實體上的平
這一支就是核心畫面本身，其他用法都是從這裡搬出去的。
r · C1
In a way that lies level against a surface or stretches out level, with nothing lifted up or sticking out.
平貼地、平坦地
核心畫面
One way to hold flatly: picture something pressed down until the whole of it touches — a sticker smoothed onto a book, sand running level to the sea. Nothing lifted, nothing sticking out, nothing to catch hold of. That is the plain physical use. Move the same picture onto speech and it works twice over. A no said flatly has no gap in it, nothing to argue with, nothing to pull at. A sentence said flatly has no rise and fall in it, so there is nothing in the voice for a listener to read. One surface; two things that can be made level — an answer, and a voice.
可以想成一樣東西被壓到整個面都貼上去：貼紙抹平在書上，沙地一路平到海邊。沒有翹起來的地方，沒有凸出來的地方，也沒有可…更多收起
可以想成一樣東西被壓到整個面都貼上去：貼紙抹平在書上，沙地一路平到海邊。沒有翹起來的地方，沒有凸出來的地方，也沒有可以勾住的地方。這是最實在的用法。把同一個畫面搬到說話上，它一次可以用在兩件事上。一句 flatly 說出來的「不」，中間沒有縫，沒得爭，也拉不動。一句 flatly 說出來的話，語調沒有高低，聽的人在聲音裡讀不到東西。同一個「平」，一個壓在答案上，一個壓在聲音上。From the word’s history
Wiktionary gives flatly as flat plus -ly, tracing flat back through Middle English to Old Norse flatr and Proto-Germanic *flataz. So the level surface is the word's starting point, and the speech uses are that surface carried over.
Wiktionary 把 flatly 拆成 flat 加 -ly，並把 flat 一路追到古諾斯語 flatr 和原始日耳曼語 *flataz。所以「平面」是這個字的起點，用在說話上的兩個意思，都是把這個平面搬過去用的。
Wiktionary, 'flatly' (adv) etymology tree, supplied in evidence packet (source_ref kaikki:3f6f69a190036ae4:1351097204)
Two branches
說話上的平
把「整面貼平、沒有縫隙」這個畫面搬到嘴上：可以壓平的是答案，也可以壓平的是語調。
r · B2
Used before verbs like refuse, deny, reject and contradict to say that someone said no in a short, direct way that leaves no room for argument.
斷然地、一口回絕地