The Methods of Construction of the Earliest Tables of Logarithms

Abstract

The first table of logarithms was published by John Napier in 1614 under the title of Mirifici Logarithmorum Canonis Descriptio…, at Edinburgh, but the explanation of the construction was not then given. The author, however, promised to publish this later, when he had been assured that the leading mathematicians of the day approved of his work. Any doubt on this point was very soon removed for, within a short time, Edward Wright, who, after studying at Cambridge, had devoted himself to navigation, was engaged in translating the Descriptio into English. Henry Briggs, Gresham Professor in London since 1596, lectured to his students on the work of Napier as soon as he had grasped its significance, and he took it up with great enthusiasm. Soon he was in communication with the inventor and even travelled twice to Scotland in the summers of 1615 and 1616, before Napier’s death, which took place in 1617. The Descriptio seems to have taken some time to reach the Continent, for it was not till 1617 that Kepler first saw a copy. He apparently did not realise its importance at that time, but in the following year he became so enthusiastic that he wrote a letter to Napier (i.e. after the latter’s death) expressing his admiration and hoping for the publication of the method of construction of the Canon. In 1619 the posthumous work of Napier appeared with the title, Mirifici Logarithmorum Canonis Constructio. The construction of the table of logarithms is fully given and the exposition of the procedure, step by step, is exceedingly simple and beautiful. This work was admirably translated by W. R. Macdonald in 1889.