We have re-analyzed the data used by Bessel, von Struve, and Henderson in the 1830s to measure the first parallax distances to stars. We can generally reproduce their results, although we find that von Struve and Henderson have underestimated some of their measurement errors, leading to optimistic parallax uncertainties. We find that temperature corrections for Bessels measured positions are larger than anticipated, explaining some systematics apparent in his data. It has long been a mystery as to why von Struve first announced a parallax for Vega of 0.125 arcsec, only later with more data to revise it to double that value. We resolve this mystery by finding that von Struves early result used two dimensions of position data, which independently give significantly different parallaxes, but when combined only fortuitously give the correct result. With later data, von Struve excluded the problematic dimension, leading to the larger parallax value. Allowing for likely temperature corrections, and using his data from both dimensions, reduces von Struves parallax for Vega to a value consistent with the correct value.
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