Eratosthenes' Ratio for the Obliquity of the Ecliptic

@article{Fowler1983EratosthenesRF,
  title={Eratosthenes' Ratio for the Obliquity of the Ecliptic},
  author={D. Fowler and D. Rawlins},
  journal={Isis},
  year={1983},
  volume={74},
  pages={556 - 562}
}
A recent article in Isis by Dennis Rawlins on Eratosthenes' astronomy raises many issues, one of which I would like to return to here: the assertion, in connection with Eratosthenes' ratio for the obliquity of the ecliptic, that "the ancients had stumbled upon the continued-fraction method (repeated inversion and dropping of the integer) . . ." with the following example of such a calculation: 
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