Hyperbolic logarithm
Logarithm Log"a*rithm (l[o^]g"[.a]*r[i^][th]'m), n. [Gr. lo`gos word, account, proportion + 'ariqmo`s number: cf. F. logarithme.] (Math.) 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.

Note: The relation of logarithms to common numbers is that of numbers in an arithmetical series to corresponding numbers in a geometrical series, so that sums and differences of the former indicate respectively products and quotients of the latter; thus, 0 1 2 3 4 Indices or logarithms 1 10 100 1000 10,000 Numbers in geometrical progression Hence, the logarithm of any given number is the exponent of a power to which another given invariable number, called the base, must be raised in order to produce that given number. Thus, let 10 be the base, then 2 is the logarithm of 100, because 10^{2} = 100, and 3 is the logarithm of 1,000, because 10^{3} = 1,000. [1913 Webster]

{Arithmetical complement of a logarithm}, the difference between a logarithm and the number ten.

{Binary logarithms}. See under {Binary}.

{Common logarithms}, or {Brigg's logarithms}, logarithms of which the base is 10; -- so called from Henry Briggs, who invented them.

{Gauss's logarithms}, tables of logarithms constructed for facilitating the operation of finding the logarithm of the sum of difference of two quantities from the logarithms of the quantities, one entry of those tables and two additions or subtractions answering the purpose of three entries of the common tables and one addition or subtraction. They were suggested by the celebrated German mathematician Karl Friedrich Gauss (died in 1855), and are of great service in many astronomical computations.

{Hyperbolic logarithm} or {Napierian logarithm} or {Natural logarithm}, a logarithm (devised by John Speidell, 1619) of which the base is e (2.718281828459045...); -- so called from Napier, the inventor of logarithms.

{Logistic logarithms} or {Proportional logarithms}, See under {Logistic}. [1913 Webster]

The Collaborative International Dictionary of English. 2000.

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• Hyperbolic logarithm — Hyperbolic Hy per*bol ic, Hyperbolical Hy per*bol ic*al, a. [L. hyperbolicus, Gr. ?: cf. F. hyperbolique.] 1. (Math.) Belonging to the hyperbola; having the nature of the hyperbola. [1913 Webster] 2. (Rhet.) Relating to, containing, or of the… …   The Collaborative International Dictionary of English

• Hyperbolic — Hy per*bol ic, Hyperbolical Hy per*bol ic*al, a. [L. hyperbolicus, Gr. ?: cf. F. hyperbolique.] 1. (Math.) Belonging to the hyperbola; having the nature of the hyperbola. [1913 Webster] 2. (Rhet.) Relating to, containing, or of the nature of,… …   The Collaborative International Dictionary of English

• hyperbolic cosines — Hyperbolic Hy per*bol ic, Hyperbolical Hy per*bol ic*al, a. [L. hyperbolicus, Gr. ?: cf. F. hyperbolique.] 1. (Math.) Belonging to the hyperbola; having the nature of the hyperbola. [1913 Webster] 2. (Rhet.) Relating to, containing, or of the… …   The Collaborative International Dictionary of English

• Hyperbolic functions — Hyperbolic Hy per*bol ic, Hyperbolical Hy per*bol ic*al, a. [L. hyperbolicus, Gr. ?: cf. F. hyperbolique.] 1. (Math.) Belonging to the hyperbola; having the nature of the hyperbola. [1913 Webster] 2. (Rhet.) Relating to, containing, or of the… …   The Collaborative International Dictionary of English

• hyperbolic sines — Hyperbolic Hy per*bol ic, Hyperbolical Hy per*bol ic*al, a. [L. hyperbolicus, Gr. ?: cf. F. hyperbolique.] 1. (Math.) Belonging to the hyperbola; having the nature of the hyperbola. [1913 Webster] 2. (Rhet.) Relating to, containing, or of the… …   The Collaborative International Dictionary of English

• Hyperbolic spiral — Hyperbolic Hy per*bol ic, Hyperbolical Hy per*bol ic*al, a. [L. hyperbolicus, Gr. ?: cf. F. hyperbolique.] 1. (Math.) Belonging to the hyperbola; having the nature of the hyperbola. [1913 Webster] 2. (Rhet.) Relating to, containing, or of the… …   The Collaborative International Dictionary of English

• Logarithm — Log a*rithm (l[o^]g [.a]*r[i^][th] m), n. [Gr. lo gos word, account, proportion + ariqmo s number: cf. F. logarithme.] (Math.) One of a class of auxiliary numbers, devised by John Napier, of Merchiston, Scotland (1550 1617), to abridge… …   The Collaborative International Dictionary of English

• Hyperbolic angle — A hyperbolic angle in standard position is the angle at (0, 0) between the ray to (1, 1) and the ray to ( x , 1/ x ) where x > 1.The magnitude of the hyperbolic angle is the area of the corresponding hyperbolic sector which is loge x .Note that… …   Wikipedia

• Hyperbolic distribution — Probability distribution name =hyperbolic type =density pdf cdf parameters =mu location (real) alpha (real) eta asymmetry parameter (real) delta scale parameter (real) gamma = sqrt{alpha^2 eta^2} support =x in ( infty; +infty)! pdf… …   Wikipedia

• Logarithm — The graph of the logarithm to base 2 crosses the x axis (horizontal axis) at 1 and passes through the points with coordinates (2, 1), (4, 2), and (8, 3) …   Wikipedia