This instrument represents a perfect synthesis of the mathematical culture of the Renaissance. Its operations could be used to solve all of the arithmetical and geometric problems of the abacus tradition: the rule of three, exchanging currencies, calculating interest, extracting square and cube roots, determining the proportional division of lines, constructing polygons, squaring the circle, the proportional means, the duplication of areas and volumes, ratios of weight and volume among various materials, measuring gauges, adjusting the elevation of canons, measuring slopes, heights, distances and depths. All of this without carrying out complicated calculating procedures, thanks to the various proportional scales appearing on the two sides of the compass. On the front are the arithmetic, geometric, stereometric and metallic lines, on the back are the polygraphic, the tetragonic lines and the so-called added lines for squaring sectors of a circle. Other scales are found on the detachable quadrant that transforms the compass into a gunners' square, into an astronomical quadrant, a quadrant for measuring slopes, and a quadrant for measuring by sight.
Galileo Galilei, ca. 1606