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One of a class of auxiliary numbers, devised by John Napier, of Merchiston, Scotland (1550-1617), to abridge arithmetical calculations, by the use of addition and subtraction in place of multiplication and division.

See Logarithmic.

Logarithmically.

Of or pertaining to logarithms; consisting of logarithms. Logarithmic curve (Math.), a curve which, referred to a system of rectangular coördinate axes, is such that the ordinate of any point will be the logarithm of its abscissa. -- Logarithmic spiral, a spiral curve such that radii drawn from its pole or eye at equa…

By the use of logarithms.

The number corresponding to a logarithm. The word has been sometimes, though rarely, used to denote the complement of a given logarithm; also the logarithmic cosine corresponding to a given logarithmic sine. -- An`ti*log`a*rith"mic, a.

A logarithm of the cosine or cotangent. [Obs.] Kepler. Hutton.

arithmetic; according to the rules or method of arithmetic. Arithmetical complement of a logarithm. See Logarithm. -- Arithmetical mean. See Mean. -- Arithmetical progression. See Progression. -- Arithmetical proportion. See Proportion.

odies. -- Artificial lines, lines on a sector or scale, so contrived as to represent the logarithmic sines and tangents, which, by the help of the line of numbers, solve, with tolerable exactness, questions in trigonometry, navigation, etc. -- Artificial numbers, logarithms. -- Artificial person (Law). See under Per…

The number from which a mathematical table is constructed; as, the base of a system of logarithms.

nction of an element, or of two compounds performing the function of elements. -- Binary logarithms, a system of logarithms devised by Euler for facilitating musical calculations, in which 1 is logarithm of 2, instead of 10, as in the common logarithms, and the modulus 1.442695 instead of .43429448. -- Binary measure…

rations, for the most part invented by Charles Babbage and G. and E. Scheutz. It computes logarithmic and other mathematical tables of a high degree of intricacy, imprinting the results on a leaden plate, from which a stereotype plate is then directly made.

The integral part (whether positive or negative) of a logarithm.

A compliment. [Obs.] Shak. Arithmetical compliment of a logarithm. See under Logarithm. -- Arithmetical complement of a number (Math.), the difference between that number and the next higher power of 10; as, 4 is the complement of 6, and 16 of 84. -- Complement of an arc or angle (Geom.), the difference between that…

ic equation; an algebraic equation; a transcendental equation; an exponential equation; a logarithmic equation; a differential equation, etc.

A logarithmic line on Gunter's scale, used for performing the multiplication and division of numbers mechanically by the dividers; -- called also line of lines, and line of numbers.

o the circle; and hence, called hyperbolic sines, hyperbolic cosines, etc. -- Hyperbolic logarithm. See Logarithm. -- Hyperbolic spiral (Math.), a spiral curve, the law of which is, that the distance from the pole to the generating point varies inversely as the angle swept over by the radius vector.…

ock, watch, or other registering machine; a hand that points to something. -- Index of a logarithm (Math.), the integral part of the logarithm, and always one less than the number of integral figures in the given number. It is also called the characteristic. -- Index of refraction, or Refractive index (Opt.), the num…

g; contrivance or construction of that which has not before existed; as, the invention of logarithms; the invention of the art of printing.

on the scale of 60; as, logistic, or sexagesimal, arithmetic. Logistic, or Proportional, logarithms, certain logarithmic numbers used to shorten the calculation of the fourth term of a proportion of which one of the terms is a given constant quantity, commonly one hour, while the other terms are expressed in minutes a…