By looking at the original publications, rather than only at the articles and books talking of them, one finds
Galileo Galilei (1564-1642).
Dialogo sopra i due massimi sistemi del mondo, Tolemaico e Copernicano (1632)
Galilei states the relativity principle, without using the term, as a consequence of the experimental evidence, by stating that all possible experiments, with bodies interacting in any possible ways, performed inside a ship cannot show whether the ship is moving or not, provided the motion is uniform. The principle is stated to be valid for all the phenomena.
After having performed a number of experiments inside a ship standing in the harbour,
“... have the ship moving with whatever velocity, then (provided that the motion be uniform and not fluctuating in one or the other direction) you will not recognise any variation in any of the just mentioned effects, neither you will be able to recognise from any of them whether the ship is moving or standing.”
Jules Henri Poincaré (1854-1912)
L’état actuel et l’avenir de la Physique Mathématique (1904)
For the first time the term “Relativity Principle” is introduced and stated, on the basis of all the experiments performed at the time, including Michelson Morley, as
“According to the “Relativity Principle” the laws of the physical phenomena must be the same for a standing observer and for one in uniform translation motion; so that we have no means, neither we can have any, to chose whether we are or not transported in such a motion”
Albert Einstein (1879-1955)
Ist die Trägheit eines Körpers von seinen Energiehalt abhänging?, Ann. d. Phys, 18 (1905), 639
Principle of Relativity: “The laws by which the states of physical systems undergo change are not affected, whether these changes of state be referred to the one or the other of two systems of co-ordinates in uniform translatory motion.”
Hendrik Antoon Lorentz (1853-1928)
Deux mémoires de Henri Poincaré dans la physique mathématique, Acta mathematica 38 (1921), 293-308 (written in 1914)
“It was not me to establish the Relativity Principle as rigorously and universally valid. Poincaré on the contrary obtained the perfect invariance of the electrodynamic equations and formulated the “Relativity Principle”, a term that was first to use.”
Does anybody understand why usually only the last one, Einstein, is quoted, and the other forgotten?