Napier spent over 20 years developing various methods of simplifying calculations and in Mirifici logarithmorum canonis descriptio , his work introducing logarithms, was finally published. The impact of his invention was enormous. More rapid calculation was now available to mariners for navigation, to land and military surveyors for their plans and particularly to astronomers.
Although travel and communication was slower and more difficult in those days, Napier was not working in academic isolation, but was part of a European network of scholars. Some advance by adding: 1,2,3,4, Napier worked out a correspondence between two series, and filled in the gaps between the numbers, a particularly laborious task. Among other properties, logarithms provide an efficient means of calculation, particularly transforming multiplication into addition and division into subtraction.
They were usually used listed in tables in books, or as logarithmic scales on slide rules. While logarithms remain a significant part of mathematics today, it is interesting to see that the way they are defined has changed.
Up until about the encyclopaedia definitions followed Napier, by first mentioning logarithms as a number series. After this date the definitions mostly start from the concept of a base and exponent, as in Wikipedia :. The logarithms we most commonly use today are called base 10 logarithms. Henry Briggs of Gresham College, London, discussed the problem with Napier and published the first base 10 logarithms in However, the considerable labour of calculating the revised logarithms was done by Briggs, or potentially unacknowledged students and helpers.
Napier worked on other calculating methods, probably using them to speed up the work of calculating his logarithms. He was the first to introduce the use of the decimal point and to propose using binary numbers in calculations. These could be assembled in different ways to multiply or divide large numbers by reading across the columns of figures. Isaac Newton recommended their use for repetitive computation.
Wooden set of Napier's bones, made between and , on display in the Discoveries gallery at the National Museum of Scotland. Set of Napier's bones in ivory, in a small leather case, c. Arithmetical compendium, combining strip form Napier's Bones and bead-type abacus, in boxwood case, by Robert Jole of London, c.
Napier's bones, Les Reglettes Financieres: ten wooden rods numbered '0' to '9', in cardboard box with one fixed wooden index rod, made by Eugene Belin et Fils of Paris, c. These let people use logarithms without the number tables. In , Edmund Gunter introduced rules with logarithmic scales which could be used with dividers for calculation.
When they started using stone to count their animals or the possession they never knew that this day will lead to a computer of today.
People today started following a set of procedure to perform calculation with these stones, which later led to creation of a digital counting device, which was the predecessor the first calculating device invented, was know as ABACUS. Which was used to be performed addition and subtraction easily.
This device was a first develop Ed by the Egyptians in the 10th centaury B. C, but it was given it final shape in the 12th centaury A. They help you to do multiplication. There are 9 different 'bones' or strips with numbers on - see below. You may need several copies of each strip.
If you look at these strips, you will see that they are really the times tables. Each square gives 2x, 3x, and so on, but the tens and units are divided by a slanting line. You also need a frame to fit them in. The side with the numbers and the bottom are raised slightly, so you can slot the number strips next to them.
Napier's bones are good for multiplying a long number by a single digit number. Let's multiply by 7. First take the strips for 4, 2, 5, 9, 2 and 8, and fit them into the frame. They must fit snugly.
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