  Recent advances in techniques of critical close reading of historical texts
can now be applied to records of pre-telescopic celestial observations -
allowing significant progress for analyzing and solving orbits of past comets:
we exemplify our method by solving the orbit of the comet in AD 760 only with
historical observations and then identify it with 1P/Halley. A detailed
eyewitness record with drawing of a comet in AD 760 in the Syriac Chronicle of
Zuqnin (finished AD 775/6) was not yet included in the study of its orbit - the
Chinese reports alone do not yield a sufficient number of dated positions. We
analyze the Syriac and Chinese sources with critical methods for quantitative
astronomical usage, we also consider a few further records from the
Mediterranean and West Asian area. With our conservatively derived dated
positions we can determine the best fitting Keplerian orbital solution by least
squares fitting yielding the orbital elements; the parameter ranges for
non-periodic solutions and highly eccentric periodic solutions are consistent
with each other. The allowed parameter ranges for perihelion distance and
inclination are sufficiently small to identify the comet with 1P/Halley.
Although 1P/Halley is the only comet, where the telescopic orbit is credibly
linked to pre-telescopic returns, e.g. to AD 760, our identification confirms
claims from extrapolating telescopic observations backward in time - here
independently based on historical data. In particular, we obtained a precise
perihelion time (760 May 19.1 \pm 1.7). The inferior conjunction between comet
and Sun as on the previously published orbit (760 May 31.9) is shifted by about
one day compared to our new orbit (June 1.8), only the new one is consistent
with the last observation (June 1.0) before conjunction as reported in the
Chronicle of Zuqnin. We also study the comet's brightness evolution ...
