/kloc-In the first half of the 6th century, Europeans were keen on geographical exploration and ocean trade, and needed more accurate astronomical knowledge. In the study of astronomy, a lot of complicated calculations are needed, especially the multiplication of trigonometric functions. Scottish mathematician John Werner first introduced the multiplication and difference formulas of trigonometric functions, namely:

①sinαsinβ=[cos(α-β)-cos(α+β)]/2，

②cosαcosβ=[cos(α-β)+cos(α+β)]/2。

Kepler used logarithmic tables to simplify the complicated calculation of planetary orbits. Mathematician Laplace said, "Logarithm shortens the calculation time and doubles the life span of astronomers".

Before the invention of extended data logarithm, people were familiar with the method of converting the product of trigonometric functions into the sum or difference of trigonometric functions.

From the process of logarithmic invention, we can find that Napier did not use the reciprocal relationship between exponent and logarithm when discussing the concept of logarithm. The main reason for this situation is that there was no clear concept of exponent at that time, and even the exponent symbol was written by French mathematician Descartes (R.Descartes, 1596- 1650) more than 20 years later.

It was not until the18th century that the Swiss mathematician Euler discovered the reciprocal relationship between exponent and logarithm. In a book published by 1770, Euler was first used to define? He pointed out: "Logarithm originates from exponent".

Baidu Encyclopedia-John Napier

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