Astrolabe
The night sky folded into brass — an analog computer that solved problems of astronomy and timekeeping long before the geared machines.
The instrument projects the celestial sphere onto a plane and lets the user "compute" by turning a movable star map against a graduated scale. With it one could find the time, the altitude of a star, sunrise, or one's own latitude — calculations that otherwise demanded tables and trigonometry. Its roots reach back to ancient Greece (Hipparchus), but it was refined above all in the Islamic world from the ninth century onward.
For centuries it was the astronomer's, navigator's, and astrologer's most important instrument, often called "the mathematical jewel". Like the Antikythera mechanism, it ranks among the oldest analog computing aids humans have built.