Counting the sky 

To record a star you need coordinates, and coordinates need a frame. Ancient astronomers had two natural choices. One was tied to the celestial equator, the projection of Earth's equator onto the sky. The other was tied to the ecliptic, the circle the Sun appears to travel through the year, which is also roughly the road the planets take. Both were in use, and ancient sources describe star positions in both, sometimes in a mixed form using a star's distance from the equator together with its position along the zodiac.

The instruments were simple and demanding. A gnomon, a vertical rod, gave the Sun's height from the length of its shadow. A dioptra was a sighting tube or bar mounted so it could be turned and read against a graduated circle. Later texts describe an armillary instrument of nested rings set to the ecliptic and equator, which let an observer read off two coordinates at once. Ptolemy credits Hipparchus with a four-cubit dioptra used for measuring the apparent diameters of the Sun and Moon, and describes instruments he says were built on earlier principles.

Reading such a device to a fraction of a degree by eye, at night, on a stone terrace, is harder than the diagram suggests. Graduations were hand cut. The instrument had to be levelled and aligned to true north. The observer had to judge when a star crossed a wire or an edge. Estimates of ancient positional accuracy generally land in the range of a fraction of a degree, which is close to the practical limit of the unaided eye and steady mounting.

Time was the other problem. The sky rotates about fifteen degrees an hour, so a position measured against the horizon is worthless unless you know the moment of measurement. The usual solution was to avoid absolute time altogether: measure a star's position relative to another star, or note the moment a known star crossed the meridian and work in differences. Chains of relative measurements, carefully closed, beat any single absolute reading.

Then comes the arithmetic. Greek astronomers worked in sexagesimal fractions borrowed from Mesopotamia, wrote numbers as letters of the alphabet, and had no algebra. Every conversion between coordinate systems is a spherical trigonometry problem solved by geometric construction and table lookup. Hipparchus is credited with compiling one of the earliest tables of chords, the ancestor of the sine table, which is exactly the tool such conversions demand.

The result, as later reported, was a catalog of roughly eight hundred and fifty to a thousand stars, arranged by constellation, with positions and brightness estimates. Counts differ between sources, and the original is lost, so the figure should be held loosely.

One further thing made the project possible, and it came from outside the Greek world entirely: centuries of records kept by scribes in Babylon.