你翻译的很好：在文明人中曾经（有人）认为…
by some magical power 介词短语,意思是 “通过某种魔力）,作方式状语.by "通过.”
又如：He earns his living by writing (他通过写作谋生） by不能用其他词代替
that ginger root by some magical power could improve这是一个主语从句,从句中ginger root是主语,could improve 是谓语.the memory 是宾语.
我们把这个主语从句改为宾语从句：Among civilized people ,some people thought that ginger root by some magical power could improve the memory.
意思是：在文明人中,有些人认为,姜根通过某种魔力的制作可以改进记忆力.