Semi- is a Latin prefix meaning "half" and colon is another punctuation. Should I therefore say that semicolon is a halved colon?
Yes, a semi-colon (;) is half a colon (:) above a comma (,).
You Have a Point There. A Guide to Punctuation and its Allies (PDF) by Eric Partridge says:
As THE name semicolon, half a colon, indicates, the semicolon comes historically after the colon; but in practice it is more important—at least, in the sense of being more popular. If anybody uses one more than the two simple points, period and comma, that additional point is usually the semicolon. By its very form (;) it betrays its dual nature: it is both period and comma. As it is half a colon, so is it also a modified period and a strengthened comma.
The earliest citation in the OED:
a1637 B. Jonson Eng. Gram. in ˆ (1692) 690 A Semicolon is a distinction of an imperfect Sentence, wherein with somewhat a longer Breath, the Sentence following is included.
I found a 1636 from The principles of musik, in singing and setting by Charles Butler:
As de de Ditti is distinguished wit Points, [Period, Colon, Semicolon, and Comma ;] so is de Harmoni, answering unto it, wit Pauses, and Cadences.
It may also appear in Butler's The English grammar: or, The institution of letters, syllables, and words, in the English tongue : whereunto is annexed an index of words like and unlike (1633); Google Books returns it as a result but doesn't show the text and I can't find an online copy.