In 1794 Vega’s second estimate of was published . Vega used Euler’s formula of the form . The picture from  ("results from Thesaurus") shows that he calculated to 143 decimal places and the other values to 144 places. In fact he took the calculation of from his first calculation of π, which was correct to 137 decimals.
To calculate , he summed positive and negative terms separately: . Here , , , , ….
So Vega's calculation is presented as , where and are the sums of the positive and negative terms of the series for .
Comparing exact Mathematica calculations with  shows that Vega calculated the positive part correctly to 139 decimals, the negative part correctly to 142 decimals, and the final estimate of was correct to 136 decimals.