Here assuming is a linking word, not the -ing of a verb in progress. You use it when you take a possible situation as true for a moment, and then say what follows: Assuming it doesn't rain, we'll eat outside. It means “if we treat this as true…” and it often pairs with that (assuming that the train is on time).

Here assuming is a linking word這裡的 assuming 是一個連接詞，not the -ing of a verb in progress不是進行式動詞的 -ing。You use it when you take a possible situation as true for a moment你用它的時候，是先把一個可能的情況當成暫時成立，and then say what follows然後接著說接下來會怎樣：Assuming it doesn't rain, we'll eat outside「Assuming it doesn't rain, we'll eat outside」（假設不下雨，我們就在外面吃）。It means "if we treat this as true…"它的意思是「如果我們把這件事當作成立的話……」and it often pairs with that而且常常跟 that 搭配 (assuming that the train is on time)（assuming that the train is on time，假設火車準時）。

It is everyday and polite, a softer cousin of if. Speakers use it when the “if” is a working guess, not a wild dream.

It is everyday and polite這是日常又客氣的說法，a softer cousin of if是 if 比較柔和的近親。Speakers use it when the "if" is a working guess說話者用它的時候，這個「if」是一個站得住腳的推測，not a wild dream而不是天馬行空的幻想。

Though actually, assuming can also be an adjective meaning “too sure of yourself, a bit arrogant” — an assuming manner — but that use is older and rarer; students almost always meet the “if we take this as true” use.

Though actually不過事實上 assuming can also be an adjective meaning "too sure of yourself, a bit arrogant"assuming 也可以當形容詞，意思是「太自信、有點自大」——an assuming manner「an assuming manner」（自大的態度）——but that use is older and rarer不過這個用法比較老舊、也比較少見；students almost always meet the "if we take this as true" use學生幾乎都是遇到「把這件事當作成立」的這個用法。

Put a comma when the assuming-clause comes first. And notice it does not prove the thing will happen; it only builds the next sentence on that guess.

Put a comma當 assuming 子句放在前面時 when the assuming-clause comes first要加逗號。And notice而且要注意 it does not prove the thing will happen它並不能證明那件事一定會發生；it only builds the next sentence on that guess它只是把接下來的句子建立在這個推測上。