Gauss's thesis: Theory of equations or hypergeometric functions, or both?

Question

I had read in multiple places, and always believed, that the first good proof of the fundamental theory of algebra (that a polynomial of degree $n$ over $\Bbb{C}$ has $n$ roots, with suitable treatments for multiple roots) was provided by Gauss's doctoral thesis.

But it is also stated (for example, in Concrete Mathematics) that Gauss's dissertation presents many of the subtle properties of hypergeometric functions with two upper and one lower index (which are now called "Gaussian Hypergeometric Functions").

It is certainly plausible that a thesis contains multiple loosely-related topics; my thesis in Supergravity was like that. Still, these two topics are two towering results, and I naively can find no connection between them at all. For all I know, there may be other important results in the same thesis as well. Which brings me to my real question:

Is there a readable translation of Gauss's doctoral dissertation/thesis?

Answer 1

Here's a good translation. Gauss' original writing is a little old fashioned but still perfectly readable.

http://archive.larouchepac.com/node/12482

The flaw doesn't have anything to do with hypergeometric functions as far as I know. The trouble is he assumes without proof that a real algebraic curve that enters a circle must leave it again.

Answer 2

The MacTutor biography mentions "Disquisitiones generales circa seriem infinitam" as introducing the hypergeometric functions. This was not his doctoral thesis: it is dated 1812. His doctoral dissertation "Demonstratio Nova Theorematis Omnem Fvnctionem Algebraicam Rationalem Integram Vnus Variabilis In Factores Reales Primi Vel Secvndi Gradvs Resolvi Posse" from Helmstedt was in 1799, and was about the Fundamental Theorem of Algebra.