a. (and sb.) Math. [f. LOGARITHM + -IC. Cf. F. logarithmique.]

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  A.  adj. Of or pertaining to logarithms. Also in logarithmic sine, tangent, secant, etc., used (somewhat incorrectly) to denote the logarithm of the function named; opposed to natural.

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  Logarithmic curve (or line), a curve having its ordinates in geometrical progression and its abscissas in arithmetical progression, so that the abscissas are the logarithms of the corresponding ordinates. Logarithmic ellipse, hyperbola (see quots. 1851). Logarithmic spiral, a spiral that intersects all its radiants at the same angle.

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1698.  Keill, Exam. Th. Earth (1734), 243. The Applicate of the Logarithmick curve DEF.

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1706.  W. Jones, Syn. Palmar. Matheseos, 261. The Curve describ’d by their Intersection is called the Logarithmic Line…. A Point from the Extremity thereof, moving towards the Centre with a Velocity decreasing in a Geometric Progression, will generate a Curve called the Logarithmic Spiral.

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1752.  Robertson, in Phil. Trans., XLVIII. 100. Now subtract the logarithmic versed sines of such degrees … as are intended to be put on the scale, from the logarithm versed sine of 180°.

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1797.  Encycl. Brit., II. 423/2. Constructing logarithmic tables to facilitate their [sc. astronomers] calculations.

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1851.  J. Booth, Elliptic Integrals, Pref. I have named them [two curves] the spherical parabola, and the logarithmic ellipse…. The latter [may be traced] on a paraboloid of revolution. Ibid., 159. If a right cylinder, standing on a plane hyperbola as a base, be substituted for the elliptic cylinder, the curve of intersection with the paraboloid may be named the logarithmic hyperbola.

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1878.  Clifford, Elem. Dynamic, I. 78. A point is said to have logarithmic motion on a straight line when the distance from a fixed point on the line is equally multiplied in equal times.

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1881.  Maxwell, Electr. & Magn., II. 347. Another point which moves with uniform angular velocity in a logarithmic spiral.

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  b.  Pertaining to the logarithmic curve.

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1875.  R. F. Martin, trans. Havrez’ Winding Mach., 17. A round steel rope of logarithmic form … would weigh only 1594 kilogs.

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  B.  sb. = Logarithmic curve or line.

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1753.  Chambers, Cycl. Supp., s.v., Let AVD be a logarithmic, and its ordinates AB, VC, DQ.

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1797.  Brougham, in Phil. Trans., LXXXVIII. 396. The common logarithmic has its subtangent constant.

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