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In this Note it is worked out a new set of Laplace-Like equations for quaternions through Riemann-Cauchy hypercomplex relations otained earlier  . As in the theory of functions of a complex variable, it is expected that this new set of Laplace-Like equations might be applied to a large number of Physical problems, providing new insights in the Classical Fields Theory.doi:10.12732/ijpam.v90i4.2 fatcat:o4xxlryu5vdtjbtgnz7bty5uam