Be有沒有現在分詞?

BE = am, are, is ( present tense)
BE = was , were = past tense
BE = have / has been = present perfect tense
BE = had been = past perfect tense
BE = will be/ shall be = future tense

While (When Is better) I was at the library , I saw two naughty boys

"Being" is correct.

首先檢查吓條題目:
While I .... at in library
這頭句已經有多個錯處
又at 又in 亦冇the的library似乎本身是錯的句式
再者用While作開頭的句意思上是講在某段時間進行(主動詞)時的"同時"後句的情況發生了。
但這例句的場景和動詞是"在圖書館內"而不是我在進行某動作"期間"我見到兩個頑皮男孩。

假如不理句子本身我就只會寫
When I was in the library, I saw two naughty boy.
因為我是在講述之前我在圖書館時發生了的情況
所以除了用past tense同意原例句外，「在圖書館時」這處境並不是"進行中"的，因此不能/不應該用while.
除非句字的內容講述是
While I was reading the newspaper in the library, I saw two naughty boy playing round the bookshelves.當中while的情況是指「我看在報紙的那段時間」。

另外還可以討論was being的意思並不是"正在那裏"的過去進行式，being是指本質或個人的狀態。
Being a mother, I need to take care of my baby all the time.
I was being foolish to trust him with my money on that investment fund.