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2-dimensional A(Sf admissible lattice arbitrarily small automorph basis boundary of Jf boundary point bounded bounded set Cassels Chapter clearly co-ordinates concludes the proof continued fractions convex body theorem convex set convex symmetric Corollary critical lattice Davenport defined definite quadratic form denote determinant dimensional diophantine approximation distance function distance-function equivalent exist finite number follows at once geometry of numbers given Hence homogeneous linear transformation hyperplane inequality infimum infinitely integers lattice constant Lemma Let F(x linear forms linearly independent points Lond Mahler Math Minkowski-Hlawka Theorem Minkowski's convex body Minkowski's theorem Mordell non-singular packing parallelopiped point of Sf points x1 positive number Proc proof of Theorem proportional to integral quotient space real numbers result Rogers satisfies sequence set of points set Sf shape sphere star-body successive minima suppose without loss symmetric convex tac-plane Theorem IV Theorem VII trivial V(Sf values vectors VIII volume