body follow one another. We must now examine this more closely.
If for any plane figure two positions P Q and P^ Q l in the same plane be given, the figure can in every case be moved from the one position to the other by turning about some point in the plane, which can be determined by joining PP: and Q Q and finding the intersection of perpendiculars drawn from the middle points of these two lines. This intersection, 0, is the required point, because the two triangles P Q and P l Q 1 are similar and equal, P being equal to P l and Q to Q r The point is called the temporary centre for the given change of position.
Q
Fig. 17.
If the temporary centres for further changes of position, from P l Q 1 to P 2 Q 2 , P B Q 3 and so on, be determined in f he same way, we obtain a series of points O l 2 3 etc., which may be joined together by straight lines. We thus obtain a polygon which has the centres for its corners, and which we may therefore call a central polygon. If the figure PQ return into its original place after a series of changes of position, the polygon is closed, other- wise it is open. The figure itself in every case makes a series of turnings about the temporary centres, its points, that is, move always in arcs of circles; these are completely determined if the
