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The principle of relativity first appeared in its modern form in 1905 in the works of Henri Poincaré “On the dynamics of the electron”. However, establishing the (Galilean) principle of relativity of (Newtonian) mechanics as a general principle of physics had a complex gestation in Poincaré’s works. We discuss his physics course at the Sorbonne in 1889 in which he generalized Fresnel’s conclusions of 1818 on refraction in Arago’s prism experiment (the “principle of relative motion” extended to optics). Then we discuss his scientific articles in the journal Éclairage électrique in 1895 in which he confronted Lorentz’s theory with the Newtonian principle of reaction that applies to matter alone (his “objection” to the theory). Poincaré emphasizes herein the “connection” of this principle with the principle of relative motion. In order to better understand this issue, we return in detail to Poincaré’s fundamental article “The theory of Lorentz and the principle of reaction” on the occasion of the December 1900 Jubilee celebration of Lorentz’s defence of his doctoral thesis in which he specifies the conditions required to extend these principles to electrodynamics. In conclusion, we will see how in 1905, the principle of relative motion becomes the “postulate of relativity” in connection with the “perfect coherence” of Lorentz’s theory. To our knowledge our article is the first to give an overall perspective of the works of Poincaré from 1889 to 1900 as mentioned above and to the logic that connects them.