Proposition 21

A regular Polygon of an even number of sides being inscribed in a circle as ABC...A'...C'B'A' so that AA' is a diameter if two angular points next but one to each other as B, B' be joined, and the other lines parallel to BB' and joining pairs of angular points be drawn as CC', DD',...., then

(BB' + CC' +.... ) / AA' = A'B / BA

Here is the polygon with multiple of 4 sides inscribed in a shpere in its largest cross section(great circle of sphere )