The only reason this confuses moderns is because of the nonconstructive brain damage infesting math. The ancients knew that in order to use the method of exhaustion, you had to bound the quantity from both sides, above and below. Modern students are instead taught to work with limits, which approach the quantity in question from one side or the other or sometimes by schizophrenically oscillating about it. The bounds from both sides are still there, of course, but the details are hidden away in an epsilon-delta proof that they're told not to worry about until they take analysis, which the engineers never do. It is no surprise that they misapply the concept, and you get confusion like pic related.