Napier's bones

Napier's bones are numbered rods devised by John Napier to simplify multiplication and division. They encode multiplication tables so calculations can be performed by arranging and reading the rods.

Multiplication table: A table listing products of pairs of numbers. Each rod displays one number's multiplication table, arranged by place value.
John Napier: A Scottish mathematician who introduced logarithms and devised Napier's bones. He designed and published the calculating rods that bear his name.
Multiplication: An arithmetic operation that combines equal groups or scales one quantity by another. The rods were chiefly designed to reduce multiplication to lookup and addition.
Slide rule: A mechanical analog calculator that uses logarithmic scales to perform multiplication, division, and related operations. It followed Napier's arithmetic innovations with a different handheld calculation technology.
Lattice multiplication: A written multiplication method that separates products into a grid of digits and diagonals. Both methods organize partial products by diagonals, but lattice multiplication uses a drawn grid.
Rabdologia: John Napier's 1617 book describing arithmetic instruments, including his numbered rods. It is the original printed account of the bones and their use.
Division: An arithmetic operation that partitions a quantity into equal groups or determines a ratio. The rods assist division through repeated multiples and subtraction.
Pascaline: A mechanical calculator built by Blaise Pascal to perform addition and subtraction. It represents a later move from lookup-based calculation toward mechanical automation.
Long multiplication: A standard written algorithm that multiplies digits and adds shifted partial products. It performs the same arithmetic without physical rods or diagonal reading.
Logarithms: The inverse functions of exponentiation, useful for transforming products into sums. Napier's bones appeared alongside his broader program of simplifying numerical calculation.

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