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Napier's Rods


John Napier's rods (1617) (Napier Rechenstäbchen), also known as Napier's bones, are one of his most important contributions to the world of mathematics and alongside William Oughtred's invention of the Slide Rule (1615), represents one of the most revolutionary developments in calculation devices since the abacus.  The rods were basically multiplication tables inscribed on sticks of wood or bone.  In addition to multiplication, the rods were also used in taking square roots and cube roots.


By looking at our representation of Napier's rods on the left, you'll notice each rod is inscribed with a multiplication table of a number from 0 to 9.  The rod to the extreme left, with numbers from 0 to 9  is used as an index for quick reference.

By placing any of the rods side by side, one is able to multiply larger numbers with equal ease. In this case, add the thousands, hundreds, tens, and single units to the the numbers appearing on row 9, as per our example below:


9 X 6(1000) = 54000
9 X 4(100) = +3600
9 X 9(10) =   +810
9 X 7(1) =     +64
9 X 6497 = 58474



John Napier's works are believed to be in the public domain, and have been transcribed from an original translation by Edward Wright (1616).
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Last modified: October 07, 2002