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Heaviside (1888, 1889) and Thomson (1889) first correctly calculated the scalar and vector potentials of a steadily moving point charge by transforming d'Alembert's equation for the potential for a steadily moving charge into Poisson's form for a static charge by elongating a coordinate axis lying along the direction of the charge translation. They thus developed a way to solve dynamic problems like static problems, using an auxiliary equation in the form of Poisson's potential equation. The present authors use this ingenious mathematical approach to derive from Maxwell's field equations alone many useful electrodynamic equations, including auxiliary Lorentz transformation equations.