書き留める: to write down

大切たいせつなことはメモに書き留かきとめておく。

I jot down important things in a memo.

稗田阿礼ひえだのあれという人ひとが覚おぼえていた話はなしを、書き留かきとめたといわれています。

It is said that he wrote down the stories that a person named Hieda no Are had memorized.