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a'nn absolute value arbitrarily large arbitrarily snail arithmetic mean assume Bachmann boundary classical theorem coefficients completely proved conclude consecutive convergents continued fraction correspond degree of Doctor Denoting determinant unity diagonals Doctor of Philosophy equal exist factor form f forms of determinant fully adequate geometric mean given by Tchebychef grams hand side Hence Hermite inequality integral values irrational Kence large enough n last equation Lemma Lenna less limit linear forms m n p method minima Minkowski's nade arbitrarily nx-my=N obtain Oeuvres outlined parallelo parallelogram plane Professor Blichfeldt published a proof quadratic quantities is never read this thesis real numbers relatively prime integers Remak rill scope and quality snail for large solution in Integers STANFORD UNIVERSITY LIBRARIES substitution Supposing Tchebychef's theorem theorem is completely theorem is proved tine trie true Tv/o variables write x-ay