Space, Time, Matter
In this classic text first published in German in 1918-this is a translation by HENRY L. BROSE (1890-1965) of the 1921 fourth edition-Weyl considers the role of Euclidean space in physics and the mathematics of Einstein's general theory of relativity, exploring: foundations of affine and metrical geometry conception of n-dimensional geometry tensor algebra the stationary electromagnetic field Riemann's geometry affinely connected manifolds space metrics from the point of view of the Theory of Groups relativistic geometry, kinematics, and optics electrodynamics of moving bodies mechanics of the principle of relativity mass and energy gravitational waves concerning the interconnection of the world as a whole and more.HERMANN KLAUS HUGO WEYL (1885-1955)was a German mathematician who spent most of his life working in Zurich, Switzerland. When the Nazi party began to gain power he fled to a job at the Institute of Advanced Study in Princeton, New Jersey where he continued to develop his representation theory. He was one of the most influential mathematicians of the 20th century. He greatly impacted theoretical physics and number theory and was the first to combine general relativity and electromagnetism
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according affine geometry affine relationship arbitrary assume atom axioms bilinear body characterised co-efficients co-ordinate system conception condition congruent transformation const constant contra-gredient contra-variant components corresponding curvature curve definite denote density derived determined differential form dimensional direction distance Eiemann's Einstein electric electron energy Euclidean geometry Euclidean space expressed force formula four-dimensional function fundamental geodetic given gravitational equations gravitational field hence holds independent inertia infinitely infinitely near points infinitesimal integral invariant linear form linear transformations magnetic manifold mass mathematical matter Maxwell's Maxwell's equations means measure mechanics metrical field metrical groundform metrical space metrical structure motion non-Euclidean geometry ordinate system orthogonal parallel displacement plane point-mass positive potential principle of relativity proper-time quadratic differential quadratic form quantities respect result rotation scalar second order skew-symmetrical sphere statical straight line surface symmetrical tensor-density theorem theory of relativity vanish variables velocity vide note world-line world-point