Etymonline: aim (v.), c. 1300, first sense “to estimate, calculate, count.” From Latin aestimare via Old French aesmer. The physical sense — directing a missile — arrives late 14c. The archer came a full century after the accountant.
Fond Archer Hope, who tak’st thine aim so farre, That still, or short or wide, thine Arrows are.
— Crashaw, “On Hope” (1670)
Aim here is doing both things at once — and doing them in collision. The reckoning sense is right there in “tak’st thine aim”: Hope calculates, estimates, aestimat. But the arrow always misses. Crashaw is saying that estimation without grounding isn’t aim at all — it’s the accountant’s math without the archer’s contact with reality. The word carries its whole history in the failure: Hope is always in the aestimare register and never arrives at the physical sense. The century between the senses is exactly the gap Hope falls into.