Definition:Napier's Bones

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.

Also see

• Results about Napier's bones can be found here.

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, John (1550-1617)
• 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, John (1550-1617)
• 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