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How To Use Napier's Bones

Here is an example of how Napier’s bones work:

Let’s multiply 8253 by 7.  We start by multiplying 7 x 3, so that that can fill in the units place.  For this, we look at the seventh diagonal square on the third rod.  This is 21.  We repeat for 7 x 5, and work our way up the problem.  Once the multiplications are in, add vertically and that is the product:

 

   7 x 8 = 56

   7 x 2 =  14

   7 x 5 =   35

   7 x 3 =    21

7 x 8253 = 57771

Calculators

Napier's Bones (1617)

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John Napier's Multiplicative Device:
Napier's Bones, a.k.a. Napier's Rods

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Napier's Bones

Napier's Bones are constructed using ten individual rods.  Each rod is divided into ten squares.  The top square has a number (1 through 9).  Each of the last nine squares are cut diagonally and the two spaces become the tens and the ones unit of the multiples of that number.  For example the fifth diagonal square on the #3 rod has a 1 and a 5 in the diagonal spaces. 

Bio
Scotman John Napier (1550-1617) started attending St. Salvator’s College in St. Andrews at age 13 and studied there for two years, though it appears he left college without obtaining a degree.  He continued his studying around Europe, probably in Paris or Holland.  In about 1572, Napier returned home to his estate and to his family.  As an adult, he had a variety of occupations including clergyman, philosopher, and mathematician.  It was common in this time, for a scholar to be well versed in science, religion, and philosophy, as there was not much separation of the three.  In mathematics, he is best known for his invention of logarithms.  These logarithms made calculations easier for all mathematicians and scientists, as well as aiding the invention of other calculating devices.  Astronomy felt a huge impact by the invention of logarithms because astronomers could now spend more time getting their hands into real astronomy, not taking large amounts of time to do the math needed.  

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John Napier

In addition, Napier is also known for his calculating device called Napier's Bones, or Napier's Rods.  This device made multiplication and division possible through addition and subtraction.  This invention, along with logarithms, made other calculating devices possible.  In addition to this math, Napier also helped his government by designing weapons of war, most of which we still use today:  tank, submarine, machine gun.

Click here to try your own multiplicaiton problem using Napier's Bones.

Jessica Carlson