Gaussian Intrinsic differential geometry and non-euclidean geometry

Aim To study the relations between the thought of Gaussian intrinsic differential geometry and Gauss′s earlier research on non-Euclidean geometry.Methods Sources investigation and analysis,and the comparative historical approach of mathematics.Results A view of better understanding origins of Gaussian intrinsic differential geometry is presented,and the intrinsic relation between Gauss′s thought of intrinsic differential geometry and of his non-Euclidean geometry is brought to light and discussed.Conclusion By presenting his disquisitions generales circa superficies curves in 1827,Gauss presented in fact the essential idea of his earlier research on non-Euclid geometry in his unique way as well.