Definition of "methought"

The clouds methought would open and show riches / Ready to drop upon me, that when I wak'd / I cried to dream again.

1610–1611 (date written), William Shakespeare, “The Tempest”, in Mr. William Shakespeares Comedies, Histories, & Tragedies […] (First Folio), London: […] Isaac Iaggard, and Ed[ward] Blount, published 1623, [Act III, scene ii]

Methought I saw my late espoused saint / Brought to me, like Alcestis, from the grave,

1673, John Milton, Methought I Saw my Late Espoused Saint

Methought I was immersed in a cataleptic trance of more than usual duration and profundity.

1844, Edgar Allan Poe, The Premature Burial

Then, methought, the air grew denser, perfumed from an unseen censer / Swung by Seraphim whose foot-falls tinkled on the tufted floor.

1845 February, — Quarles [pseudonym; Edgar Allan Poe], “The Raven”, in The American Review‎, volume I, number II, New York, N.Y., London: Wiley & Putnam, […]

And then methought my dream changed, and two Great Giants with heading-axes came striding over the bed, […]

1862 February, George Augustus [Henry] Sala, “The Strange Adventures of Captain Dangerous; a Narrative in Plain English, […] Chapter the Fourth. My Grandmother Dies, and I am Left Alone, without So Much as a Name.”, in George Augustus Sala, editor, Temple Bar: A London Magazine for Town and Country Readers, volume IV, London: Office of "Temple Bar," 122 Fleet Street; Ward and Lock, 158 Fleet Street; New York, N.Y.: Willmer and Rogers, page 304