LATIN DICTIONARYLexicon Latīnum
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“sensible” in Latin

The English word sensible itself goes back to Latin sentiō, through sēnsibilis.

Riddle & Arnold A Copious and Critical English–Latin Lexicon, 1864

sensible
That falls under the cognizance of the senses, sensibus or sub sensus subjectus: sensibus perceptus: quod sentiri or sensibus percipi potest, sensibilis (☞ not in Cic., but as early as Vitr., 5, 3, 6). Sensible objects, ea, quae sub sensus subjecta sunt; res quae subjectae sunt sensibus (both Cic.).
Sensitive, Vid:
Of good sense, intelligens: sapiens: prudens.
Persuaded, convinced; Vid: CONVINCE

Quick answer

What is the Latin word for sensible?
The usual Latin words for “sensible” are sēnsus, sēnsibilis, sapiō; also prūdēns, sēnsitīvus. The right choice depends on the sense; see the distinctions below.

Entry from J. E. Riddle & T. K. Arnold, A Copious and Critical English–Latin Lexicon (rev. C. Anthon, New York: Harper, 1864), digitised by Fergus J. P. Walsh, CC BY-SA 4.0; Latin markup adapted by latindictionary.co.