Lewis & Short

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syllŏgismătĭcus, a, um, adj., = συλλογισματικός, consisting of syllogisms, syllogistic: breviloquium Aristotelis, Fulg. Myth. 1 praef. fin.

syllŏgismus or -os (syllogismus, Sid. Pan. 205), i, m., = συλλογισμός, a form of reasoning in which a conclusion is drawn from two premises, a syllogism (post-Aug.), Gell. 2, 8, 7; Sen. Ep. 108, 12; 113, 26; Plin. Ep. 2, 3, 3; Quint. 3, 6, 43; 3, 6, 77; 3, 6, 88; 3, 6, 103; 5, 10, 88; 5, 14, 14 al.

syllŏgistĭcus, a, um, adj., = συλλογιστικός, of or belonging to a syllogism, syllogistic: (Cicero) statum syllogisticum ratiocinativum appellat, Quint. 5, 10, 6.
Hence, adv.: syllŏgistĭcē, syllogistically, in syllogisms, Boëth. Arist. Anal. Post. 1, 9, p. 530.