(1) Can anybody suggest a readable reference for Schneider's theorem that the number
$$
\beta(a, b)=\frac{\Gamma(a)\Gamma(b)}{\Gamma(a+b)}
$$ is transcendental for $a, b \in \mathbb{Q}$ such that none of $a, b, a+b$ is an integer? 


(2) Fix some integer $n \geq 3$ Is the degree of transcendence of the field generated over $\mathbb{Q}$ by 
$$
\left(\beta(\tfrac{i}{d}, \tfrac{j}{d})\right)\_{i, j=1, \ldots, d-1}
$$ known? 



transcendence of beta values
Scheider's original paper is available [online](http://www.digizeitschriften.de/dms/img/?PPN=PPN243919689_0183&DMDID=dmdlog12). The theorem you quote is proved at the end of Section 1, on Page 114. I don't know the answer to your second question, but my guess is "no".


