GenailleLucas

Genaille-Lucas is a historical calculating device used to perform long division and multiplication. Developed in the late 19th century by French mathematician Édouard Lucas in collaboration with Henri Genaille, the device consists of a stack of interlocking sliding rulers, each printed with a sequence of digits. When set with a dividend and a divisor, the user reads successive digits off the rulers to obtain the quotient digits.

The rulers are designed so that borrows are handled automatically by precomputed complements, eliminating the need for mental arithmetic beyond reading the digits. To operate, the user aligns the divisor along the left edge and places the dividend on the rulers. As the division proceeds, the top line of digits across the rulers shows the quotient, while the lower lines encode borrow information. The result of each subtraction is reflected in the arrangement of digits on the rulers, so the next digit to read is the next item in line. This makes long division and, to some extent, multiplication, possible with minimal calculation.

The Genaille-Lucas devices were popular as teaching aids and novelty calculators in the late 19th and early 20th centuries. With the advent of more practical mechanical and electronic calculators, their use declined, but surviving examples are valued by collectors and historians as demonstrations of algorithmic thinking and early attempts to mechanize arithmetic.

Surviving examples are preserved in science museums and private collections, and the devices are discussed in histories of mathematical instrumentation and education.