This is simple class field theory plus Galois theory. Consider a quadratic number field $K$ with class number divisible by $3$. For constructing an unramified cyclic cubic extension $L/K$, adjoin the cube root of unity, and denote the resulting field by $K'$. The Kummer generator of the Kummer extension $L' = K'(\sqrt[3]{\mu})$ must be an ideal cube for the extension to be unramified: $(\mu) = {\mathfrak m}^3$. Since $L'/K$ is abelian, Galois theory shows that the ideal class of ${\mathfrak m}$ must come from the quadratic subfield $F$ different from $K$ and ${\mathbb Q}' = {\mathbb Q}(\sqrt{-3})$. Thus the unramified cubic extensions of $K$ correspond roughly to the $3$-class group of $F$; any differences come from the fact that $\mu$ might be a unit.

The reflection theorem was found independently by Reichardt and then generalized by Leopoldt. For a dvi file of Scholz's article, see here. I might actually have an English translation in my files; if I do, I'll put it here.

This is simple class field theory plus Galois theory. Consider a quadratic number field $K$ with class number divisible by $3$. For constructing an unramified cyclic cubic extension $L/K$, adjoin the cube root of unity, and denote the resulting field by $K'$. The Kummer generator of the Kummer extension $L' = K'(\sqrt[3]{\mu})$ must be an ideal cube for the extension to be unramified: $(\mu) = {\mathfrak m}^3$. Since $L'/K$ is abelian, Galois theory shows that the ideal class of ${\mathfrak m}$ must come from the quadratic subfield $F$ different from $K$ and ${\mathbb Q}' = {\mathbb Q}(\sqrt{-3})$. Thus the unramified cubic extensions of $K$ correspond roughly to the $3$-class group of $F$; any differences come from the fact that $\mu$ might be a unit.

The reflection theorem was found independently by Reichardt and then generalized by Leopoldt. For a dvi file of Scholz's article, see here.

Edit.Here's an English translation.