Napier's bones (1617) is a physical implementation of pre-existing lattice ('gelosia') multiplication, not an original algorithm

Napier's bones — the set of engraved numbered rods John Napier published in 1617 for performing multiplication and division — is not an original algorithm. The rods mechanize a paper technique that predates Napier: lattice (or gelosia) multiplication, in which the partial products of a long multiplication are read off a diagonal-ruled grid. The rods simply pre-print the grid's columns so a user can assemble the lattice by selecting and aligning rods rather than drawing it.

Napier coined the umbrella term "rabdology" (from Greek, roughly "rod-calculation") for his rod method, publishing it in his Rabdologiae. The coinage names the device, not the underlying arithmetic — the arithmetic was centuries old by 1617 and had its own long transmission history, traced at claim-lattice-multiplication-india-maghreb-italy-transmission-chain. What Napier contributed was the packaging: turning a pencil-and-paper grid method into a reusable physical calculating instrument.

This places Napier's bones in the same family as other early tactile/physical calculating aids in the vault, such as Nicholas Saunderson's pin-and-board "palpable arithmetic" (claim-saunderson-palpable-arithmetic-tactile-calculating-device), the note whose seed instruction ("redirect toward the history of calculating instruments") launched the hop that produced this claim. The distinctive move in both cases is the substitution of a manipulable physical layout for written symbolic work.