History of the theory of equations: John Colson This is an EDIT version of my original question:
Recently I've been interested in the history of the Theory of Equations. The thing is that I learned about this mathematician named John Colson, he published a very interesting paper: Aequationum Cubicarum & Biquadraticarum, tum Analytica, tum Geometrica & Mechanica, Resolutio Universalis in the Philosophical Transactions, he was a contemporary of De Moivre, althought he published his infamous formula in 1722, also in the Philosophical Transactions (I made a question about it before) and Colson in 1706.
Now, on to the paper, remember, I'm not fluent in latin, so there might be things that I miss.
He presents his work with the three roots of a given universal cubic equation, & the way he presents them is by representing them as linear combination of the roots of unity, first he shows with 7 examples that considering the roots as such, works!
Subsequently to the examples, he actually shows how he got that the roots can be written like that. I was thinking of writing down all the procedure, but is very long, and is actually very understandable from the paper. However, if you want to know my interpretation from a particular sentence, I'm pretty much done with the translation (just the cubic part), just remember I'm not fluent in latin, & probably I committed big mistakes with the interpretation.
I consider his work to be very original (diferent) for his time, I don't know when the use of roots of the unity was introduced, probably before him, but he definitely gave them some play, since (almost) everything related to solving those equations seemed very geometrically based, i.e., a lot of the things people would use to solve the cubic, for example, were derived from geometric properties, we can see that he works the other way around,  remember the name of the article: "Universal solution of the biquadratic and cubic equations, both analytical and geometrical and mechanical", from algebra he gets the geometry.
I don't know if I'm making much sense, but let see if this picture helps. I belive this is something Descartes said, I don't remember very well, but this was the way people of Colson's time used to think.

What this represents, is that if you have a problem in geometry, then you can represent it with algebra, and if you have a problem in algebra, then it belongs to a problem in geometry. I hope this helps to illustrate my point.
(BTW, Galois, Abel and others later showed us that this not true)
Now the point of my question is, if Colson could represent the start of the independence of algebra from geometry. If we look at the big picture, and since many of us were born in the XX century, we know how this is going to end, so would it be so naive of my part to consider Colson as this kind of hero? Who could be a better representative for this?
Thanks!
 A: 
Now the point of my question is, if Colson could represent the start of the independence of algebra from geometry. [...] Who could be a better representative for this?

I would imagine Thomas Harriot would be a better representative than John Colson in terms of separating algebra from geometry.
From page 490 of Jacqueline A. Stedall. (2000). "Rob’d of Glories: The Posthumous Misfortunes of Thomas Harriot and His Algebra," Archive for History of Exact Sciences, vol. 54, pp. 455–497:

What should we now consider to be the ‘Improvements of Algebra to be found in
  Harriot’? The first and most obvious must be his notation: the use of lower case letters,
  with repetition to indicate multiplication, freed algebra for the first time from the geometrical connotations it had always previously carried. [...]
Dispensing with geometrical baggage, however, led to more than just the simplification
  of notation: it also made possible Harriot’s second great achievement, the handling
  of equations at a purely symbolic level. If the achievement of Descartes was to show how
  algebra could be applied to geometry, the achievement of Harriot was to liberate algebra
  from geometry altogether, so that for the first time it could become truly a subject in its
  own right. [...] Harriot’s finest contribution, however, was ‘to treat of
  Algebra purely by itself, and from its own principles, without dependance on Geometry,
  or any connexion therewith’. [...]  Harriot should be seen as the first to dispense entirely with geometric considerations, and as the first forerunner of modern abstract algebra.

Harriot's Artis analyticae praxis (The Practice of the Analytic Art) was published in 1631, ten years after his death.
