What calculating instrument did Galileo's 1606 manual explain?

Galileo's 1606 manual explained the geometrical and military compass.

The work was titled Le Operazioni del Compasso Geometrico et Militare, meaning The Operations of the Geometrical and Military Compass. Galileo published it in Padua in 1606 to explain how to use an instrument he had developed and promoted for practical calculation.

Unlike an ordinary drawing compass, this sector-like device had graduated scales that allowed users to solve problems involving proportion, geometry, surveying, fortification, and military logistics. It could assist with calculations such as scaling figures, determining angles, and working with the sizes and quantities needed in artillery or construction.

The compass also became a commercial matter. Galileo trained instrument maker Marcantonio Mazzoleni to produce examples, and sales helped support Galileo financially. This is why the manual is more than a purely theoretical mathematical text: it combines geometry with the practical culture of Renaissance instrument making.

The instrument should not be confused with Galileo's telescope, his hydrostatic balance, or the later pendulum-clock design. The 1606 book was specifically an operating guide for the geometrical and military compass.