1. If in a closed area CD a point O is given, and through this point a straight line MN is to be drawn such that the segment MCN so determined may be a minimum or a maximum, this condition is satisfied by drawing through O a chord MN having O for its mid point. Of the two segments which are separated by this chord and which are obtained by rotating the chord round O, the one MDN will be the maximum and the other MCN will be the minimum. The sum of the segments is equal to the whole area of the contour, and consequently if one of them corresponds to the minimum, the complementary segment corresponds to the maximum. The two segments interchange, the one into the other, when the chord MN, turning round the point O, undergoes a displacement equivalent to the angle π.