Elements of Geometric Sequence from One where First Element is not Power of Number

Theorem

 * If as many numbers as we please beginning from an unit be in continued proportion, and the number after the unit be not square, neither will any other be square except the third from the unit and all those that leave out one. And, if the the number after the unit be not cube, neither will any other be cube except the fourth from the unit and all those that leave out two.