Both Briggs and Vlacq engaged in setting up log trigonometric tables. In the 18th century tables were published for second intervals, which were convenient for seven-place tables. In general, finer intervals are required for logarithmic functions in which the logarithm is taken of smaller numbers; for example, in the calculation of the functions log sin x and log tan x.
The related functions modified by division by x in the argument of the logarithm are easily calculated by series for small values of x. The availability of logarithms greatly influenced the form of plane and spherical trigonometry. Convenient formulas are ones in which the operations that depend on logarithms are done all at once. The recourse to the tables then consists of only two steps. One is obtaining logarithms, the other obtaining antilogs.
The procedures of trigonometry were recast to produce such formulas. Logarithm , mathematical power or exponent to which any particular number, called the base, is raised in order to produce another particular number. Common logarithms use the number 10 as the base. Natural logarithms use the transcendental number e as a base. The first tables of logarithms were published independently by Scottish mathematician John Napier in and Swiss mathematician Justus Byrgius in The problem in constructing a table of logarithms is to make the intervals between successive entries small enough for usefulness in calculating.
Logarithm tables have been replaced by electronic calculators and computers with logarithmic functions. Each logarithm contains a whole number and a decimal fraction, called respectively the characteristic and the mantissa.
In the common system of logarithms, the logarithm of the number 7 has the characteristic 0 and the mantissa. The logarithm of the number 70 is 1.
The logarithm of the number. Last Updated on 2 July, For suggestions please mail the editor in chief. John Napier1 was born in Edinburgh Scotland. John Napier started work on his tables and spent the next twenty years completing. More specifically, at any moment the distance not yet covered on the second finite line was the sine and the traversed distance on the first infinite line was the logarithm of the sine. This had the result that as the sines decreased, Napier's logarithms increased.
Furthermore, the sines decreased in geometric proportion, and the logarithms increased in arithmetic proportion. We can summarize Napier's explanation as follows Descriptio I, 1 p.
Figure 3. The relation between the two lines and the logs and sines. Napier generated numerical entries for a table embodying this relationship. However in terms of the way he actually computed these entries, he would have in fact worked in the opposite manner, generating the logarithms first and then choosing those that corresponded to a sine of an arc, which accordingly formed the argument. The values in the first column in bold that corresponded to the Sines of the minutes of arcs third column were extracted, along with their accompanying logarithms column 2 and arranged in the table.
The appropriate values from Table 1 can be seen in rows one to six of the last three columns in Figure 4. The excerpt in Figure 4 gives the first half of the first degree and, by symmetry, on the right the last half of the eighty-ninth degree.
To complete the tables, Napier computed almost ten million entries from which he selected the appropriate values. Napier himself reckoned that computing this many entries had taken him twenty years, which would put the beginning of his endeavors as far back as Sign up to join this community. The best answers are voted up and rise to the top. Stack Overflow for Teams — Collaborate and share knowledge with a private group.
Create a free Team What is Teams? Learn more. Who are the two men credited with inventing logarithms? Ask Question. Asked 6 years, 11 months ago. Active 6 years, 11 months ago. Here, he shares some insights into his work. A: John Napier of Merchiston was a Scottish theologian and mathematician who is best known for his invention of logarithms, which are a convenient way of computing with large numbers.
By greatly reducing the time and improving the accuracy of such laborious computations, he provided astronomers, navigators, scientists, engineers, surveyors and actuaries with an indispensable tool to advance their work.
0コメント