ABSTRACT
PO with P , , P I with P2 and so on by segments, we obtain a polygonal line, which is inscribed into y and whose vertices are P;. Consider the length of the inscribed polygonal line. If we take some new points in [a, h] and the corresponding new points on y, we obtain a new polygonal line inscribed into y, and its length is greater than the length of the preceding inscribed polygonal line. It is clear that if we have chosen a new point Q E y situated between points Pi, Pi+,, the sum of the lengths of the segments PiQ and QPi+l is greater than the length of the segment Pip,+'; hence the length of the new polygonal line P O . . .P;QPi+l . . . P, inscribed into y is greater than the length of the preceding one PO. . . P;P;+l . . . P,.
