History of Algebra: when did Geometric terminology evolve into more modern Algebraic terminology?

[topsquark]

I'm not sure how to do a search on this.

I was recently looking over a post that mentioned something along the lines of "we didn't used to use symbols for unknowns..." Clearly when "The Elements" were written variables weren't used quite the way we use them now. I think what I'm asking is when did Geometric terminology evolve into more modern Algebraic terminology like "x + 2 = 3, x + 2 - 2 = 3 - 2, etc." to solve problems?

-Dan

 

[JeffM]

I think you were quoting me.

My recollection is that Vieta started using letters to stand for unknowns or variables in the late 16th century; Cardano was still using words like "cosa" in the mid-16th century. But Vieta's method was not the same as ours. So our method evolved during the 17th century, perhaps led by Descartes. My impression is that it evolved rapidly and was stabilized by about 1650, but I am not sure of those facts. I have never seen a history of the development of moderb mathematical notation.

 

[Dr.Peterson]

I have a copy of Cajori's A History of Mathematical Notations sitting within arm's reach. It's a big book.

A sort of summary of this topic, much of it referenced to that book, can be found here.