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1Eisenstein’s Lattice Points . . . . . . . . . . . . . . . . . . . . . . . . . . . 42Chapter 1Introduction1.1Observation and Induction in MathematicsThere are even many properties of numbers with which weare well acquainted, but which we are not yet able to prove; onlyobservations have led us to their knowledge. Hence we see thatin the theory of numbers, which is still very imperfect, we canplace our highest hopes in observations; they will lead uscontinually to new properties which we shall endeavor to proveafterwards. The kind of knowledge which is supported only byobservations and is not yet proved must be carefully

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