GNU Collaborative International Dictionary of English
Found one definition
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Mesmerize (?), v. t. [imp. & p. p. Mesmerized (?); p. pr. & vb. n. Mesmerizing (?).] [Also spelled mesmerise.]
1. To bring into a state of mesmeric sleep; to hypnotize.
[1913 Webster]
2. To produce an intense fascination in; to spellbind.
[PJC]