The invention of mathematical instruments was driven, since antiquity, by the demands of astronomical observation, navigation, and cartography. Some of the older instruments, such as the armillary sphere or the parallactic ruler, were described in Ptolemy's Almagest. Arab astronomers were responsible for the extraordinary invention of the astrolabe and its variants: the quadrant, the equatorium, the torquetum, and the geometrical square. These instruments were also used in the Middle Ages, together with the Jacob's staff, for measuring terrestrial distances and determine latitude. The map-making and military needs of the Renaissance gave rise to a wide range of instruments often assembled into what were known as mathematical compendia: these contained surveyor's magnetic compasses, proportional compasses, surveyor's compasses, folding squares, goniometers, calipers, plumb levels, and numerous accessories. The scientific collections of the leading European courts of the sixteenth and seventeenth centuries also comprised other types of mathematical instruments: surveying instruments, sundials, and calculating machines.