Abstract
The area between the arc and chord of a circle is called Hosichun whose figure looks like a bow and an arrow, and had been evaluated by the two formulas $\textit{H}_{n1}$=a(a＋y)/2 and $\textit{H}_{n2}$=3ay/4, where $\alpha$ is the length of the arrow and y the chord of the circle. By the inspection of the area of the Hosichun, some errors of the numeration table in Thurmans S. Peterson's CALCULUS were found easily, that is, the area of the Hosichun is smaller than its subarea in the same Hosichun and perhaps has been to be the worldwide and centurial invalid standard. From now on, the chain proofreadings of the errors will be necessary in our mathematical world. This paper is intended to introduce some such problems related to a circle and another Pythagorean Theorem which is the ratio of the side and diagonal of five and seven In a square.