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From: Webster's Revised Unabridged Dictionary (1913)

 Syl·lo·gize v. i. [imp. & p. p. Syllogized p. pr. & vb. n. Syllogizing ]  To reason by means of syllogisms.
    Men have endeavored . . . to teach boys to syllogize, or frame arguments and refute them, without any real inward knowledge of the question.   --I. Watts.