History of logarithms
The history of logarithms is the story of a correspondence between multiplication on the positive real numbers and addition on real number line that was formalized in seventeenth century Europe and was widely used to simplify calculation until the advent of the digital computer. The Napierian logarithms were published first in 1614. E. W. Hobson called it "one of the very greatest scientific disco
"Briggs addressed... [Napier], "My Lord, I have undertaken this long journey purposely to see your person, and to know by what engine of wit or ingenuity you came first to think of this most excellent help in astronomy viz., the logarithms.""
"When... Schoner came to write his commentary on the work of Ramus, in 1586, a decided advance was made, for not only did he give the usual series for positive exponents, but, like Stifel, he used the geometric progressions with fractions as well, although... not with negative exponents."
"Although the has largely given way to the pocket calculator... the pedagogical value of making ones own [slide or other] rules of various kinds remains. Napiers rods are easily made by schoolchildren and the historical route by which the modern slide rule evolved can be followed through with advantage. If has been taught at some stage, the principles of Napiers rods will already be understood. Many different kinds of graduated rule can be experimented with, including those of arithmetic scales (to be used for addition and subtraction) and those with geometric scales (for multiplication and division). It is not necessary to mention the word logarithm; it is sufficient to introduce arithmetic and and to utilize the rules themselves in order to introduce the principles of logarithms."
"As the Indian figures are on infinite service in all branches of mixed Mathematics, and particularly in Astronomy... the next considerable improvement in this science was by the introduction of DECIMAL ARITHMETIC. This, according to Dr. Wallis, in his Preface to his Algebra was first done by , about the year 1450. But the greatest improvement of all was made by the introduction ofLOGARITHMS.For, by their means, numbers almost infinite, and such as are otherwise impracticable, are managed with ease and expedition. They are the incontestable invention of the Lord Neper, a Scotchman, about the year 1614."
"Jost Burgi, a Swiss clockmaker and mathematician, invented logarithms independently of Napier and Briggs, although it is not clear when he started work on them. Some historians have suggested that Burgi may have invented logarithms earlier than Napier, but his work was not published until 1620, when the German mathematician and astronomer Johannes Kepler asked him to do so. ...six years after the publication of Napiers work."
"In [1620] a table of the logarithms... of sines and tangents of angles in the first quadrant was brought out by Edmund Gunter... Four years later [he] introduced a "line of numbers," which provided a mechanical method for finding the product of two numbers: this was the precursor of the slide-rule, first described by Oughtred in 1632."
