Does the highlighted sentence mean:
1. even when kings gradually gave way to democracy, statesmanship and military valour were still important
or
2. when kings gradually gave way to democracy, statesmanship and military valour became important
Context:
Greek achievements in science and the arts went hand in hand with chronic war between the many city-states. As a result, while the rule of kings gradually gave way to democracy, statesmanship and military valour received high esteem. Human activity became the measure of all things – gods differed from people only in being immortal. If
humankind warred, so did the gods. In their buildings, the Greeks included battle scenes. Many pediments and friezes on their numerous temples feature military conquest and sculptures of fallen warriors. Often, as in the Temple of Zeus at Olympia (468–460 bc), the scenes were symbolic.
I think #2 is the correct interpretation.
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It's closer to your #1. The second interpretation is wrong.
Statesmanship and military valour are the sorts of things that were valued in the days of kings, therefore they could not have become an important part of life when democracy was starting up.
The kings had given way to democracy, but the remnants of their era continued to be important.
The writer has not made the meaning clear. The relation between the rule of kings and the esteem in which statesmanship and valor are held is not explicit in the paragraph, and it is not apparent to the mind. If the writer meant your #1, he should have written "although the rule of kings gradually gave way to democracy, statesmanship and military valour continued to receive high esteem." If he