Complex sentence: Lagrange gave a proof in 1775, based on his study of quadratic forms, which was simplified by Gauss in his "Disquisitiones Arithmeticae" (art.182).
Split into simpler sentences: Lagrange gave a proof in 1775 that was based on his study of quadratic forms. This proof was simplified by Gauss in his "Disquisitiones Arithmeticae" (art.182).