The origin of the theory of trepidation comes from the Small Commentary to the Handy Tables written by Theon of Alexandria in the 4th century CE.
Theon states that certain (unnamed) ancient astrologers believed that the precession, rather than being a steady unending motion, instead reverses direction every 640 years.
A more sophisticated version of this theory was adopted in the 9th century to explain a variation which Islamic astronomers incorrectly believed was affecting the rate of precession.
[2] This version of trepidation is described in De motu octavae sphaerae (On the Motion of the Eighth Sphere), a Latin translation of a lost Arabic original.
The third chapter of the Suryasiddhanta, verses 9-10, provides the method for computing it, which E. Burgess interprets as 27 degree trepidation in either direction over a full period of 7200 years, at an annual rate of 54 seconds.