Mathematician here; I don't even know what you are speaking about. There have always been homogeneous and inhomogeneous equations, treated somewhat differently (because solutions of homogeneous equations are stable under dilation). So I highly suspect your premise to be completely wrong (there has never been such a thing as a Law of Homogeneity). For one thing, Viète was instrumental in solving the third- and fourth-degree polynomial equations, which are decidedly inhomogeneous.

What might have hampered somewhat mathematicians is the lack of abstraction: i.e. needing to represent all quantities in an equation as lengths or surfaces, etc. However, the progress of abstraction and notation was quite parallel to the progress of techniques (see the apparition of Arabic digits in the 13th century, the + and - signs in the 15th, the = sign and abstract variables in the 16th, and powers in the 17th and 18th centuries).