Wiktionary
note down
vb. To write down, especially hurriedly.
Usage examples of "note down".
And why didn't someone meet us instead of having a kid hand me a note down at the docks?
Send a note down to Amy that she cannot give her new literary pet-what's his name?
The lobsters would back down if we'd ram a stiff note down their throat.
But if we were able to note down the distances of places whence and whither cometh the body which is moved, or its parts, if it moved as in a wheel, we can say in how much time the motion of the body or its part, from this place unto that, was performed.