Posteriors of the cosmological parameters S₈, Ω_m, and Ω_b, analysing a synthetic Euclid DR1 joint data vector of second- and third-order weak lensing statistics. We consider several cases. First, a gravity-only (GrO) data vector was analysed with a GrO model (purple contours). We obtain the black contours when baryonic effects are included in the data vector but not in the model. In orange, we illustrate the constraints we get when all elements of the data vector are excluded where the baryonic data vector deviates by more than 0.4σ from the GrO data vector. Lastly, we show the results if the model includes baryonic feedback in red and blue, where we fixed the baryon parameters to the truth in the blue case and marginalised over all five parameters for the red. The grey dashed line indicates the underlying D3A cosmology.