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Genaille Lucas Calculating Rulers

Genaille Lucas Calculating Rulers
Édouard_Lucas (1842-1891)

Édouard Lucas was born April 4, 1842 in Amiens France and educated at the École Normale Supérieure – a graduate school in Paris. During the Franco-Prussian War (1870-1871) Lucas served as an artillery officer.

Genaille Lucas Rulers

In 1885 Lucas posed an arithmetic problem to the French Association for the Advancement of Science (often abbreviated as AFAS) that caught the attention of Henri Genaille – a French civil engineer who worked for the railway. As part of his solution to Lucas’s problem, Genaille invented a form of Napier’s bones that eliminated the need to carry digits from one column to the next when reading partial products. The rulers were demonstrated to the AFAS in 1891 and published in the book Les Réglettes Multiplicatrices.

There are two sets of rulers – one for multiplication and one for division. Genaille developed the multiplication rulers first. On the rulers for multiplication, the partial products found on Napier’s bones are replaced by black triangles.

Genaille Lucas Multiplication Rulers

The right side of the triangle covers the unit digits of a partial product added to a possible carry from the right. The left corner of the triangle is placed in height corresponding to the tens figure of the partial product.

Multiplication is done by arranging the rods for the numbers needed, then following the arrows from right to left to read out the result.

The rulers for division were developed by Genaille after the multiplication rulers. They’re arranged similarly to the multiplication rulers with the addition of a special ruler for the remainder.

Genaille Lucas Division Rulers

Division is done by arranging the rods for the numbers needed, then following the lines from left to right to read out the result digits and the remainder.

This set is of the highest presentation quality - supplied with an exquisitely finished walnut box with a clear top to showcase the rods, a tablet to hold the bones during calculations, and a booklet that provides instructions for multiplication and division.

It's a great gift to recognize a colleague, an heirloom present for a young person, and a compelling conversation piece for collectors of all ages.

For Sale

Armstrong Metalcrafts is building a limited number of these for sale. The retail price is $295. To inquire about a purchase, please use our contact form or send an email to "sales" at

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