Original: One of those states (Schwarzburg-Arnstadt) was based in Arnstadt; it was founded in 1574 and existed until 1716, when it fell to Schwarzburg-Sondershausen.
Simplified: One of those states (Schwarzburg-Arnstadt) was based in Arnstadt; it was founded in 1574 and existed until 1716, when it became part of Schwarzburg-Sondershausen.