His conquest of Thrace in 356 B.C. had given him command of gold mines which at once began to yield him precious metal to ten times the amount then coming to Athens from the failing silver of Laurium. = 

(1)

His conquest of Thrace in 356 B.C. had given him command of gold mines 

(2)

which（=gold mines ） at once began to yield him precious metal 

(yield him precious metal = yield precious metal to him )

(3)

to + ten times the amount / then coming to Athens 

(then coming = that came at that time)

(4)

from the failing silver of Laurium.

Laurium是希腊山名， 

failing 这里指银产量苟延残喘，即将倒闭

from = 来自

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Thrace 色雷斯：巴尔干半岛东南部一地区和古国