In the following sentence, what does 上的 mean?
I translated it as "Archaeologists know the Xia, Shang and Zhou collectively as the Bronze Age." I think I have the gist of it, but I don't understand how 上的 is functioning.
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You have made a wrong pause in the sentence……
It should be "中国历史学上的|夏、商、周|属于|考古学上的|青铜时代。".
It is "in Chinese history". "in Chinese history" = "中国历史学上的"
It can be roughly translated to "in" in English. 夏商周 in history belongs to the bronze age in archeology.
上 here means based on some theory / academic field.
历史上 means 'in history'.
The full sentence translates as:
The Xia, Shang and Zhou dynasties in Chinese history all belong to the Bronze Age in archeology.
历史上最大的帝国 The largest empire in history
You can regard "A 上的 B" as "B in the field of A"
This may help you understand how the sentence is organised and find a proper translation.
技术上的问题=Problem in the field of technique=technical problem.
__ 上的 can be translated into different word under different context, but the general idea is that it confines or narrows our discussion. ...上 means on the topic of ... or in the sense of ...
考古學上的發現 - archaeological findings 生物學上的實驗 - biological experiments 物質生活上的快樂 - material happiness 精神上的體驗 - spiritual experience 理論上而言 - theoretically speaking 基本上 - tasically 金錢上的報酬 - monetary reward 科技上的發展 - technological advancement
We use ...上的 especially when talking about some subject of study or science. You insert pretty much anything that is a field of science or study before 上的：文學上的、科學上的、哲學上的、心理學上的、物理學上的、化學上的、地質學上的、地理學上的......
In the sentence "中国历史学上的", "上的" means "in the scope" of previous mentioned domain. In your case, "中国历史学上的" means "in the scope of Chinese Historiography".
However, this is only the translation of the meaning. Depending of the context, it could be translated in a better way.