logarithmn.

Brit.

/ˈlɒɡərɪð(ə)m/,

/ˈlɒɡərɪθ(ə)m/, U.S.

/ˈlɔɡəˌrɪðəm/,

/ˈlɑɡəˌrɪðəm/

Forms: Also 1600s logorythm.

Etymology: < modern Latin logarithmus (Napier, 1614), < Greek λόγος word, proportion, ratio + ἀριθμός number. Napier does not explain his view of the literal meaning of logarithmus . It is commonly taken to mean ‘ratio-number’, and as thus interpreted it is not inappropriate, though its fitness is not obvious without explanation. Perhaps, however, Napier may have used λόγος merely in the sense of ‘reckoning’, ‘calculation’ (compare logistic adj. and n.).

Mathematics.

One of a particular class of arithmetical functions, invented by John Napier of Merchiston (died 1617), and tabulated for use as a means of abridging calculation. The essential property of a system of logarithms is that the sum of the logarithms of any two or more numbers is the logarithm of their product. Hence the use of a table of logarithms enables a computer to substitute addition and subtraction for the more laborious operations of multiplication and division, and likewise multiplication and division for involution and evolution.The word is now understood to refer only to systems in which the logarithm of any number a^x is x, a being a constant which is called the base of the system. The logarithms (of sines) tabulated by Napier himself were not logarithms in this restricted sense, but were functions of what are now called Napierian (also Neperian), hyperbolic, or natural logarithms, the base of which, denoted by the symbol ε or e, is 2·71828 +. This system is still in use for analytical investigations, but for common purposes the system used is that invented by Napier's friend Henry Briggs (died 1630), the base of which is 10; the Briggsian or Briggian logarithms are also known as common logarithms (see common adj. and adv. Compounds 2) or decimal logarithms. For binary, Gaussian logarithm, see the adjectives. logistic logarithms (see quot. 1795); also called proportional logarithms.In mathematical notation ‘the logarithm of’ is expressed by the abbreviation ‘log’ prefixed to numeral figures or algebraical symbols. When necessary, the base of the system is indicated by adding an inferior figure: thus ‘log₁₀a’ means ‘the logarithm of a to the base 10’.

ΘΚΠ

the world > relative properties > number > arithmetic or algebraic operations > logarithm > [noun]

logarithm1616

logarism1630

log1858

the world > relative properties > number > arithmetic or algebraic operations > logarithm > [noun] > types of

hyperbolic logarithm1704

logistic logarithms1795

log log1910

lod score1977

1614 Napier (title) Mirifici Logarithmorum Canonis descriptio [etc.].]

1616 H. Briggs Let. in R. Parr Life J. Usher (1686) Coll. xvi. 36 Napper [sic], Lord of Markinston, hath set my Head and Hands a Work, with his new and admirable Logarithms.

1616 E. Wright in tr. J. Napier Logarithms Ded. This new course of Logarithmes doth cleane take away all the difficultye that heretofore hath beene in mathematicall calculations.

a1630 H. Briggs Logarithm. Arithm. (1631) i. 1 The Logar. of 1 is 0.

a1630 H. Briggs Logarithm. Arithm. (1631) i. 2 The Log. of proper fractions is Defective.

a1637 B. Jonson Magnetick Lady i. vi. 35 in Wks. (1640) III Sir Interest..will tell you instantly, by Logorythmes, The utmost profit of a stock imployed.

1706 W. Jones Synopsis Palmariorum Matheseos 173 Mr. Halley..has..drawn a very curious Method for Constructing Logarithms.

1795 C. Hutton Math. & Philos. Dict. at Logarithms Logistic Logarithms, are certain Logarithms of sexagesimal numbers or fractions, useful in astronomical calculations.

1827 W. Scott Life Napoleon VI. ii. 80 Buonaparte said that his favourite work was a book of logarithms.

c1865 J. Wylde Circle of Sci. I. 519/1 This advantage, which the base 10 has over any other, was first seen and applied by Briggs..; the logarithms are, therefore, sometimes called the ‘Briggian Logarithms’.

This entry has not yet been fully updated (first published 1903; most recently modified version published online June 2022).

单词	logarithm
释义	logarithmn. Brit. /ˈlɒɡərɪð(ə)m/, /ˈlɒɡərɪθ(ə)m/, U.S. /ˈlɔɡəˌrɪðəm/, /ˈlɑɡəˌrɪðəm/ Forms: Also 1600s logorythm. Etymology: < modern Latin logarithmus (Napier, 1614), < Greek λόγος word, proportion, ratio + ἀριθμός number. Napier does not explain his view of the literal meaning of logarithmus . It is commonly taken to mean ‘ratio-number’, and as thus interpreted it is not inappropriate, though its fitness is not obvious without explanation. Perhaps, however, Napier may have used λόγος merely in the sense of ‘reckoning’, ‘calculation’ (compare logistic adj. and n.). Mathematics. One of a particular class of arithmetical functions, invented by John Napier of Merchiston (died 1617), and tabulated for use as a means of abridging calculation. The essential property of a system of logarithms is that the sum of the logarithms of any two or more numbers is the logarithm of their product. Hence the use of a table of logarithms enables a computer to substitute addition and subtraction for the more laborious operations of multiplication and division, and likewise multiplication and division for involution and evolution.The word is now understood to refer only to systems in which the logarithm of any number a^x is x, a being a constant which is called the base of the system. The logarithms (of sines) tabulated by Napier himself were not logarithms in this restricted sense, but were functions of what are now called Napierian (also Neperian), hyperbolic, or natural logarithms, the base of which, denoted by the symbol ε or e, is 2·71828 +. This system is still in use for analytical investigations, but for common purposes the system used is that invented by Napier's friend Henry Briggs (died 1630), the base of which is 10; the Briggsian or Briggian logarithms are also known as common logarithms (see common adj. and adv. Compounds 2) or decimal logarithms. For binary, Gaussian logarithm, see the adjectives. logistic logarithms (see quot. 1795); also called proportional logarithms.In mathematical notation ‘the logarithm of’ is expressed by the abbreviation ‘log’ prefixed to numeral figures or algebraical symbols. When necessary, the base of the system is indicated by adding an inferior figure: thus ‘log₁₀a’ means ‘the logarithm of a to the base 10’. ΘΚΠ the world > relative properties > number > arithmetic or algebraic operations > logarithm > [noun] logarithm1616 logarism1630 log1858 the world > relative properties > number > arithmetic or algebraic operations > logarithm > [noun] > types of hyperbolic logarithm1704 logistic logarithms1795 log log1910 lod score1977 1614 Napier (title) Mirifici Logarithmorum Canonis descriptio [etc.].] 1616 H. Briggs Let. in R. Parr Life J. Usher (1686) Coll. xvi. 36 Napper [sic], Lord of Markinston, hath set my Head and Hands a Work, with his new and admirable Logarithms. 1616 E. Wright in tr. J. Napier Logarithms Ded. This new course of Logarithmes doth cleane take away all the difficultye that heretofore hath beene in mathematicall calculations. a1630 H. Briggs Logarithm. Arithm. (1631) i. 1 The Logar. of 1 is 0. a1630 H. Briggs Logarithm. Arithm. (1631) i. 2 The Log. of proper fractions is Defective. a1637 B. Jonson Magnetick Lady i. vi. 35 in Wks. (1640) III Sir Interest..will tell you instantly, by Logorythmes, The utmost profit of a stock imployed. 1706 W. Jones Synopsis Palmariorum Matheseos 173 Mr. Halley..has..drawn a very curious Method for Constructing Logarithms. 1795 C. Hutton Math. & Philos. Dict. at Logarithms Logistic Logarithms, are certain Logarithms of sexagesimal numbers or fractions, useful in astronomical calculations. 1827 W. Scott Life Napoleon VI. ii. 80 Buonaparte said that his favourite work was a book of logarithms. c1865 J. Wylde Circle of Sci. I. 519/1 This advantage, which the base 10 has over any other, was first seen and applied by Briggs..; the logarithms are, therefore, sometimes called the ‘Briggian Logarithms’. This entry has not yet been fully updated (first published 1903; most recently modified version published online June 2022). < n.1616
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