# Definition:Napier's Bones

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## Definition

**Napier's bones** is a device for performing the operation of multiplication of numbers.

The device consists of:

- a set of
**rods**, one for each digit $0$ to $9$, containing the multiples of that number, again from $0$ to $9$, in a column, written as $2$ digits, divided by a diagonal line.

- a
**board**upon which the**rods**can be placed, labeled $1$ to $9$ down a column on the left hand side, each digit corresponding to the numbers on the**rods**

The multiplicand is assembled by placing the rods for each of its digit next to each other on the **board**.

The multiplier corresponds to the number down the left hand side of the **board**

For each digit in the multiplicand, the numbers adjacent to each other on the row corresponding to the multiplier in each of the compartments formed by the diagonal lines aligned together are added together.

The product is thus formed.

## Also known as

**Napier's bones** are also known as **Napier's rods**.

## Source of Name

This entry was named for John Napier.

## Historical Note

**Napier's bones** are described by John Napier in his *Rabdologiae* of $1617$.

## Sources

- 1989: Ephraim J. Borowski and Jonathan M. Borwein:
*Dictionary of Mathematics*... (previous) ... (next):**Napier's bones** - 1998: David Nelson:
*The Penguin Dictionary of Mathematics*(2nd ed.) ... (previous) ... (next):**Napier's bones** - 2008: David Nelson:
*The Penguin Dictionary of Mathematics*(4th ed.) ... (previous) ... (next):**Napier's bones** - 2008: Ian Stewart:
*Taming the Infinite*... (previous) ... (next): Chapter $5$: Eternal Triangles: Logarithms - 2014: Christopher Clapham and James Nicholson:
*The Concise Oxford Dictionary of Mathematics*(5th ed.) ... (previous) ... (next):**Napier's bones** - 2021: Richard Earl and James Nicholson:
*The Concise Oxford Dictionary of Mathematics*(6th ed.) ... (previous) ... (next):**Napier's bones**