This sense existed in Shakespeare's time, spelled both "digest" and "disgest". Brutus says to Cassius: "You shall disgest the venom of your spleen" (Julius Caesar, IV.iii.47). But it was only one of several senses that had developed earlier, to do with "processing", reflecting the multiple meanings of the Latin source-word. It means "disperse" when King Henry tells his nobles to "digestYour angry choler on your enemies" (Henry VI Part 1, IV.i.167). It means "endure" (or "stomach") when Surrey says "But will the KingDigest this letter of the Cardinal's?" (Henry VIII, II.ii.53). And it means "assimilate" when Lear tells Cornwall and Albany:
"With my two daughters' dowers digest the third" (King Lear, I.i.128).
There is often a play on words between mental and physical meanings, as when Richard says to Buckingham: "let us sup betimes, that afterwardsWe may digest our complots in some form" (Richard III, III.i.200).
David Crystal is author, with Ben Crystal, of Shakespeare's Words, published by Penguin