An Alexandrine is a verse of iambic hexameter — i.e., a verse of six feet, each of which has the stress on the second beat.
Although twelve-syllable verses are very common in French poetry, they’re rare in English. Alexandrines are sometimes introduced into predominantly pentameter verse for the sake of variety. The Spenserian stanza, for instance, is eight lines of pentameter followed by an Alexandrine. In the Restoration and eighteenth century, poetry written in couplets is sometimes varied by the introduction of a triplet in which the third line is an Alexandrine, as in this example from Dryden, which introduces a triplet after two couplets:
But satire needs not those, and wit will shine
Through the harsh cadence of a rugged line:
A noble error, and but seldom made,
When poets are by too much force betrayed.
Thy generous fruits, though gathered ere their prime,
Still showed a quickness; and maturing time
But mellows what we write to the dull sweets of rhyme.
From the Guide to Literary Terms by Jack Lynch.
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Note: This guide is still in the early stages of development.
Three question marks mean I have to write more on the subject. Bear with me.