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Neper Multiplication Applet

Genaille-Lucas Applets
(multiplication and division)

Napier's bones is an abacus created by John Napier for calculation of products and quotients of numbers that was based on Arab mathematics and lattice multiplication used by Matrakci Nasuh in the Umdet-ul Hisab[1] and Fibonacci writing in the Liber Abaci. Also called Rabdology (from Greek ῥάβδoς [r(h)abdos], "rod" and -λογία [logia], "study"). Napier published his version of rods in a work printed in Edinburgh, Scotland, at the end of 1617 entitled Rabdologiæ. Using the multiplication tables embedded in the rods, multiplication can be reduced to addition operations and division to subtractions. (Wikipedia)

To obtain the product, simply note, for each place from right to left, the numbers found by adding the digits within the diagonal sections of the strip (using carry-over where the sum is 10 or greater).

Example: 46785399 x 7

Neper Napier bones

Neper Java applet

To multiply a multi-digit number by a multi-digit number, calculate partial products and add:

Example: 874 x 73 = 874 x 70 + 874 x 3

neper multiplication

neper multiplication example

874 x 7 = 6118
874 x 3 = 2622

add  874 x 70  =    61180

and 874 x 3 =       +2622

result:                  63802


Napier's bones (Wikipedia)

Early Calculation (Ed Thelen)

Napier's Bones, Genaille-Lucas Rulers (Georgi Dalakov)

Napier's Bones and the Genaille-Lucas Rulers (Brian Borchers)

Digitale Rechengeräte

Rods for Multiplication and Division

Napier Bones in Various Bases (Cut the Knot)

Von der Pythagoreischen Rechentafel zu den Neperschen Rechenstäben (Univ. Würzburg)


Updated: 2023, Oct 06