The book titled "Discourses & Mathematical Illustrations pertaining to the Extinction Shift Principle under the Electrodynamics of Galilean Transformations" in a published treatise on a replacement for the Theory of Relativity. The book summarizes manuscripts that illustrate the solutions to physics problems that made Relativity famous, obtaining the exact mathematical equivalence to Relativity but without any use of Relativity whatsoever.
The "pure" classical solutions of all the famous problems, both pertaining to electromagnetism and gravitation, has been treated in this book. A completely overlooked alternative using only Galilean transformations in Euclidean Space Geometry under Principal Axioms of the Extinction Shift Principle was demonstrated with step by step mathematical illustrations. Problems such as the text book examples pertaining to the invariance of the wave equations demonstrates how current orthodox treatments have consistently, incorrectly applied Galilean Transformations and thereby incorrectly concluded that the Wave Equations were not invariant under Galilean Transformations. The not measurable, undisturbed phenomenon of the primary wave and the electrodynamics of the re-emission thereof, until now, has never been correctly treated and applied.
In this book, the invariance of the "wave equation", the velocity dependent "effective" mass as opposed to relativistic mass, the transverse relative time shift as opposed to Time Dilation, the planet Mercury perihelion drift and the PSR1913+16 Perihelion Drift, gravitational redshift, solar light bending, etc., getting the precise mathematical equivalence to Relativity, but without any use of Relativity whatsoever, was demonstrated. As single set of Principal Axioms governing the application of Galilean Transformations in Euclidean Space were successfully used for the very first time, in both the Electromagnetism and Gravitation, in the mathematical illustrations pertaining to the Extinction Shift Principle. The procedures that lead to the pure classical solutions were explainable using basic, elementary mathematics and intuitive reasoning, requiring essentially 100 pages.