This meaning was beginning to come into the language in Shakespeare's day: Ford describes Pistol as "a good sensible fellow" (The Merry Wives of Windsor, II.i.37). But usually, at that time, the word was used with the older, literal meaning, "capable of receiving sensation" - in other words, "responsive, sensitive". This is the meaning required when Constance in King John describes herself as "not mad, but sensible of grief" (III.iv.53) or Antipholus of Ephesus in The Comedy of Errors tells his servant Dromio:
"Thou art sensible in nothing but blows" (IV.iv.26). Closely related is the meaning "perceptible by the senses, evident", heard most famously in Macbeth's speech to a dagger: "Art thou not, fatal vision, sensibleTo feeling as to sight?" (Macbeth, II.i.36). And Horatio says of the Ghost: "I might not this believeWithout the sensible and true avouchOf mine own eyes" (Hamlet, I.i.57).
David Crystal is author, with Ben Crystal, of Shakespeare's Words published by Penguin