Genaille–Lucas rulers (also known as Genaille’s rods) is an arithmetic tool invented by Henri Genaille, a French railway engineer, in The following other wikis use this file: Usage on مساطر جينايل لوكاس. Usage on Genaille–Lucas rulers. Napier’s Bones and the Genaille-Lucas Rulers. Introduction. In , John Napier published Rabdologia, a book that contained a description of the rods that he.

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Genaille—Lucas rulers also known as Genaille’s rods are an arithmetic tool invented by Henri Genaillea French railway engineer, in ruulers The device is a variant of Napier’s bones. By representing the carry graphically, the user can read off the results of simple multiplication problems directly, with no intermediate mental calculations.

Napier’s Bones and the Genaille-Lucas Rulers

Genaille, already known for having invented a number of arithmetic tools, created his rulers in the genaille-lucae of solving the problem. The popularity of Genaille’s rods was widespread but short-lived, as mechanical calculators soon began to displace manual arithmetic methods.


A full set of Genaille—Lucas rulers consists of eleven strips of wood or metal. On each strip is printed a column of triangles and a column genaille-luczs numbers:.

Consider multiplying by 4. Five rulers, one for each digit ofare arranged side-by-side, next to the “index” geenaille-lucas. Then we simply read off the digits that we visited.

The product, shown in red, is Soon after rluers development by Genaille, the rulers were adapted to a set of rods that can perform division.

The division rods are aligned similarly to the multiplication rods, with the index rod on the left denoting the divisorand the following rods spelling out the digits of the dividend.

After these, a special “remainder” rod is placed on the right.

Applet: Genaille-Lucas Rulers

The quotient is read from left to right, following the lines from one rod to the next. The path of digits ends with a number on the remainder rod, which is the remainder given by the division.


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