Hipparchus on the distances of the sun and moon

TLDR: In the case of the sun, it is quite uncertain not merely how great a parallax it has, but whether it has any at all as discussed by the authors, which is a consequence of certain other properties of the Sun and Moon that when the distance of one of the luminaries is given that of the other is also determined, the ratios of the moon's distance [to the earth's radius] came out different for each of the hypotheses he set out.

Abstract: "Hipparchus' investigation of this topic is based principally on the sun. For since it is a consequence of certain other properties of the sun and moon (which we shall discuss below) that when the distance of one of the luminaries is given that of the other is also determined, he tries to demonstrate the distance of the moon by guessing the distance of the sun. He first assumes that the sun has only the least perceptible parallax, in order to find its distance, and afterwards uses the solar eclipse which he adduces. At one time he assumes that the sun has no perceptible parallax, at another that it has a significant [ixavov] parallax : as a result the ratios of the moon's distance [to the earth's radius] came out different for him for each of the hypotheses he set out. For in the case of the sun it is quite uncertain not merely how great a parallax it has, but whether it has any at all".