Did Ptolemy and other Greek scientists actually measure the distance to the Sun?

Question

According to Subhash C. Kak: Early Theories on the Distance to the Sun: “Pancavimsa Brahmana states that the heavens are 1000 earth diameters, de, away from the earth. The sun was also taken to be halfway to the heavens, so this suggests a distance of the sun, Rs, about 500 earth diameters from the earth. The confirmation for this supposition comes from the later theories (c. 500 AD) from the same region and from Greek ideas that speak of roughly the same distance."

In contrast to Hipparchus and Ptolemy’s accounts, I assume that the Veda scriptures do not mention any measurement approach. However, given the errors – se below - we must assume prevailed in the measurements of the e.g. Sun-Moon-Earth right angle triangle at half Moon makes one wonder if the distance to the Sun (in Earth units) was perhaps fitted to earlier references such as the one above, assuming there were exchanges of information perhaps via Babylonian astronomers. Is there any account of the actual measurement available?

From Erik Høg: Astrometric accuracy during the past 2000 years, Niels Bohr Institute, Copenhagen, https://arxiv.org/ftp/arxiv/papers/1707/1707.01020.pdf.

Answer 1

No, they did not. Several methods were proposed but they do not give "correct" distances. Of course, all depends on the exact meaning of the word "measure" and "correct". But their estimates were orders of magnitude away from the true numbers.

Some details are given here: Historical knowledge of Distance of Earth from Sun

and also here the related subjects are discussed: Who first measured the distance to the Moon? How was it done?

Where did Ptolemy compare the Earth to the distance of fixed stars?

How did Ptolemy calculate the distance to the moon

Edit. On the source of the number 10000 seconds. This is about 1/4 of a degree, which is the usual precision of numbers given in Ptolemy. With this accuracy Ptolemy knew that "the Sun has no parallax". Which gives a LOWER estimate of the distance. Speaking of Hipparchus, almost none of his writings survive (the only surviving text is not mathematical), so our principal source on Greek astronomy is Ptolemy, and it is open to wide speculation what exactly in Ptolemy comes from Hipparchus or other earlier astronomers.