In 1617, John Napier developed a mechanical method for performing multiplication and division using rods printed with simple multiplication tables.  This method, eventually described as “Napier’s bones.”   As the world’s first practical calculator, “Napier’s Bones,” can be used to multiply, divide and find simple square and cube roots.  In a time when the average person probably couldn’t multiply 5 by 5, Napier provided both tradesmen and merchants with a simple tool that could be used by almost anyone to handle tasks involving large numbers.  Computations with “bones” does not require an understanding of the mathematics behind simple addition and subtraction.

The origin of Napier’s Bones is somewhat of a historical puzzle. While John Napier is generally given the entire credit for their invention, this device is so simple you can easily imagine it being used in antiquity.  The rods are a clever use of multiplication tables, and these were first described around 572 BCE by Pythagoras.  While Napier published how to make and use the rods, neither he nor anyone writing of them in later years discussed the mathematics behind them. The method is clearly based on Pythagoras’ approach to multiplication using what he called the “quadrilateral.”

Using Pythagoras’ approach, you can quickly find products of two numbers by reading directly across the table by splitting the digits in the table and adding the digits in each parallelogram found in the row and column combination that describes the product.  The drawback to this method is that only combinations appearing on the table can be computed.  Napier’s Bones gets around this by placing each column on a rod so that the rods can be assembled in any order.

For example, to compute 425 × 6, bones for 4, 2, and 5 are placed into the board, in sequence. These bones show the larger figure which will be multiplied. Then using Pythagoras’ method, the product is read from row 6 as 2550 (ie 2 and 4+1 and 2+3 and 0).

Of course, Napier’s other contribution to mathematics, the logarithm, would almost immediately supplant the use of “bones” in many fields.  These logarithms, especially with placed on a simple ruler as Rev Edmund Gunter will do in 1624 would further simply complex arithmetic operations to simple measures with a set of calipers.

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