Einstein considered the theoretical aspects. It can be derived from Maxwell's equations that the speed at which electromagnetic waves travel is:
c = (ϵ0μ0)^(−1/2) = 1/√ϵ0μ0.
Since light is an electromagnetic wave, that means that the speed of light is equal to the speed of the electromagnetic waves.
ϵ0 and μ0 are properties of the vacuum and are constants, so c will also be a constant.
According to Maxwell equations, an electromagnetic wave moving with velocity
v = 1/√ϵ0μ0.
Since light is an electromagnetic wave, that means that light is also propagating at this speed in vacuum.
And since both ϵ0 and μ0 are constant, that means 1/√ϵ0μ0 is also a constant. Hence light moves at a constant speed in vacuum.
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