I have been seeing this use of would in a book I am reading. Although I understand the meaning I don't understand the grammar. Is it the correct use of would? Here is an example of it:
"I would we leave here as soon as we can."
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As others have mentioned,
Would that ___ were _____.
Would that it were!
is an largely obsolete way of expressing regret and desire mentioned in more detail here, and I suppose amounts to a sort of odd emphatic subjunctive mood.
Those of us of a certain age (or those of us of 'a certain ilk, stamp or kidney') can remember when such phrases were still common enough to not only be said on pretentious BBC quizzes, but to be lampooned by the great Fry and Laurie, as you can see here.
And for English language learners who are utterly confused by that sketch, you should know that Robert Robertson, possessor of the most epic combover ever seen, was a British television presenter of various highbrow quizzes and word games in the 70s and early 80s, and delighted in such archaic linguistic affectations.