Hipparchos was a Greek astronomer and mathematician said to have lived about BC 190 - 120.
Ptolemy attributes to him astronomical observations in the period from 147 BC to 127 BC.
Some of these are stated as made in Rhodes. Some earlier observations since 162 BC might also have been made by Hipparchos.
Although he wrote at least fourteen books, relatively little of Hipparchos' direct work survived into modern times (ref 1).
However, there are a few observations probably made by Hipparchos himself, which are mentioned by later authors and are detailed enough to give us a possible dating.
The solar eclipse. The first is a solar eclipse used by Hipparchos to determine the size and distance of sun and moon.
Cleomedes writes: "Once when the Sun was wholly eclipsed in the Hellespont, it was observed in Alexandria to be eclipsed except for the fifth part of its diameter."
We are looking for a solar eclipse which is total in the Hellespont region and of magnitude 0.8 in Alexandria, occuring during the active time of Hipparchos as an astronomer. There are five matching eclipses in the time span -199 to 200 (ref 2)!
The eclipse of -128 Nov. 20 is regarded by many as the most likely match for this observation. It is total in the Hellespont and has a magnitude of 0.79 in Alexandria. But, it comes very late in Hipparchos' active life.
We might now redate Hipparchos by 232 years towards our time according to our previous hypothesis. If this is right he most likely has been active as an astonomer between AD 70 to 105.
One of the eclipses matching the observation is within this time span, on AD 71 Mar. 20! If this is Hipparchos' eclipse, he would have observed it when he was 29 years old.
The lunar eclipse. The second observation is a lunar eclipse described by Pliny as follows:
"He also discovered for what exact reason, although the shadow causing the eclipse must from sunrise onward be below the earth, it happened once in the past that the moon was eclipsed in the west while both luminaries were visible above the earth." (ref 3)
We are looking for a total lunar eclipse visible in Greece or Asia Minor, where the moon is setting eclipsed exactly at sunrise.
This is a typical midwinter observation. The nearer to winter solstice the better and longer the observability, probably also enhanced by refraction near the horizon line.
The frequency of such an occasion is about 1 to 4 per century.
Toomer (ref 6) argued that this must refer to the large total lunar eclipse of
-138 Nov. 26, when over a clean sea horizon as seen from Rhodes, the Moon was eclipsed in the northwest just after the Sun rose in the southeast.
If Hipparchos has lived 232 years nearer our time (AD 42 to 112) as redated above he could have observed the large total lunar eclipse of 65 Jan. 11 when he was about 23 years old, i.e. five years before his observations gained reputation.