泰 here is the old sense 'extreme / utmost', so
泰西 = 'the far west'. Coined by Ming-dynasty Jesuits like Matteo Ricci (
利玛窦 Lì Mǎ-dòu) to refer to Europe, and dominant through the late Qing — you'll find it in titles like 《
泰西新史揽要》(A Survey of Western History, 1894). Modern usage replaced it with
西方 (xī-fāng) and
欧美 (Ōu-Měi).
