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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク History of logarithms ： ウィキペディア英語版 History of logarithms The history of logarithms is the story of a correspondence between the positive real numbers and the real number line that was formalized in seventeenth century Europe. The Napierian logarithms came first, then Henry Briggs introduced common logarithms. A breakthrough generating the natural logarithm was the result of a search for an expression of area against a rectangular hyperbola, and required the assimilation of a new function into standard mathematics. ==Predecessors== The Babylonians sometime in 2000–1600 BC may have invented the quarter square multiplication algorithm to multiply two numbers using only addition, subtraction and a table of quarter squares. Thus, such a table served a similar purpose to tables of logarithms, which also allow multiplication to be calculated using addition and table lookups. However, the quarter-square method could not be used for division without an additional table of reciprocals (or the knowledge of a sufficiently simple algorithm to generate reciprocals). Large tables of quarter squares were used to simplify the accurate multiplication of large numbers from 1817 onwards until this was superseded by the use of computers. The Indian mathematician Virasena worked with the concept of ardhaccheda: the number of times a number of the form 2n could be halved. For exact powers of 2, this is the logarithm to that base, which is a whole number; for other numbers, it is undefined. He described relations such as the product formula and also introduced integer logarithms in base 3 (trakacheda) and base 4 (caturthacheda). Michael Stifel published ''Arithmetica integra'' in Nuremberg in 1544, which contains a table of integers and powers of 2 that has been considered an early version of a table of binary logarithms.〔 〕〔 〕 In the 16th and early 17th centuries an algorithm called prosthaphaeresis was used to approximate multiplication and division. This used the trigonometric identity :$\backslash cos\backslash alpha\backslash cos\backslash beta\; =\; \backslash frac12(+\; \backslash cos(\backslash alpha-\backslash beta))$ or similar to convert the multiplications to additions and table lookups. However, logarithms are more straightforward and require less work. It can be shown using Euler's formula that the two techniques are related. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「History of logarithms」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.