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John Napier

Updated on September 5, 2013

John Napier, Laird of Merchiston, was born in Merchiston Castle in Edinburgh, Scotland in 1550. As the eighth laird of Merchiston, Napier was first educated in France in 1561. He became a student of the University of St Andrews in Scotland at the age of 13 but he left without taking a degree. He had a fine mind and vivid imagination and spent his early years on his properties experimenting in agriculture.

Napier was also a theologian of very definite views, writing his “A Plain discovery of the whole revelation of St Johnin 1593. He was also an inventor of war machines such as “burning mirrors” to stop a Spanish Armada, artillery pieces capable of clearing a field four miles in circumference and tank-like chariot.

It was in mathematics, that he made his name. He devoted most of his leisure time to study of mathematics particularly to devising methods of making computations easier. As a mathematician, he was already considering imaginary roots and experimenting with methods to extract all real roots of any positive numbers. It is hard to establish when he first began to develop the concept of logarithms but by 1549 his work was already well advanced.

Napier also discovered that if

For the rest of his life he developed, simplified and worked on his logarithmic tables. In the course of his work he introduced the present decimal notation.

Logarithms is the greatest of his inventions. In 1614, Napier published his new system, “Mirifici Logarithmorum Canonis Descriptio". He began working on this computational method as early as 1594, gradually elaborating his computational system whereby roots, products and quotients could be quickly determined from tables showing powers of a fixed number used as a base.

Napier’s invention of logarithms is shared with Jobst Burgi (1552-1632), a Swiss watchmaker, whose independent discovery was published six years later. His tables appeared in 1620 under the title of “Arithmetische und Geometrische Progress Tabulen”. Both men worked independently of each other and Napier had his works published first. A slight change in Napier’s definition which arose from his collaboration with Briggs gave logarithms as we know them today.

The “Rabdologia” was published in 1617. In it Napier explained how numbered rods, known as Napier’s bones maybe used for performing multiplication and division. This device was the forerunner of the slide rule. He also derived an ingenious method using counters on a chess board for performing multiplication, division and the extraction of roots.

The word Logarithm was first used by John Napier. It means ratio number. His admirer Henry Briggs, suggested to him that he use a base 10. Napier heeded his advice.

In 1624 Briggs also introduced the word ”Mantissa”, in Latin meaning an addition but used here as meaning an appendix. It was not commonly used until Leonardo Paul Euler, a Swiss Mathematician, adopted it in his ‘Introductio in Analysin Infinitorum” in 1748. Carl Gauss, a German mathematician and scientist suggested that it be used for the fractional part of decimals. Briggs in 1624 also suggested that the term "characteristic" be used.

Napier’s invention of logarithms overshadows his other mathematical work. John Napier also designed mirrors which burned and destroyed at a distance and a means of “sayling under water.” Some people accused him of black art. Others praised his ingenuity.

In April 04, 1617 he died in the same castle in which he was born.


1. " A History of Mathematics", by D. E. Smith. Dover Publication.

2. "An Introduction to the History of Mathematics", by Howard Eves. Holt, Rinehart and Winston.

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    • profile image

      reconciled heart 8 years ago

      Well written, interesting article about a talented man. Interesting to learn about the origins of "logarithm". Thank you for posting!

    • mega1 profile image

      mega1 8 years ago

      What's that word - submerged? very interesting thanks for the diversion

    • William F. Torpey profile image

      William F Torpey 8 years ago from South Valley Stream, N.Y.

      Interesting history and good reading. Thanks.