Euler and the Gaussian Summation Formula for the Hypergeometric Series

We show that in his paper ``Plenior expositio serierum illarum memorabilium, quae ex unciis potestatum binomii formantur" E663 (E663: ``A more thorough exposition of those memorable series that are formed from the binomial coefficients") Euler could have found the Gaussian summation formula for the hypergeometric series from his own formulas in that same paper, if he actually set the task for himself.