Old English þencan "imagine, conceive in the mind; consider, meditate, remember; intend, wish, desire" (past tense þohte, past participle geþoht), probably originally "cause to appear to oneself," from Proto-Germanic *thankjan (source also of Old Frisian thinka, Old Saxon thenkian, Old High German denchen, German denken, Old Norse þekkja, Gothic þagkjan).
Old English þencan is the causative form of the distinct Old English verb þyncan "to seem, to appear" (past tense þuhte, past participle geþuht), from Proto-Germanic *thunkjan (source also of German dünken, däuchte). Both are from PIE *tong- "to think, feel" which also is the root of thought and thank.
The two Old English words converged in Middle English and þyncan "to seem" was absorbed, except for its preservation in archaic methinks "it seems to me."
As a noun, think, "act of prolonged thinking," is attested by 1834. The figurative thinking cap is attested from 1839.
"one who has cultivated the powers of thought," mid-15c., agent noun from think (v.).
1805; see think (v.) + -able. Possibly a back-formation from unthinkable.