If, as Newton insisted, (oẋ)2 and (oẋ)3 and higher powers of oẋ were equal to zero, then oẋ itself must be equal to zero.* On the other hand, if oẋ was zero, then dividing by oẋ as we do toward the end is the same thing as dividing by zero—as is the very last step of getting rid of the o in the top and bottom of the oẏ/oẋ expression. Division by zero is forbidden by the logic of mathematics.
