Editing Hipparchus (section)

==Astronomical instruments and astrometry==
Hipparchus and his predecessors used various instruments for astronomical calculations and observations, such as the [[gnomon]], the [[astrolabe]], and the [[armillary sphere]].

Hipparchus is credited with the invention or improvement of several astronomical instruments, which were used for a long time for naked-eye observations. According to [[Synesius]] of Ptolemais (4th century) he made the first ''astrolabion'': this may have been an [[armillary sphere]] (which Ptolemy however says he constructed, in ''Almagest'' V.1); or the predecessor of the planar instrument called astrolabe (also mentioned by [[Theon of Alexandria]]). With an astrolabe Hipparchus was the first to be able to measure the geographical [[latitude]] and [[time]] by observing fixed stars. Previously this was done at daytime by measuring the shadow cast by a gnomon, by recording the length of the longest day of the year or with the portable instrument known as a ''[[scaphe]]''.

[[Image:equatorial ring.png|thumb|right|200px| [[Equatorial ring]] of Hipparchus's time.]]

Ptolemy mentions (''Almagest'' V.14) that he used a similar instrument as Hipparchus, called ''[[dioptra]]'', to measure the apparent diameter of the Sun and Moon. [[Pappus of Alexandria]] described it (in his commentary on the ''Almagest'' of that chapter), as did [[Proclus]] (''Hypotyposis'' IV). It was a four-foot rod with a scale, a sighting hole at one end, and a wedge that could be moved along the rod to exactly obscure the disk of Sun or Moon.

Hipparchus also observed solar [[equinox]]es, which may be done with an [[equatorial ring]]: its shadow falls on itself when the Sun is on the [[equator]] (i.e., in one of the equinoctial points on the [[ecliptic]]), but the shadow falls above or below the opposite side of the ring when the Sun is south or north of the equator. Ptolemy quotes (in ''Almagest'' III.1 (H195)) a description by Hipparchus of an equatorial ring in Alexandria; a little further he describes two such instruments present in Alexandria in his own time.

Hipparchus applied his knowledge of spherical angles to the problem of denoting locations on the Earth's surface. Before him a grid system had been used by [[Dicaearchus]] of [[Messina, Italy|Messana]], but Hipparchus was the first to apply mathematical rigor to the determination of the [[latitude]] and [[longitude]] of places on the Earth. Hipparchus wrote a critique in three books on the work of the geographer [[Eratosthenes]] of Cyrene (3rd century&nbsp;BC), called ''Pròs tèn Eratosthénous geographían'' ("Against the Geography of Eratosthenes"). It is known to us from [[Strabo]] of Amaseia, who in his turn criticised Hipparchus in his own ''Geographia''. Hipparchus apparently made many detailed corrections to the locations and distances mentioned by Eratosthenes. It seems he did not introduce many improvements in methods, but he did propose a means to determine the [[geographic coordinate system|geographical longitudes]] of different [[city|cities]] at [[lunar eclipse]]s (Strabo ''Geographia'' 1 January 2012). A lunar eclipse is visible simultaneously on half of the Earth, and the difference in longitude between places can be computed from the difference in local time when the eclipse is observed. His approach would give accurate results if it were correctly carried out but the limitations of timekeeping accuracy in his era made this method impractical.