Lattice or Gelosia Multiplication

A simple and powerful method for multiplications, which quickly spread to various parts of the world, from China to Europe. Its first documented examples date back to the Middle Ages

The first printed example of gelosia multiplication is found in “Treviso Arithmetica” (1478) — Image taken from David E. Smith, “History of Mathematics”, Vol. 2 (1958)

Lattice multiplication is an ancient method to multiply two numbers of any length, even with decimals, widespread in many cultures since the Middle Ages. Its use in Europe is attested for the first time in Tractatus de minutis philosophicis et vulgaribus, a treatise in Latin dating back to about 1300.

To carry out the multiplication, it is necessary to draw a grid of as many columns as the multiplicand’s digits and as many rows as the multiplier’s digits. The multiplicand is written along the top of the grid, one digit per column, starting from the left. The multiplier is written along the right edge of the grid, one digit per row, starting from the top.

In this way, a table is created, made up of square cells, each located at the intersection between a digit of the multiplicand and one of the multiplier. Each cell is divided into two triangles by a diagonal, starting from the upper right corner and ending in the lower-left corner.