5. Compass; circuit; inclosure.
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              In the circle of this forest.         --Shak.
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     6. A company assembled, or conceived to assemble, about a
        central point of interest, or bound by a common tie; a
        class or division of society; a coterie; a set.
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              As his name gradually became known, the circle of
              his acquaintance widened.             --Macaulay.
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     7. A circular group of persons; a ring.
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     8. A series ending where it begins, and repeating itself.
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              Thus in a circle runs the peasant's pain. --Dryden.
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     9. (Logic) A form of argument in which two or more unproved
        statements are used to prove each other; inconclusive
        reasoning.
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              That heavy bodies descend by gravity; and, again,
              that gravity is a quality whereby a heavy body
              descends, is an impertinent circle and teaches
              nothing.                              --Glanvill.
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     10. Indirect form of words; circumlocution. [R.]
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               Has he given the lie,
               In circle, or oblique, or semicircle. --J.
                                                    Fletcher.
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     11. A territorial division or district.
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     Note:
  
     The Circles of the Holy Roman Empire, ten in number, were
        those principalities or provinces which had seats in the
        German Diet.
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     Azimuth circle. See under Azimuth.
  
     Circle of altitude (Astron.), a circle parallel to the
        horizon, having its pole in the zenith; an almucantar.
  
     Circle of curvature. See Osculating circle of a curve
        (Below).
  
     Circle of declination. See under Declination.
  
     Circle of latitude.
         (a) (Astron.) A great circle perpendicular to the plane
             of the ecliptic, passing through its poles.
         (b) (Spherical Projection) A small circle of the sphere
             whose plane is perpendicular to the axis.
  
     Circles of longitude, lesser circles parallel to the
        ecliptic, diminishing as they recede from it.
  
     Circle of perpetual apparition, at any given place, the
        boundary of that space around the elevated pole, within
        which the stars never set. Its distance from the pole is
        equal to the latitude of the place.
  
     Circle of perpetual occultation, at any given place, the
        boundary of the space around the depressed pole, within
        which the stars never rise.
  
     Circle of the sphere, a circle upon the surface of the
        sphere, called a great circle when its plane passes
        through the center of the sphere; in all other cases, a
        small circle.
  
     Diurnal circle. See under Diurnal.
  
     Dress circle, a gallery in a theater, generally the one
        containing the prominent and more expensive seats.
  
     Druidical circles (Eng. Antiq.), a popular name for certain
        ancient inclosures formed by rude stones circularly
        arranged, as at Stonehenge, near Salisbury.
  
     Family circle, a gallery in a theater, usually one
        containing inexpensive seats.
  
     Horary circles (Dialing), the lines on dials which show the
        hours.
  
     Osculating circle of a curve (Geom.), the circle which
        touches the curve at some point in the curve, and close to
        the point more nearly coincides with the curve than any
        other circle. This circle is used as a measure of the
        curvature of the curve at the point, and hence is called
        circle of curvature.
  
     Pitch circle. See under Pitch.
  
     Vertical circle, an azimuth circle.
  
     Voltaic circuit or Voltaic circle. See under Circuit.
        
  
     To square the circle. See under Square.
  
     Syn: Ring; circlet; compass; circuit; inclosure.
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